to an observed value of 32wt%, Anderson and Bass, 1986), but we would not ...... Hales and Roberts, 1970; Randall, 1971; Jordan and Anderson,. 1974; Gilbert ...
51
The Earth's Interior
Thorne Lay
University of California, Santa Cruz, USA
1. Introduction Earth is composed of minerals and metal alloys under pressure and temperature conditions that allow elastic waves with frequencies ranging from 0.0003 to 30 Hz to transmit through the planet with relatively little deviation from linear elasticity. In other words, an initial rapid input deformation applied to near-surface rocks, such as that accompanying sudden stress release on a fault or an underground explosion, produces stress imbalances that transmit through Earth in the form of nearly elastic P and S waves that convey the nature of the source deformations to distant locations in a way that is readily decipherable. This remarkable attribute is akin to the transmission of sound waves through air, for which there is a direct correspondence between atmospheric pressure ¯uctuations produced at a source, say by speci®c oscillations of vocal cords, and those detected on our ear drums, allowing the sound to be interpreted (even if there are many echoing reverberations that travel multiple paths to our ears as well as unrelated background noise). If the source energy is large enough, on the order of a magnitude 5.0 earthquake, elastic wave arrivals can be detected above typical ambient noise levels over the Earth's entire surface, and seismic instruments are now capable of recording the full bandwidth of ground vibrations induced by common sources. The quasi-elasticity of Earth over a wide range of ground motions combines with the predominantly concentrically layered structure of the planet to yield straightforward relationships between observations of seismic waves at various distances from a source and the properties of the deep interior of the planet. For about 100 years seismologists have been systematically accumulating global recordings of ground shaking, locating sources of elastic wave radiation, and extracting characteristics of Earth's interior from the travel times, amplitudes and waveshapes of seismic waves. Seismological models have been interpreted by mineral physicists, geochemists, and geodynamicists for many decades to infer the composition, physical state, and dynamical processes INTERNATIONAL HANDBOOKOF EARTHQUAKE AND ENGINEERING SEISMOLOGY, VOLUME 81A Copyright # 2002 by the Int'l Assoc. Seismol. & Phys. Earth's Interior, Committee on Education. All rights of reproduction in any form reserved.
occurring inside the planet. This effort has resulted in a remarkable understanding of our planet's interior, although many important issues have not yet been resolved. This chapter outlines some of our understanding of the Earth's interior derived from seismology.
2. Earth Stratification and Chemical Differentiation The most fundamental approach to gleaning Earth structure from seismic waves is to measure arrival times of ground vibrations as a function of distance from the source. Seismograms from distant earthquakes are characterized by a sequence of discrete body wave arrivals followed by dispersed surface wave trains. Given networks of seismic instrumentation with relatively uniform ground motion response, it is straightforward to pick consistent arrival times of the discrete body wave phases. Triangulation procedures can be used for natural sources to determine the source location and origin time for an assumed seismic velocity model, and the arrival times can then be plotted as a function of distance from the estimated (or known, in the case of explosions) source location. When this is done on a global scale, as in Figure 1, it is apparent that coherent arrivals associated with distinct travel time branches exist, with behavior that is predominantly dependent on epicentral distance. These arrivals correspond to various portions of the P- and S-wave fronts sweeping along the surface of the Earth, with the discreteness of the arrivals indicating that simple wave front refraction at depth dominates over 3D scattering effects. This organized transmission of seismic energy through the Earth was recognized very early in the 20th century, and pioneering seismologists began the labor of identifying each travel time branch and deducing the internal structures and source radiation effects that give rise to the complexity of seismograms. The improved structures were used to provide more accurate event locations, allowing the models to be re®ned in a bootstrapping manner.
ISBN: 0-12-440652-1
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FIGURE 1 Arrival times of P and S seismic phases as a function of epicentral distance in the Earth for shallow earthquake sources, along with predicted travel-time curves for a radially symmetric model of P- and S-velocity variations with depth. P and S are direct phases, PcP, ScP, and ScS re¯ect from the core±mantle boundary, PKiKP and SKiKP re¯ect from the inner core±outer core boundary, PP, SS, PS re¯ect once from the Earth's surface, and PKP, SKP, SKS, SKKS are phases that traverse the Earth's core. (From Kennett and Engdahl, 1991. Reprinted with permission from the Royal Astronomical Society.)
Given an understanding of elastic wave behavior based on the theory of elasticity that had been extensively developed in the 19th century (Chapter 8 by Udias; Aki and Richards, 1980; Lay and Wallace, 1995), it was quickly appreciated that the multibranch complexity of Earth's travel-time curve stems largely from the existence of re¯ections from the surface and from a major internal boundary overlying a region of low seismic velocities in the central region of the planet. The low velocity core of the Earth was detected in 1906 by Oldham. By 1913 the depth to the boundary of the core was quite accurately established by Beno Gutenberg, and with the discovery of the inner core in 1936 by Inge Lehmann, the basic layering of the crust, mantle, and core had been established. For a source and receiver at the surface and a 1D model of the Earth, with P or S velocities, c(r), that vary only with radius, r, basic linear elasticity yields parametric equations for P or S wave travel times, T, as a function of epicentral angular distance, , given by: Z r0 p 2 p2 T p 2 dr
1 r rt
1000
2000
3000 4000 Depth (km)
5000
6000
FIGURE 2 P and S velocity as functions of depth in the Earth for the classic Gutenberg and Jeffreys±Bullen earth models. The letters indicate classic subdivisions of the interior based on behavior of the travel time curves and inferred velocity structures. Arrows highlight the low velocity zone in the Gutenberg model and the change in velocity gradient de®ning the transition zone onset in the Jeffreys± Bullen model (From Anderson, 1963).
Z 2p
rt
r0
dr p r 2 p2
2
where r/c(r), rt is the radius to the turning point of the seismic raypath, p (r sin i)/c(r) is the seismic ray parameter which is constant for a given raypath, and r0 is the radius of the sphere. These basic equations, valid for homogenous regions of the Earth with velocity increasing smoothly with depth, can be used to build up piecewise models of the radial P and S velocity structure either by forward calculation or inversion using the Herglotz±Wiechert method (c.f., Lay and Wallace, 1995). All of the necessary information for determining c(r) is provided by the observed travel time curve for waves that turn continuously in a given homogeneous region. The travel time curves must be well enough sampled that stable estimates of the slope of the travel time curve, dT/ d p, can be empirically measured (when seismic arrays began to be deployed in the 1960s this value could be directly estimated, greatly improving the accuracy of inferred velocity models). Internal boundaries separating homogeneous layers can be accounted for by solving boundary value problems that result in Snell's law for raypath kinematics and in re¯ection and transmission coef®cients for amplitudes (c.f., Aki and Richards, 1980; Lay and Wallace, 1995). From the 1920s to 1940s, interpolated observed travel-time tables such as the Jeffreys±Bullen Tables (Jeffreys and Bullen, 1940) were used in the Herglotz±Wiechert method to produce accurate 1D seismic velocity models for the entire Earth, including the classic Jeffreys and Gutenberg models (Fig. 2).
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These particular models served as standard Earth models for decades, and the J-B travel-time tables are still used in earthquake location procedures because they provide accurate predictions of P and S wave arrival times (including major surface- and core-re¯ected and converted phases) to within a small fraction of a percent at teleseismic ranges. Although body wave travel-time analysis remains a primary tool for studying Earth structure, complete waveform analysis has allowed even more information to be gleaned from seismic recordings, and has unraveled the complex interference effects involved in surface waves and normal modes (see Chapter 9 by Chapman, Chapter 10 by Lognonne and E. Clevede and Chapter 11 by Romanowicz). Seismic wave amplitudes and waveforms can now be synthesized for Earth models, allowing comparison of data and synthetics. The strengths of velocity discontinuities, structure of low velocity zones, diffractions, scattering, and complex interference of multiple arrivals can be modeled and constrained by complete waveform modeling. An example of a contemporary 1D velocity structure for the mantle and core (the thin low-velocity crust is not included) is shown in Figure 3, along with a density structure determined by matching normal mode observations (see Chapter 10 by Lognonne and Clevede), total mass and moment of inertia values, and petrological models of the interior. Seismic velocities increase systematically with depth across the mantle as in the classic models of Jeffreys and Gutenberg, but we are now aware of the existence of abrupt velocity and density increases at the 410 and 660 km seismic discontinuities. The details of the transition zone region from 410 to about 800 km were not resolved prior to the mid-1960s, but it had been recognized as early as 1926 that complexity is present at this depth in contrast to the smoother variations of seismic structure in the lower mantle (below 800 km). Near 2900 km
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FIGURE 3 The ak135 Earth model indicating P velocity, , and S velocity, , as well as density, and attenuation (Q is the solid line, Q is the dotted line) (from Kennett and van der Hilst, 1998).
depth the S velocity drops to zero, indicating the ¯uid state of the outer core, while the P velocity drops greatly across the core±mantle boundary before increasing smoothly with depth down to the inner core±outer core boundary. Over vast reaches of Earth the seismic velocities increase very smoothly, i.e., across the lower mantle from 800 to 2700 km depth, and across the outer core and inner core. This is a direct inference from the smooth concave-downward travel-time curves in Figure 1, with lateral variations about the mean velocity at each depth being bounded to only a few percent except in regions near boundary layers (near the Earth's surface, near the core±mantle boundary, and in sinking lithospheric slabs). Thermodynamic calculations indicate that the composition of each major subsection of the Earth may be uniform, with gravitational self-compression fully accounting for the variation in laterally averaged velocity with depth. Solid-state phase transitions in the major Earth mineral olivine provide viable explanations for the discontinuities near 410 and 660 km depth, and cosmochemical arguments and density constraints indicate that the core is predominantly made of iron. The bulk composition of the planet can be approximated by the relative abundance of refractory materials in the Sun or by the bulk composition of undifferentiated chondritic meteorites, with the mantle composition being inferred by allowing for separation of the core alloy and continental crust (for a good review, see O'Neill and Palme, 1998). Thus, the ®rst-order characterization of the Earth is of a chemically differentiated body in which a thin veneer of light materials has segregated into the enduring continental crust, while basalt is extracted by melting from upper mantle material to produce the recycling oceanic crust, with an extensive mantle of crystalline silicates and oxides of nearly uniform overall composition overlying the molten iron-alloy core of which the center has solidi®ed because the geotherm intersects the solidus at the inner core boundary. If one pauses for a moment to question how much we would know about even these ®rst-order aspects of the interior without seismology, it is clear that predictions could be made about planetary layering for a given cosmochemical model (e.g., the assumption of a chondritic abundance of major rockand core-forming elements, with the light alloy component of the core being O, predicts a core size of 30.1 wt%, compared to an observed value of 32 wt%, Anderson and Bass, 1986), but we would not necessarily know that there is an inner core, could not preclude a very complex compositionally strati®ed mantle, and would not have direct means to test and re®ne the assumed multiphase chemical model (by matching laboratory measurements of appropriate compositions to the observed velocities and densities). As described below, further details of the seismological structure provide the key to understanding the dynamics of the interior as well, which would otherwise remain highly speculative. There is thus no question that seismology plays a major role in our understanding of Earth's interior.
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Continental arc
Earth's crust is the most important region of the interior, providing the environment, natural resources, and geological hazards that affect humanity. The complexity of structure and geological history of the continental crust are readily apparent from surface observations, providing important clues in our efforts to understand Earth's interior, however it is essential to know the structure at depth. With very sparse drilling being con®ned to the upper 10 km of the crust, much of our knowledge of the in-situ structure of the oceanic and continental crust has been provided by seismological investigations, as described elsewhere in this volume (see Chapter 54 by Mooney et al. and Chapter 55 by Minshull). It is again the properties of elastic waves, particularly their re¯ection and refraction at interfaces across which there are abrupt changes in material properties (e.g., density, compressibility, rigidity) that enables detailed models of the crustal layering and crust±mantle boundary (a seismically de®ned compositional boundary called the MohorovicÆic or ``Moho'' boundary in recognition of its discoverer in 1909) to be determined by analysis of dense pro®les of ground motion recordings for both natural and human-induced sources. Seismology provides information about the interface geometries, absolute seismic velocities, presence of partial melting, and structural anisotropy of the crust, which can then be interpreted in terms of rock compositions and deformation histories by comparison to laboratory measurements of ®eld samples, accompanied by geological reconstructions. Gross differences between oceanic and continental crustal properties were ®rst revealed in the 1950s by a combination of refraction and gravity studies and the ®rst analyses of Rayleigh and Love wave dispersion observations in the period range 10±70 sec. Love wave observations in particular provided compelling evidence for an average oceanic crustal thickness of about 6 km, with both Rayleigh and Love waves indicating a typical continental thickness of 35 km or so (e.g. Ewing et al., 1957). Advances in computational capabilities, inverse theory, and data quality have allowed increasing resolution of internal crustal layering by surface wave inversion, culminating in the present day capabilities described in Chapters 11 (by Romanowicz) and 54 (by Mooney et al.). Surface waves provide relatively limited resolution models of crustal properties, involving extensive depth and lateral averaging of the actual structure, but the integral constraints from surface waves can be combined with body wave information to give reliable detailed crustal structures. High resolution of internal crustal properties is attained by using seismic body waves with frequencies of 1±100 Hz, and even higher for very shallow imaging, accompanied by close station spacing (meters to kilometers) to avoid spatial aliasing. The data collection and processing involved in analysis of dense linear and 2D deployments of high frequency
seismographs is generally de®ned as the ®eld of Re¯ection Seismology, with distinct strategies being needed for analysis of much sparser data sets available for sampling the deeper interior on a global scale (see chapters on crustal imaging). At intermediate levels of resolution, the methods of Refraction Seismology, the study of primary direct, re¯ected and headwave arrivals traversing the crust from both natural and human-induced sources, provide constraints on the overall crustal waveguide. Gross attributes of crustal velocity structure, thickness, and regional variations have been summarized by Christensen
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FIGURE 4 Summary of crustal refraction and re¯ection pro®ling for diverse crustal regimes indicating thickness and typical P velocities of crustal layers (From Mooney et al., 1998).
The Earth's Interior
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and Mooney (1995) and Mooney et al. (1999). Re¯ection and refraction studies from hundreds of locations around the world have established that there are characteristic crustal structures in distinct tectonic environments. P velocities and thickness for various crustal types are summarized in Figure 4. Note that water layer thickness is included for oceanic structures. The average P velocity of the crust is 6.45 0.21 km sec 1, the average continental crustal thickness is about 40 km and average oceanic crustal thickness is 12.6 km, including 4.0 km of ocean water (Christensen and Mooney, 1995). A contour map of crustal thickness, including water depth, with 5 5 resolution is shown in Figure 5. Seismic models of the crust like these provide a basis for petrological interpretations using
laboratory measurements of velocities in plausible crustal materials under appropriate pressures and temperatures. Christensen and Mooney (1995) summarize current inferences about crustal petrology; upper continental crust is matched by diverse lithologies including low-grade metamorphic rocks and silicic gneisses of amphibolite facies grade, middle continental crust is consistent with tonalitic gneiss, granitic gneiss and amphibolite, and lower continental crust is consistent with gabbro and ma®c granulite. There appears to be increasing garnet content with depth and ma®c garnet granulite comprises the lowermost crust. Localized crustal models also play a key role in unraveling tectonic histories, mountain building and extensional events, shallow volcanic processes, and basin
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FIGURE 5 Mercator projection of crustal thickness for a 5 model. Extrapolations based on tectonic province and crustal age have been made (from Mooney et al., 1998).
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evolution, not to mention the critical role of high resolution models in oil and mineral resource exploration. Many additional details about crustal structure are given in the accompanying chapters on crustal structure. Recognizing that continental and oceanic crust have been extracted from the interior by melting processes, and that the crustal dynamics and history are manifestations of deeper seated processes, the remainder of this chapter will elaborate on the techniques and results of seismological analyses of deeper Earth structure.
4. Upper Mantle and Transition Zone The existence of complex upper mantle structure is immediately evident from the bimodal distribution of continental and oceanic crust. Preserving highly differentiated rocks dating back more than 3.8 billion years, continental crust clearly has different relationships to its underlying upper mantle than does basaltic oceanic crust, of which very little more than 200 million years old can be found. Given only sparse direct sampling of upper mantle rocks provided by upthrust blocks and xenoliths from deep-seated magmatism, with signi®cant chemical alteration prevalent in both environments, seismology plays a prominent role in constraining our knowledge of upper mantle structure. The revelations of sea¯oor spreading in the 1960s provided a context for oceanic upper mantle as an extensive, fairly uniform composition material from which midocean ridge basalts (Ca and Na-rich pyroxene plus an Al-rich phase) are extracted by localized decompression melting in upwellings, and to which both crust and depleted upper mantle material return by subduction of oceanic slabs. Quanti®cation of basalt petrogenesis has played a key role in developing and testing models of upper mantle composition, with the important conclusion that the upper mantle is largely peridotitic (composed of olivine [(Mg,Fe)2SiO4] and orthopyroxene [(Mg,Fe)SiO3]) rather than eclogitic (mainly clinopyroxene and garnets) in chemistry (e.g., Ringwood, 1975; Green and Falloon, 1998). Ted Ringwood proposed the ``pyrolite'' model for upper mantle composition as essentially the sum of basalt and peridotite compatible with chondritic abundances. The oceanic crust and the underlying depleted, harzburgitic mantle material are embedded in a conductive thermal boundary layer, the upper half or so of which is relatively cold (< 650 C) and stiff, yielding a mechanically competent lithospheric plate (note the distinction between thermal and mechanical boundary layers). As the temperature increases with depth, approaching the melting point of the mantle material, the thermal boundary layer undergoes transitions in mechanical integrity, with viscous lateral shearing, and in thermal transport, with the latter progressively becoming dominated by solid-state advection rather than conduction. Seismological investigations of the suboceanic mantle seek to characterize the layering of the basalt-depleted zone of the
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lithosphere, to detect any strain-induced fabrics in the oceanic plate or in the strongly sheared region in the lower part of the thermal boundary layer and below it, often called the asthenosphere, and to detect any variations with depth that correspond to effects of increasing temperature and phase transitions. For subcontinental mantle, the context of plate tectonics provides far fewer well-de®ned questions, and basic issues such as the thickness of the continental lithosphere, the extent of and nature of compositional depletion of the subcontinental upper mantle, and the thermal history and structure of the subcontinental upper mantle are all open questions, with seismological imaging playing a key role in characterizing the structural elements. As noted below, the distinctions between continental and oceanic upper mantle persist down to depths of 200±350 km, below which any obvious relationships between mantle structure and surface tectonic features rapidly disappear.
4.1 The Seismic Lid In both continental and oceanic regimes, the uppermost mantle region below the Moho overlies a seismic low velocity zone. The high-velocity layer from the Moho down to the lowvelocity zone is called the upper mantle ``lid,'' and this corresponds to the ``seismic lithosphere.'' (Long-term rheological behavior and seismic velocity structure need not correspond directly, for they involve factors such as time of loading, temperature, and stress; however, it is likely that a common underlying in¯uence is the onset of partial melting which affects both seismic velocity and viscosity and de®nes the bottom of the seismic lid and the rheological transition from the mechanical boundary layer to the ductile asthenosphere.) The most straightforward aspect of mantle lid velocity structure that can be determined is the velocity just below the Moho discontinuity, as this is manifested in the slope of the Pn and Sn ``headwaves'' along the crust±mantle boundary. Usually, a linear ®t to the headwave branches is suf®cient, with measured P velocities of 7.6±8.6 km sec 1 and S velocities of 4.4±5.0 km sec 1 being inferred by many studies from 1950 on (see reviews by Christensen and Mooney, 1995; Christensen and Salisbury, 1979). The average Pn velocity beneath continents is 8.09 0.2 km sec 1 (Christensen and Mooney, 1995), whereas the average oceanic Pn velocity is 8.15 0.31 km sec 1 (Christensen and Salisbury, 1979). These velocities are typical of olivine- and pyroxene-rich peridotitic upper mantle rocks from which crustal rocks have been chemically differentiated. Substantial effort has gone into mapping lateral variations in uppermost mantle velocity structure as shown in Figure 6 (e.g., Braile et al., 1989; Hearn et al., 1991; Hearn, 1999), with it being established that the lateral variations in velocity are associated with lateral variations in thermal structure and associated age of tectonic activity. Active rift zones tend to have low Pn velocities whereas
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FIGURE 6 Contour map of Pn velocity under the United States based on many localized studies. Note the lower velocities characteristic of the tectonically active western region. (From Braile et al. 1989).
stable cratons and platforms tend to have higher Pn velocities. A complicating factor is that substantial seismic velocity anisotropy is observed for Pn in oceanic (Raitt et al., 1969) and continental areas (Bamford, 1977), presumably as a result of plate-motion or orogenically induced alignments of the upper mantle minerals, particularly olivine. This produces azimuthal dependence of the Pn velocity, which must be accounted for when seeking an accurate seismic and petrological model for the uppermost mantle (e.g., Hearn, 1999). The velocity structure just below the Moho generally involves slowly increasing velocity with depth, which produces a whispering gallery of phases that complicate Pn and Sn arrivals and the interpretation of the apparent velocities of these phases. Beneath some continental regions, a small abrupt increase in P and S velocity occurs near 60±90 km (e.g., Hales, 1969; Revenaugh and Jordan, 1991), possibly as a result of a phase transition from spinel to garnet facies in aluminous peridotite. This feature is detected in regional travel-time curves as well as in near vertical re¯ections. This uppermost mantle region is highly heterogeneous from region to region, largely as a result of chemical and thermal variations in the oceanic and continental lithosphere. In fact, the strongest lateral variations in upper mantle structure are found at mantle lid depths from 50 to 100 km, with greater than 10%
variations in S velocity and several percent variations in P velocity. Continental regions appear to have end-member lid structures associated with stable cratonic and platform regions with relatively high sub-Moho S velocities of 4.7±4.8 km sec 1, and P velocities of 8.2±8.4 km sec 1, whereas tectonically active areas have S velocities of around 4.3 km sec 1 and P velocities around 7.9 km sec 1. This large variation is believed to be a combined thermal and compositional effect, as cratonic lid is both thicker (150± 200 km) and chemically distinct from tectonically active continental lid (which may be only as thick as the crust in active rift environments). There is evidence for signi®cant small-scale heterogeneity in the lid structure, primarily in dense long-range pro®les collected in Eurasia, so the average properties given above are likely oversimpli®ed (e.g., Ryberg and Wenzel, 1999). Oceanic regions show systematic increases in lid thickness with plate age, presumably as a result of progressive cooling of the oceanic lithosphere. This has been most systematically characterized by regionalized or tomographic inversions of surface-wave dispersion measurements (see below). Relatively simple thermal models for aging oceanic lithosphere appear to provide a viable basis for characterizing ®rst-order radial and lateral structure of oceanic uppermost mantle lid structure (e.g., Zhang and Lay, 1999).
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4.2 The Seismic Low-Velocity Zone The presence of an upper mantle low-velocity zone is of profound importance for mantle dynamics, as it is commonly associated with a zone of partial melting, strong seismic wave attenuation, and low viscosity. Based on the body wave travel time and amplitude evidence accumulated by Beno Gutenberg for a decrease in velocity below about 60±80 km depth followed by a gradual increase commencing near 100±150 km (Gutenberg and Richter, 1939; Gutenberg, 1948, 1959) it has long been accepted that there is an upper mantle low velocity zone of some type (see the Gutenberg model in Figure 2). Low-velocity zones tend to be dif®cult to detect and to quantify due to the downward refraction of seismic energy that they cause. The upper mantle seismic low velocity channel is commonly associated with the asthenosphere, a rheologically de®ned region with strong ductile deformation and possibly partial melting underlying the lithosphere. The onset of the low velocity channel is sometimes characterized by an abrupt velocity decrease [labeled by Revenaugh and Jordan, 1991, as the ``G'' (for Gutenberg) discontinuity at about 80 km depth]. This relatively sharp feature is typically found in tectonically active regions and under oceanic crust, but in some cases there is a somewhat deeper low velocity zone found under cratons and platforms, which may or may not have an abrupt onset. Early surface wave dispersion studies of the 1950s indicated that Love and Rayleigh wave-dispersion curves beneath oceanic and continental regions tend to converge for periods longer than about 75 sec and that Rayleigh wave group velocities for ``mantle wave'' periods of 75±400 sec have an Airy phase minimum near 225 sec that suggests the presence of a decrease in shear velocity with depth in the upper mantle (e.g., Ewing and Press, 1954; Ewing et al., 1957). As inversions for models with multiple layers became viable by the early 1960s a common feature of separate ®ts of dispersion curves for Love and Rayleigh waves was the presence of a low velocity zone in the upper mantle. Highly precise measurements of great-circle data (multiple passages of the same wavetrain past a given station) began to resolve systematic differences for paths under oceanic, tectonically active continent, and stable continent regions for periods longer than 75 sec (e.g., Anderson and ToksoÈz, 1963; ToksoÈz and Ben-Menahem, 1963; ToksoÈz and Anderson, 1966; Kanamori, 1970), allowing the ®rst attempts at pure-path regionalizations based on percentage path lengths in each tectonic province. Isotropic inversions of the dispersion curves in the range 75±300 sec yielded shear velocity models with low-velocity zones between 80 and 200±350 km depth. An upper mantle lid overlying a low velocity zone with shear velocities of 4.0±4.2 km sec 1 with deeper strong positive velocity increases was a common feature of almost all surface-wave inversions of this generation. The regionalized dispersion
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measurements also suggested that velocity structures under old cratons differ from those under oceans and tectonically active continental regions down to depths exceeding 250 km (e.g., Kanamori, 1970). However, an important problem was recognized quite early on, as it proved dif®cult to simultaneously ®t precise global and pure-path Love and Rayleigh-wave observations by isotropic models (McEvilly, 1964; Anderson, 1966). This became known at the Love±Rayleigh discrepancy, and it motivated the development of anisotropic models for upper mantle structure (Anderson, 1961; and see Chapter 53 by Cara). The inclusion of anisotropy directly affects the magnitude and nature of the low-velocity zone structure obtained by ®tting surfacewave dispersion curves (e.g., Anderson, 1966; Anderson and Dziewonski, 1982). A basic requirement of most laterally and azimuthally averaged dispersion observations is that the SV velocity structure of the upper few hundred kilometers of the mantle is a few percent slower than the SH velocity structure, and initially this was addressed for regionalized data sets by performing separate isotropic inversions for the SV-sensitive Rayleigh waves and the SH-sensitive Love waves (e.g., Forsyth, 1975; Schlue and Knopoff, 1977, 1978; Yu and Mitchell, 1979; Mitchell and Yu, 1980). These pseudoisotropic studies conclusively documented the need for extensive anisotropy of either the lid or the low-velocity zone, but it was subsequently shown that it is important to perform a self-consistent inversion for an anisotropic medium to obtain accurate models (Anderson and Dziewonski, 1982; Regan and Anderson, 1984). From the early 1980s on, most surface-wave and normalmode models have allowed for at least a transversely isotropic structure in the upper mantle, with ®ve elastic constants, and this complexity was incorporated into the Preliminary Reference Earth Model (PREM) produced by Dziewonski and Anderson (1981). In PREM, which has served as the background reference model for many subsequent surface-wave tomographic inversions, making them intrinsically transversely isotropic, the horizontal propagating S velocity (VSH) is faster than the vertically propagating S velocity (VSV), and the horizontally propagating P velocity (VPH) is faster than the vertically propagating P velocity (VPV) in the upper 220 km of the mantle (Figure 7). In this model, the low-velocity zone is very subdued, and it is not necessary to have very low shear velocities as found in earlier isotropic and pseudo-isotropic inversions. The parameterization of PREM incorporates a very strong velocity discontinuity near 220 km depth, as has been reported in several continental P and S wave travel-time studies (e.g., Lehmann, 1959, 1961; Hales et al., 1980; Drummond et al., 1980; Anderson, 1979). This feature, often called the Lehmann discontinuity, was suggested by Lehmann (1959) to correspond to the bottom of the low-velocity zone, a notion that was embraced in the parameterization of PREM. However, this feature is not observed globally, and appears to be primarily
The Earth's Interior
837
VP
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600 Depth (km)
Compressional velocity (km sec–1)
Shear velocity (km sec–1), density (g cm–3) or
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FIGURE 7 Anisotropic upper mantle P velocity (Vp) and S velocity (Vs) for the transversely isotropic, 1 Hz version of the Preliminary Reference Earth Model (PREM), along with density structure () and the anisotropic parameter . Dashed lines are the horizontal components of velocity (from Dziewonski and Anderson, 1981).
a subcontinental feature of limited extent, con®ned to shield and platform regions that do not have strong low-velocity zones or G discontinuities (e.g., Shearer, 1991; Revenaugh and Jordan, 1991). A viable interpretation of the continental 220 km feature is that it corresponds to a critical temperature (about 1200 C) transition from the anisotropic subcontinental mantle to the more isotropic structure below (Revenaugh and Jordan, 1991; Gaherty and Jordan, 1995), possibly embedded within a 300±400 km thick continental root (see below). However, there is evidence for a re¯ector near 220 km in the vicinity of some subduction zones, which cannot be accounted for by this particular model (e.g., Vidale and Benz, 1992; Zhang and Lay, 1993), so uncertainty in the interpretation of this structure remains. The modern generation of shear-wave models for oceanic upper-mantle derived from waveform modeling of multimode Rayleigh waves, body waves, or complete body/surface waveforms show relatively pronounced low-velocity zones between 80 and 300 km (Fig. 8), even when transverse isotropy of the lid and low velocity zone is included in the modeling (e.g., Gaherty et al., 1996). Both P-wave and S-wave models obtained by body wave travel-time and waveform modeling for upper mantle triplication distances (10±30 ) usually include upper mantle low-velocity zones, although the resolution of such structures is limited (e.g., Grand and Helmberger, 1984; Zhao and Helmberger, 1993). Thus, it appears that the seismic low-velocity zone does exist, but is
highly variable in its properties depending on tectonic region. Rather than terminating in an abrupt discontinuity as in the PREM model, the low-velocity zone is typically underlain by a relatively steep velocity gradient with depth that persists down to the mantle transition zone. Generally this region from about 200 to 400 km depth has little structure in average Earth models (see Figs. 3 and 7). There is evidence for localized P and S velocity increases near 310 km depth in the vicinity of subduction zones (e.g., Hales et al., 1980; Revenaugh and Jordan, 1991; Zhang and Lay, 1993; Zhang, 1994), but this structure is either signi®cantly variable in depth or spatially intermittent, based on analysis of SS precursors by Shearer (1991, 1993). Revenaugh and Jordan (1991) label the 310 km feature (actually found in ScS reverberation coda at depths ranging from 275 to 345 km) the ``X'' discontinuity, and, lacking any explanation in terms of standard upper mantle mineralogy, they propose that it is associated with phase reactions in extensively hydrated mantle surrounding zones of extensive subduction.
4.3 The Transition Zone The region of relatively strong positive velocity gradients below the low-velocity zone is abruptly punctuated by a global velocity increase near 410 km depth, marking the onset of the transition zone which extends from 410 to 800 km. Early bodywave velocity models of Sir Harold Jeffreys in the 1940s
838
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FIGURE 8 Oceanic upper mantle shear velocity structures from waveform modeling studies. Note the presence of a well-developed low velocity zone (from Gaherty et al., 1996).
(see Fig. 2) incorporated a change in velocity gradients above and below 400±500 km depths (based on the so-called 20 -discontinuity ®rst pointed out by Byerly, 1926), but the detailed structure of the transition zone from 410 to 800 km depth only began to be worked out in the 1960s. Modeling of long-period surface-wave dispersion curves ®rst indicated that the upper mantle low-velocity zone is globally underlain by strong positive velocity gradients near 350±450 km and 600±700 km depths (e.g., Anderson and ToksoÈz, 1963; ToksoÈz and Ben-Menahem, 1963; ToksoÈz and Anderson, 1966). This focused attention on body-wave travel-time and apparentvelocity measurements from newly deployed regional seismic arrays for the distance range of 1000±3000 km, and it was soon recognized that two major upper mantle travel-time triplications are produced by abrupt P and S velocity increases near 410 and 660 km depths (e.g., Niazi and Anderson, 1965; Ibrahim and Nuttli, 1967; Johnson, 1967; Kanamori, 1967). Anderson (1967a) attributed these rapid velocity increases to solid±solid phase changes of (Mg,Fe)2SiO4 olivine to -phase (modi®ed-spinel structure) and -spinel to more compact oxides, respectively. The precise nature of the post-spinel transformation was not worked out for several years and it
is now known to involve a disassociative transformation to the silicate perovskite phase of MgSiO3 plus magnesiowustite (Mg,Fe)O (e.g., Liu, 1976; Ito and Takahashi, 1989; Bina and Helffrich, 1994). The combination of seismological constraints and experimental measurements which has established that these phase transitions in olivine are responsible for the two major upper-mantle discontinuities codi®ed the earlier inferences by Francis Birch and J.B. Thompson that phase transitions were responsible for the zone of steep velocity gradient in Jeffreys' velocity model (Fig. 2) between 400 and 1000 km depth (Birch, 1952). Although there had been suggestions of transition-zone discontinuities dating back to Byerly (1926), global seismic velocity models did not incorporate the 410 and 660 km discontinuities until the surge of observations in the mid-1960s demonstrated their global existence and placed bounds on the depths and velocity increases that are involved. Throughout the last three decades, numerous seismological procedures have been developed to extract increasing information about the velocity structure in the transition zone. A combination of wide-angle triplication studies and near vertical top±side and bottom±side re¯ection and conversion studies have yielded extensive information about the contrasts in velocity and density, sharpness (depth extent of the velocity increases), and topography of the 410 and 660 km discontinuities. The process is complicated by the fact that there are strong variations in the lid and low velocity zone structure above the discontinuities, as well as by limitations imposed by the distribution of seismic stations and sources. Wide-angle triplication studies exploit the complexity of the P- and S-wave travel-time curves in the so-called ``upper mantle'' distance range of 12 ±30 . This is illustrated in Figure 9, for a P velocity model appropriate for the western United States (Walck, 1984), where there is a thin lid and shallow low-velocity zone. As it encounters rapidly increasing velocity with depth the wavefront folds over on itself, with energy that turns above, at and below a discontinuity being refracted to each distance in the associated triplication range. The transition zone discontinuities produce abrupt changes in the slope of the ®rst arrival branch, and the ray parameters for each of the three arrivals of the triplications are different enough that they can be measured, as long as secondary arrivals are recognized amidst the coda generated by the ®rst arrival (Fig. 9). The velocity structure can be determined by matching the timing and amplitudes of the arrivals in the triplication range, as well as by matching the corresponding ray parameter measurements. The origin of the ``20 discontinuity'' notion is readily apparent in the overall curvature of the ®rst arrival time curve resulting from energy turning in the much different velocities above and below the transition zone. Dense sampling of the travel-time curve and recognition of secondary arrivals as triplication branches is required in order to establish that discontinuities are present, and
The Earth's Interior Velocity (km sec–1) 8 10
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14 13 12 11 10 GCA Frist arrivals Later arrivals
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40
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FIGURE 9 (a) A P-wave velocity model found for the tectonically active upper mantle below the Gulf of California. The observed and predicted travel times for this region are shown in (b) and observed and predicted ray parameter values are shown in (c) (modi®ed from Walck, 1984. Reprinted with permission from the Royal Astronomical Society).
typically only limited quanti®cation is possible by classical travel time and ray parameter modeling alone. Waveform modeling methods developed in the late 1960s and throughout the 1970s (e.g., Helmberger, 1968; Helmberger and Wiggins, 1971; Fuchs and MuÈller, 1971; Chapman, 1976, 1978; Richards, 1973) enabled complete synthesis of the triplication waveform interference and relative amplitudes for 1D, and later 2D structures (e.g., Chapman and Drummond, 1982; Helmberger et al., 1985). With these powerful tools, dozens of wide-angle studies of mantle structure have been carried out, resulting in regionalized velocity structures extending down through the transition zone. Nolet et al. (1994) consider the evidence for lateral mantle heterogeneity based on comparison of upper mantle models derived by modeling shortperiod P, long-period P, and long-period S triplications (Fig. 10). Additional shear-wave models for oceanic areas are shown in Figure 8. The majority of these models have been developed assuming isotropic transition zone structure (the data typically provide too little information to constrain anisotropic structure, but the fact that the data can be well modeled by isotropic models suggests that transition zone anisotropy is probably not very large, if present at all). Note that there are pronounced differences in lid structure, in structure of the low velocity zone, and in structure near 220 km depth, as discussed previously. Some of the variations may result from approximating laterally heterogeneous structure with 1D models. However, all models show 410 km and 660 km discontinuities, and it is accepted that these are globally present as expected for phase transformations of a primary mantle component.
There are apparently signi®cant variations in size and sharpness of the velocity increases. Wide-angle triplication modeling is typically not sensitive to density structure, but the nearly factor of 3 variation in P-velocity jump at 410 km depth seen in these models may be in¯uenced by failure to account for topography on the boundary. The S-velocity jump at 660 km in most models is about 7±8%, and appears to be stronger than that at 410 km (5%), whereas the P velocity contrasts are more similar, averaging 5±6% at 410 km and about 4% at 660 km [Estabrook and Kind (1996) present evidence for a P-velocity jump of only 2% at 660 km]. Very strong evidence for an even stronger jump of as much as 10% in S velocity at 660 km depth, along with reduced density jumps of 4±5%, has recently emerged from the systematic study of underside re¯ections as a function of angle of incidence (Shearer and Flanagan, 1999) and from amplitudes of top-side conversions (Castle and Creager, 2000). The velocity contrasts at the discontinuities provide a means for assessing the relative abundance of olivine component (for which the contrasts in velocities and densities across phase transformations can be measured in the laboratory) in the transition zone. The observed jumps are smaller than expected for a purely olivine mantle, so it is believed that there is signi®cant presence of orthopyroxene, garnet, and/or clinopyroxene (with the latter two possibly giving an eclogitic component) that ``dilute'' the percent-wise velocity increases (e.g., Bass and Anderson, 1984; Anderson, 1991). The estimates of large shear-velocity contrast tend to favor an olivine-rich composition of the transition zone. Because there is nonuniqueness in possible mixed compositions that can match the velocities and
840
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nat kca hwa hwb hwne gca gcb cjf capri fls ngr quartzn quartzs iasp91
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800 12
1000 3
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FIGURE 10. (a). Upper mantle P-velocity models derived from short-period P observations. The upper mantle model iasp91 was designed to give a reasonable average. Regional coverage: nat, North Atlantic,; hwb, hwa, hwne, west-central United States; gca, gcb, djf, western North America; capri, ¯s, ngr, northern Australia; quartzn, quartzs, Asiatic Russia. (b). Upper mantle models for P velocity derived from long-period or broadband observations. Regional coverage: t7, western North America, s25, North American Shield, k8, Eurasia; s8, northeastern United States; njpb, northern Australia, ipremc, Isotropic version of PREM model with continental crust. (c). Upper mantle models for S velocity derived from long-period or broadband observations. Regional coverage: shr14, western United States; tna, tectonic North America; sna, shield North America; njpb, northern Australia, ipremc, isotropic version of PREM model with continental crust. (From Nolet et al. 1994.)
densities, details of the bulk chemistry of the transition zone are still unresolved. The possibility that the 660-km discontinuity coincides with a chemical contrast as well as (or instead of) the spinel to perovskite transformation in olivine
has been discussed for decades, but it appears possible to fully account for the discontinuity by the phase transition. This still does not preclude the possibility that the bulk composition of the lower mantle differs from that of the transition zone as discussed later. There is a relatively steep velocity gradient between the two major transition zone velocity discontinuities, with a few models indicating rapid P or S velocity increases near 520 km depth (Fig. 10). Most S-wave models, and some P-wave models indicate a zone of steep velocity gradient extending down from the 660 km discontinuity to about 800 km depth, below which there is a reduced velocity gradient extending smoothly into the lower mantle. This feature is incorporated into recent average Earth models such as PREM (Fig. 7), IASP91 (see iasp91 in Fig. 10) and ak135 (Fig. 3). I take 800 km depth as the lower boundary of the transition zone, for the seismic models generally show only smooth velocity gradients at larger depths and the primary-phase transitions expected for major components of the upper mantle and transition zone should be completed by this depth. However, there is evidence for nonglobal discontinuities at 900 and 1200 km depth as well as deeper transitions in the spectrum of lower mantle lateral heterogeneity (see below), so there may be further localized phase transitions or chemical contrasts at greater depths. Analyses of converted and re¯ected waves also constrain properties of the transition zone discontinuities. The ®rst such phases to be exploited were precursors to PKPPKP (P 0 P 0 precursors), involving underside re¯ections from transition zone discontinuities observed near angular distances of 70 . These near-vertical incidence re¯ections are particularly sensitive to the sharpness and impedance contrast across the boundary, and were ®rst used to constrain properties of the 410 and 660 km boundaries by Adams (1968, 1971), Engdahl and Flinn (1969) and Whitcomb and Anderson (1970). These phases have subsequently been extensively studied over the years, providing limited sampling of different mantle regions and revealing stronger re¯ections for 1 Hz signals from the 660 km boundary than the 410 km boundary (e.g., Nakanishi, 1989; Benz and Vidale, 1993). This requires a sharp 660 km impedance contrast, no broader than about 4 km in many areas. In some cases the 410 km feature also gives strong 1 Hz re¯ections (e.g., Benz and Vidale, 1993; Vidale et al., 1995; Helffrich and Wood, 1996; Neele, 1996), but often it does not, implying that in some regions the 410 km feature may be spread over more than 5 km thickness or is subject to strong lateral variations or small-scale topography. The olivine to -phase transition may have nonequilibrium effects (e.g., Solomatov and Stevenson, 1994), nonuniform rate of velocity increase with depth (e.g., Bina and Helffrich, 1994; Stixrude, 1997) or complexity due to accompanying gradual transformations of garnet±pyroxene components. There are many additional top-side and bottom-side re¯ections and conversions from the mantle discontinuities
The Earth's Interior
841
that can be sought in order to constrain their properties. P waves convert to S waves (Pds) at boundaries under a station, arriving in the coda of direct P, and these can be stacked for arrays of sources to quantify the weak phases (e.g., Vinnik, 1977; Stammler et al., 1992; Dueker and Sheehan, 1997; Gurrola and Minster, 1998; Bostock, 1998; Chevrot et al., 1999). S waves convert to P at boundaries below a station, giving rise to Sdp arrivals that precede direct S (e.g., Bath and StefaÂnson, 1966; Jordan and Frazer, 1975, Faber and MuÈller, 1980; Bock, 1988). S waves from deep slab events convert to P waves (SdP) at boundaries below the sources, arriving in the P-wave coda (e.g., Bock and Ha, 1984; Vidale and Benz, 1992; Wicks and Richards, 1993; Niu and Kawakatsu, 1995; Castle and Creager, 1998a), with these phases being particularly useful for determining properties of mantle discontinuities below subducting slabs. Upgoing P and S phases from deep slab events re¯ect from the underside of boundaries and are observed at large distances ( pdP, sdS), providing a means to image properties of mantle discontinuities above deep sources (e.g., Vidale and Benz, 1992; Zhang and Lay, 1993; Flanagan and Shearer, 1998b). Near vertical ScS reverberations generate a suite of top- and bottomside re¯ections from mantle discontinuities which can be stacked to image impedance contrasts and depths (e.g., Revenaugh and Jordan, 1991a,b; Clark et al., 1995). Top- and bottom-side re¯ections also produce a suite of arrivals between P and PP and between S and SS which can be
detected and identi®ed by stacking of multiple observations (e.g., Shearer, 1991). The most important of these boundary interactions phases have been the underside re¯ectors that are precursors of PP (PdP) (e.g., Bolt, 1970; King et al., 1975; Shearer, 1991; Neele and Snieder, 1992; Estabrook and Kind, 1996; Shearer and Flanagan, 1999) or SS (SdS) (e.g., Shearer, 1990, 1993; Petersen et al., 1993). These phases provide much more extensive coverage of mantle discontinuities than most other phases, allowing global maps of topography on the boundaries to be determined (e.g., Shearer and Masters, 1993; Shearer, 1993; Estabrook and Kind, 1996; Flanagan and Shearer, 1998a). Figure 11 shows 10 radius cap-averaged values of depths to the ``410-km'' and ``660-km'' boundaries obtained from SS precursors, corrected for an upper mantle shearvelocity model. The mean depths of the two main upper mantle discontinuities are 418 km and 660 km. Although there are concerns about biases in these estimates from unresolved small-scale topography (Neele et al., 1997), relatively large-scale coherent regions appear in the topographic maps. Increased depths to the 660 km feature are found in circumPaci®c regions of current and past subduction, supporting the notion that the boundary is associated with the endothermic spinel to perovskite phase change and that subducting slabs de¯ect and produce broad cool features near this boundary. This is also consistent with studies of localized boundary de¯ections near slabs (e.g., Richards and Wicks, 1990; Wicks
Depth estimates (corrected) Mean = 418 km
Mean = 515 km
Mean = 660 km
Mean WTZ = 241 km
10 km – 10 km
FIGURE 11 Cap-averaged estimates of topography on the ``410-km'' discontinuity, the ``520-km'' discontinuity, the ``660-km'' discontinuity and the transition zone thickness between the ``410'' and ``660'' discontinuties, based on underside re¯ections that arrive ahead of SS. The estimates have been corrected for surface topography, crustal thickness, and upper mantle shear wave velocity structure beneath the SS bounce points (from Flanagan and Shearer, 1998).
842
and Richards, 1993; Niu and Kawakatsu, 1995; Vidale and Benz, 1992; Castle and Creager, 1997, 1998b). At long wavelengths the 660 km feature varies in depth by 35±40 km, which is far less than would be expected if the boundary were a compositional contrast. Topography of the 410 km feature is smaller in amplitude (20±25 km) and globally uncorrelated with the 660 km feature [although Revenaugh and Jordan (1991a) present evidence for anticorrelation of the two in some regions]. The olivine to -phase transition that is associated with the 410 km discontinuity is exothermic, and should be elevated in the vicinity of cold slabs, however, con¯icting results have been reported on the near-slab topography of this feature (e.g., Vidale and Benz, 1992; Zhang and Lay, 1993; Collier and Helffrich, 1997; Flanagan and Shearer, 1998b). A complicating factor is that the transformation of olivine may by kinetically inhibited, with untransformed material penetrating well below 410 km (e.g., Sung and Burns, 1976; Rubie and Ross, 1994). The complex thermal structure and kinetic effects near subducting slabs probably result in a rather poor re¯ector. The ¯uctuations in distance between the 410 and 660 km features shown in Figure 11 show a pronounced contrast between central Paci®c and circum-Paci®c regions, but no average difference between continents and oceans. In contrast, Gossler and Kind (1996) have proposed that the discontinuity separation is actually larger under continents, favoring very deep roots of continents. Long-period SS precursors are also extensively observed to originate near a depth of 520 km (e.g., Shearer, 1990, 1996; Flanagan and Shearer, 1998a), and the topographic variations of this re¯ector can also be imaged (Fig. 11). ScS reverberations also consistently show a weak arrival (Revenaugh and Jordan, 1991a). A shear-wave impedance contrast less than half of that found for the 410 km feature is involved, so although the 520 km boundary is probably global in extent, it may produce arrivals below noise levels in some sparsely sampled regions. It is likely that this feature is associated with transformation from -phase to -spinel (e.g., Rigden et al., 1991), which is not expected to produce a very sharp feature in seismic velocities, but should produce a several percent increase in density. As noted previously, several upper mantle P- and S-wave models obtained by modeling of wide-angle triplications incorporate some increase in velocity gradient near this depth (e.g., Helmberger and Wiggins, 1971; Helmberger and Engen, 1974; Mechie et al., 1993), however many long-period models do not require any velocity structure at this depth, and several studies of short-period P waves indicate that no sharp increase in P velocity is present (e.g., Jones et al., 1992; Cummings et al., 1992; Benz and Vidale, 1993). This set of observations can be reconciled by the existence of a several percent contrast in density, with little P-velocity or Svelocity increase, with more than 50% olivine component in the transition zone, which favors an olivine-rich pyrolitic
Lay
mantle model without much eclogite in the transition zone (Shearer, 1996). There is also evidence for an impedance contrast near 705± 770 km depth, imaged most extensively by ScS reverberations (Revenaugh and Jordan, 1991a,b), but with some evidence from wide-angle P waves (e.g., Datt and Muirhead, 1976; Muirhead and Hales, 1980) and in P 0 P 0 precursors (Sobel, 1978). Although this is not established as a global boundary, it is perhaps closely linked to the bottom of the zone of steep velocity contrast in many S-wave models which does appear to have global extent (Fig. 10). The ilmenite to perovskite transformation (Liu, 1977) is a viable candidate for the impedance contrast when it is present (Revenaugh and Jordan, 1991a), which should be in relatively cold (slabrelated?) mantle, while gradual transformations of majorite and garnet to perovskite may account for the ubiquitous steep gradient just below the 660 km discontinuity (e.g., Anderson, 1991). The principal components of upper mantle and transition zone structure are summarized in the schematic in Figure 12. Continents and oceans have signi®cant differences extending from the crust to depths near 350 km (see below), oceans have pronounced shallow low shear velocity layers, there are global discontinuities near 410 km, 520 km and 660 km depth, with temperature variation-induced topography on these boundaries compatible with their interpretation as phase transitions in the olivine component of the mantle. There are intermittent discontinuities associated with continental crust, the vicinity of subduction zones, and the base of the transition zone. All of these features, revealed by seismology, provide a basis for testing and re®ning models of the composition and state of the upper mantle and transition zone.
4.4 Tomographic Models of the Upper Mantle and Transition Zone The foregoing discussion has addressed average upper mantle and transition zone structure, with some attention paid to bimodal distinctions between continental and oceanic regions. Given the complexity of Earth's history, with its ongoing dynamical motions, it would be surprising not to ®nd complex lateral variations in structure everywhere in the mantle, which need not be directly coupled to surface geology. The variety of localized 1D models seen in Figure 10 strongly indicates that this is the case. From the early efforts at simple tectonic regionalizations for interpreting great-circle dispersion measurements (e.g., ToksoÈz and Anderson, 1966; Kanamori, 1970) methods of seismic tomography (see Chapter 52 by Curtis and Snieder) have been developed to image lateral variations relative to a reference Earth model for scales extending from borehole measurements, to crustal features, to lithospheric scales, to global 3D inversions. Seismic tomography, although commonly involving approximations to the
The Earth's Interior
A
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843 Platform (P)
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Positive reflector Negative reflector Approximate limit of thermal boundary layers
FIGURE 12 Schematic of upper mantle structural variations ranging from continental shield to ocean environments. Major velocity discontinuities are the crust-mantle Moho boundary (M), a continental velocity increase near 80 km depth (H), an oceanic velocity decrease at the base of the oceanic lid (G), a stable continental feature near 200 km (L), an intermittent discontinuity observed near subduction zones (X), and the global structures near 410, 520, and 660 km, as well as a less pronounced feature near 710 km. Cold temperatures near subducting slabs can elevate or depress the phase boundaries at 410 and 660 km, respectively,. (from Revenaugh and Jordan, 1991b).
propagation effects, is generally applied with few, if any, explicit a priori constraints on the structure to be imaged (aside from resolving lengths explicit in the model parameterization), allowing unexpected features to be detected. This enables seismology to characterize the structural elements of complex dynamical systems such as magmatic centers, plumes, subducting slabs, and mantle convective systems. Indeed, the applications are now vast in number, and extensive reviews and books are available providing extensive details about the methodology and results (e.g., Thurber and Aki, 1987; Nolet, 1987; Romanowicz, 1991; Iyer and Hirahara, 1993; Ritzwoller and Lavely, 1995). Without the seismic imaging tool, most of our understanding of dynamical features in the mantle would simply involve conceptual cartoons. The basic concept of seismic tomography is to use extensive raypath coverage through a given volume of rock to infer heterogeneous properties of the medium such as 3D velocity or attenuation structure. Typically, arrival-time measurements (or amplitudes) for each path are converted into anomalies with respect to predicted times (amplitudes) computed for a background reference model using estimated (or known, in the case of explosions) source origin parameters. The measured anomalies are treated as path integral effects, and are projected onto a spatially parameterized version of the medium, with basis functions in the form of blocks, spherical harmonics, splines, or other general representations. The
spatially varying parameters in the medium are inverted for by matching the observations subject to various constraints (smoothness of the medium, designated levels of variance reduction, etc.) with the cross-consistency between paths constructing the image of the heterogeneity (see Chapter 52 by Curtis and Snieder for mathematical details). The resulting images tend to improve in reliability with more uniform raypath sampling of the medium, larger data sets that reduce random errors, improved constraints on source locations, and iterative or nonlinear inversion methods that include the raypath perturbations and fresnel-zone sampling of the medium as the model changes. Although there had been many earlier studies of velocity heterogeneity in the crust and mantle on various scales, the ®rst (initially reported in 1974) formal application of seismic tomography without a priori tectonic regionalizations was to image the lithospheric structure beneath large seismic arrays, where ¯uctuations in relative arrival times over small distance separations provide constraint on the structure under the array (e.g., Aki and Lee, 1976; Aki et al., 1976, 1977). This led to many inversions for structure under arrays, yielding an understanding that there is small-scale (1±100 km) velocity heterogeneity almost everywhere in the upper mantle, as reviewed by Aki (1982). In parallel, arrival-time bulletins for large numbers of body waves were also applied to regionalized imaging of mantle downwellings (e.g., Hirahara,
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1977; Humphreys et al., 1984) or global mantle P velocity structure (e.g., Sengupta and ToksoÈz, 1976; Dziewonski et al., 1977; Comer and Clayton, 1983; Dziewonski, 1984). New methods were introduced for solving large matrix problems with as many parameters as necessary for full 3D descriptions of the heterogeneity in the mantle, even when only large-scale structures are allowed for. Rapidly accumulating databases of digital seismic waveforms were also being processed, primarily measuring surface-wave dispersion or free oscillation eigenfrequencies for unprecedented numbers of paths, and these data were also incorporated into inversions for aspherical mantle structure (e.g., Masters et al., 1982; Nakanishi and Anderson, 1982, 1983; Woodhouse and Dziewonski, 1984; Tanimoto and Anderson, 1984). The ®rst generation of global tomographic models established that surface geology and tectonics are clearly manifested in the velocity heterogeneity of the upper 200 km of the mantle (see Fig. 13). Relatively low velocities underly major upwellings such as midocean ridges and continental rifts (e.g., the Red Sea), systematic increases in velocity are associated with the thickening thermal boundary layer underlying aging ocean crust, low upper mantle velocities are found under continental regions with active tectonic deformation (e.g., the western US), and all large continental cratons have relatively
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high velocities which may extend as deep as 400 km. The resolution of these early models was only on the order of 5000 km, but it was established that there is strong power in the heterogeneity spectrum at long wavelength, partly as a result of the distribution of continents and ocean, as well as the scale of oceanic plates. The current generation of tomographic models for the mantle and transition zone have built on these early results, with many advances in data quantity, wave-propagation theory, and types of measurements used in the inversions. Pwave arrival times and fundamental mode surface wave observations have been supplemented by many secondary body-wave arrivals (e.g., PP, PcP, PKP, PKIKP, S, SS, SSS, ScS, SKS) and by higher mode surface waves and split multiplets in the free oscillation spectrum (see Ritzwoller and Lavely, 1995, for extensive references). The numbers of waveforms used for surface-wave inversions have grown to 50 000 and more (e.g., Zhang and Lay, 1996; Trampert and Woodhouse, 1996; EkstroÈm et al., 1997; Laske and Masters, 1996; Boschi and Dziewonski, 1999), and vast body-wave arrival-time data sets have been reprocessed and screened for high quality data (e.g., Engdahl et al., 1998). Global resolution has been improved signi®cantly in the upper mantle, with models having been presented that achieve (or purport to
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FIGURE 13 An early global shear velocity structure obtained by seismic tomography. This shows the relative perturbations of shear velocity at a depth of 150 km in model M84C. Relatively high velocities underlie old oceanic regions as well as continental regions, while relatively low velocities tend to locate under midocean ridges and in back-arc basins (from Dziewonski, 1989).
The Earth's Interior
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achieve) 500±1000 km scale resolution globally (e.g., Inoue et al., 1990; Zhang and Tanimoto, 1991; Vasco et al., 1995; Zhou, 1996; Trampert and Woodhouse, 1996; EkstroÈm et al, 1997; Grand et al., 1997; van der Hilst et al., 1997; Boschi and Dziewonski, 1999; Bijwaard, et al., 1999; Ritsema et al., 1999). For the upper mantle there is quite good compatibility between global shear-velocity models expanded in spherical harmonic degrees up to about degree 12±16 (e.g., Masters et al., 1996; Li and Romanowicz, 1996; Su et al., 1994, 1997), and images for a representative recent model are shown in Color Plate 14. This ®gure shows: improved resolution of the high-velocity structures under continents, which persist to depths greater than 300 km; low velocities at large depths under the fast-spreading mid-Paci®c ridge, but not under the slow-spreading mid-Atlantic ridge; a strong decline in velocity ¯uctuations from the upper mantle to the transition zone, with the latter showing high-velocity features due to slabs in some regions as well as a few localized low-velocity regions under the Paci®c. The heterogeneity is still dominated by longwavelength structure, so the contrast relative to earlier models (see Fig. 13) is not very dramatic. Higher resolution down to scales of 50±100 km has been achieved in regionalized models that image a limited region involving continental or island arc scale models (e.g., Grand, 1987; Spakman et al., 1989, 1993; Zhou and Clayton, 1990;
Spakman, 1991; van der Hilst et al., 1991; van der Hilst et al., 1993, 1995; Wu and Levshin, 1994; Engdahl et al., 1995; Alsina et al., 1996; van der Lee and Nolet, 1997). These regionalized models reveal strong small-scale heterogeneity in structure embedded within the larger provinces imaged by global inversions. There has been steady convergence in the features resolved by high-resolution global inversions and high-resolution regionalized inversions (e.g., Bijwaard et al., 1999). Some of the principal characteristics of upper mantle and transition zone structure revealed by seismic tomography include the deep roots of continents, the structure of subducted slabs and surrounding mantle, and the structure of upwelling plumes.
4.5 Cratonic Roots The inference that continents have anomalous structure extending down hundreds of kilometers (apparent in Fig. 13 and Color Plate 20), despite their large plate-tectonic motions, suggests the notion that cratonic roots are chemically and thermally stabilized over a thickness of 350 km or more, and this was labeled the tectosphere by Jordan (1975, 1988). Survival of such a deep keel over billions of years of continental drift is surprising, as there is general agreement that the thickness of continental mechanical boundary layer
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FIGURE 14 Cross sections through three-dimensional tomographic P wave velocity models produced by van der Hilst et al. (1991, 1993) for western Paci®c subduction zones. The seismic zone in the map is contoured in 100 km intervals. Faster velocity material (relative to the reference iasp91 model) is darker, with shading in 1% velocity variations. Dots are earthquake hypocenters along each of the cross sections. Mantle discontinuities at depths of 410 and 660 km are shown (from Lay, 1994).
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(lithosphere) is on the order of 150±200 km thick (e.g., McNutt, 1990). Although the thermal boundary layer may be twice as thick, its deeper portions would normally be sheared and any structure ephemeral, especially for cratonic age continent, unless the deep region is stabilized by unusual chemical buoyancy or by high viscosity, perhaps as a consequence of extensive volatile depletion (e.g., Polet and Anderson, 1995). It is also possible that dynamical processes sustain anomalously cool material beneath continents as a sort of stagnant layer, but this is hard to reconcile with the complex history of motion of the continents. Statistical analyses support the generalization that cratons have high velocity structure extending to at least 200 km depth (e.g., Wen and Anderson, 1997), but there is controversy over whether the roots extend as deep as the transition zone. Ritsema et al. (1998) ®nd that the deep keel of cratons survives during active continental rifting, with the root extending to 300±350 km beneath Eastern Africa, and low-velocity zones beneath the surrounding rifts extend to 300 km or more. This favors the durability of the deep portion of the root even in the presence of active breakup. Upward de¯ection of the 410-km discontinuity that might be expected for colder than average mantle in the root has not been detected in some careful studies (e.g., Bostock, 1998; Li et al., 1998; Flannagan and Shearer, 1998a; Fouch et al., 2000). Overall, current thinking is that stable archaen and early proterozoic continental crust has an upper mantle root 200± 350 km thick; this is a principal feature of the near-surface boundary layer that would not have been recognized without seismic imaging.
4.6 Slabs Aside from localized regions of partial melting in upwellings, the strongest velocity heterogeneities in the mantle are those associated with subducted oceanic lithosphere. Seismic imaging of descending slabs has involved a great variety of studies (for extensive reviews see Lay, 1994, 1996), many of which have characterized the geometry and magnitude of the velocity heterogeneity of the slab. The velocity anomaly of the slab results from three factors. (1) The relatively low temperature of the slab (with as much as a 1000 C contrast relative to surrounding ambient mantle) intrinsically produces 3±10% high P- and S-velocity slab signatures. (2) The chemical differentiation and hydration that the oceanic lithosphere has undergone combine with the thermal anomaly to produce distinct phase equilibria in the slab material relative to ambient mantle, which can locally produce 5±6% P- and S-velocity anomalies, including elevation and depression of transition zone phase boundaries. (3) The subduction process perturbs the local mantle conditions by shear heating, induced ¯ow, and lowering of the melting temperature in the overlying wedge as a result of volatile enrichment caused by hydrous phases extruded from the slab; this can induce partial melting
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and 5±10% slow P- and S-velocity anomalies. The purpose of seismic imaging of mantle slabs is thus to study the thermal, chemical, and dynamical structure of subduction. Seismicity extends as deep as 700 km for rapidly descending slabs (e.g., Wadati, 1935; Isacks et al., 1968; Stark and Frohlich, 1985), and it is believed that all earthquakes below depths of about 100 km must take place in the relatively low temperature environment within subducted material. Pore¯uid assisted brittle failure or frictional sliding are probably responsible for most earthquakes down to depths of 300 km or so, but it is controversial whether there are any free ¯uids available at greater depths (perhaps as a result of breakdown of hydrous phases), so various other mechanisms have been invoked to account for earthquakes from 400 to 700 km depth. Instabilities associated with transition zone phase transformations are an extensively discussed possibility (e.g., Green and Burnley, 1989; Green et al., 1991; Kirby et al., 1991, 1996; Green and Houston, 1995). Both the distribution of the seismicity and the inferred strain orientations of the Earthquakes have long-been used as direct constraints on the con®guration of seismically active deep slab material, the stress orientations in the slab, and the minimum depth of penetration of the downwelling (e.g., Oliver and Isacks, 1967; Isacks et al., 1968; Isacks and Molnar, 1971; Vassiliou, 1984; Apperson and Frohlich, 1987; Burbachk and Frohlich, 1986; Fukao et al., 1987, Chiu et al., 1991). The cessation of earthquake occurrence at a given depth is not a clear guide as to the fate of the deep slab. Seismicity may terminate due to heating to a critical cut-off temperature for seismicity (e.g., Isacks et al., 1968; Vlaar and Wortel, 1976; Molnar et al., 1979; Wortel, 1982; Brodholt and Stein, 1988; Wortel and Vlaar, 1988), completion of the transition to ®negrained spinel which reduces the strength of the slab (Castle and Creager, 1998a), or, for material that penetrates below 660 km depth, due to the lack of instability for the perovskite phase transformation (e.g., Green and Zhou, 1996). It is known from the history of plate tectonics that far more subducted slab material must be present in the mantle than is illuminated by the current distribution of seismicity, and this material is in varying states of thermal and chemical reassimilation into the mantle (e.g., Richards and Engebretson, 1992; Lithgow-Bertelloni and Richards, 1998). The fate of the vast quantities of aseismic slab material is of central importance to models of chemical, thermal, and dynamical evolution of the planet (e.g., Silver et al., 1988; Jordan et al., 1989; Olson et al., 1990; Lay, 1996). Although it is apparent from both their strain state and geometry that many slabs encounter increasing resistance to descent as they approach 660 km depth, this does not preclude slabs from penetrating into the lower mantle. The endothermic disassociative transformation of spinel-structured (Mg, Fe)2SiO4 into perovskite-structured (Mg,Fe)SiO3 and (Mg, Fe)O near 660 km depth has a negative Clapeyron slope of 2.8 to 4.0 MPaK 1 (e.g., Ito and Takahashi, 1989; Ito et al., 1990), which should resist slab penetration, and this
The Earth's Interior
is a likely source of resistance to subduction that causes down-dip compression for almost all transition zone earthquakes. The geometry and intrinsic thermal/density anomaly of the slab near 660 km depth will determine whether the resistance from this phase transformation is suf®cient to con®ne the slab to the transition zone or whether the slab components may simply transform to perovskite and penetrate deeper. However, even should the phase transformation be transited, there may also be viscosity increases or chemical contrasts with density increases that further prevent the slab from penetrating deeply into the lower mantle. Imaging of the seismic heterogeneity in the mantle holds the key to determining the fate of subducted slab material. The anomalous seismic wave transmission properties of slabs were ®rst manifested in anomalous patterns of seismic intensities for deep events across Japan dating back to 1918, but Utsu (1967) and Oliver and Isacks (1967) were the ®rst to clearly articulate the notion that dipping seismogenic zones beneath island arcs involve regions of low seismic attenuation and high seismic wave velocity. This observation prompted a vast number of investigations of relative arrival hyphen;time patterns, relative seismic amplitude and frequency content patterns, and secondary phase observations that constrained gross aspects of slabs and the surrounding mantle near subduction zones (see review by Lay, 1996, and Chapter 42 by Utsu). From these foundations developed the current approaches to imaging slab structures, which involve arrival time tomography, residual sphere modeling using a priori slab structures, and analysis of conversions, diffractions, and defocusing effects (Lay, 1996). Beginning with the work of Hirahara (1977), large-scale 3D models have been developed for all major subduction zones in both regionalized and global tomographic inversions. Images like those in Figure 14 are typical of current inversions that use massive data sets of arrival times from regional and teleseismic observations (e.g., Zhou and Clayton, 1990; Spakman et al., 1993; van der Hilst et al., 1991, 1993; Engdahl et al., 1995; van der Hilst, 1995; Zhao et al., 1995; Widiyantoro and van der Hilst, 1996; and many more references in Lay, 1996). Because the coverage provided by seismic rays is very nonuniform, and because there is structural information lost in the source location process, these models are blurred images of the real structures, and there are many artifacts in the models. Nonetheless, regions of high seismic velocity are found to surround the deep seismicity, and it is accepted that the primary feature being imaged is subducted oceanic slab. In order to better recover the slab velocity structure, a priori slab models may be incorporated into the model formulation, leading to improved resolution of the wedge structure (Zhao et al., 1995). Deal et al. (1999) and Deal and Nolet (1999) ®nd that many deep artifacts in largerscale models can also be removed when a prior is information about the slab is incorporated into the inversion. This is critical to establishing the depth of slab penetration, for teleseismic
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raypaths tend to have downward smearing of velocity anomalies. A common tendency is for the velocity anomalies of any possible lower mantle extension of slabs to be signi®cantly reduced relative to the slab anomaly in the transition zone. This actually makes detecting the slab structure much harder. Global inversions with high-resolution parametrizations in the vicinity of slabs also recover slab images (e.g., Inoue et al., 1990; Fukao et al., 1992; Vasco et al., 1995; Zhou, 1996; van der Hilst et al., 1997; Grand et al., 1997; Bijwaard et al., 1998), and the slab-related features are often consistent with those imaged by regional models. The resulting images do not have a simple end-member behavior for deep slabs. Deep slabs may ¯atten in the transition zone, as they do underneath the western Mediterranean, the Banda arc, the Solomon Islands, and the Izu-Bonin trench. Beneath Java and the Marianas there appear to be high velocity tabular extensions into the lower mantle, and there may be ¯attening followed by penetration under the Kuriles and Tonga. In some cases the features imaged in the high resolution tomography appear to connect up to lower mantle features found in lower resolution tomography, as discussed in the next section. The general consensus at this time based on tomographic imaging is that at least some slab material does appear to penetrate deeply into the lower mantle. The complexity of slab structures in the transition zone does appear to re¯ect the dif®culty of penetrating the 660 km discontinuity, and this may be in¯uenced by the slab dip, slab age, extent of trench roll-back, and ambient mantle ¯ow patterns. Although tomography has proved to be a powerful technique for resolving aspects of slab structure, it appears that increased use of a priori constraints in the inversions is required for suppressing artifacts. An alternate strategy for slab imaging that explicitly involves assumption of a slab structure is the residual sphere modeling approach. Residual spheres are simply focal sphere projections of arrival time anomalies at positions corresponding to their raypath azimuths and take-off angles from the source, and such plots have long been used to characterize patterns in seismic data (e.g., Davies and McKenzie, 1969; McKenzie and Julian, 1971; ToksoÈz et al., 1971; and many other references in Lay, 1996). Observed arrival-time anomalies are strongly affected by the process of locating the event, which removes degree 0 and degree 1 patterns from the observations, and it is important to account for this in the modeling. To further isolate the near-source contributions to the arrival-time patterns, corrections for propagation effects outside the slab (deep mantle and near receiver) must be made, and typically some smoothing is applied to suppress random error. For a speci®ed source location in a slab structure 3D raytracing or numerical methods are used to predict the arrival time at each station, and the model times are processed by an event location ®lter and any smoothing, with slab model parameters being perturbed to match the data.
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Jordan (1977) initiated the complete residual sphere modeling formalism, which was further developed by Creager and Jordan (1984, 1986). These studies demonstrated the sensitivity of the method to both upper mantle and transition zone slab geometry and velocity heterogeneity, as well as to geometry of any steeply dipping slab extension into the lower mantle. Provocative results based on both P and S wave modeling suggested that slab penetration to depths of at least 1000 km with little distortion other than steepening dip occurs in the Kurile, Marianas, and Japan arcs. Additional applications of the method were presented by Fischer et al. (1988, 1989), Zhou and Anderson (1989), Zhou et al. (1990), Boyd and Creager (1991), Ding and Grand (1992) and Pankow and Lay (1999). The method makes very explicit the limitations of arrival-time data, as event location effects have a huge effect on relative arrival-time anomalies if the data coverage is limited (particularly true if only teleseismic observations are used). Tomographic methods will be strongly biased by this unless the data coverage is such that residual patterns faithfully preserve the slab effects (which may be true when extensive upgoing and downgoing data are included, but not otherwise). Residual sphere modeling also makes clear the importance of deep mantle and receiver corrections, and early applications did not adequately address this issue. In fact, it has been shown that for S waves much of what was initially attributed to near-source effect is eliminated when improved path corrections are applied (e.g., Schwartz et al., 1991; Gaherty et al., 1991; Pankow and Lay, 1999). As global tomographic models improve, this will become less of a problem. Analysis of differential residual spheres for events in the same slab, as ®rst introduced by ToksoÈz et al. (1971) is one approach that has been pursued to suppress distant effects rather completely (e.g., Takei and Suetsugu, 1989; Okano and Suetsugu, 1992; Ding and Grand, 1992; Pankow and Lay, 1999). These studies indicate that in some cases slabs may penetrate to depths of 800 km or more, but signi®cant slab broadening may occur, as well as reduction of velocity heterogeneity to on the order of 2%, much weaker than in early residual sphere studies, and similar to the weak heterogeneity inferred when a priori slab structures are introduced into tomographic modeling. In addition to arrival time imaging, the velocity gradients and internal structure of subducting slabs have been extensively investigated using waveform conversions, diffractions and defocusing effects (see Lay, 1996 for a review). Conversions of P-to-S and S-to-P energy have been used to constrain the velocity contrasts, dip, and sharpness of slab features in many studies since about 1953 (e.g., Katsumata, 1953; Okada, 1971; Nakanishi et al., 1981; Matsuzawa et al., 1990; Helffrich and Stein, 1993; and many other references in Lay, 1996). Such observations are used to explore the detailed structure of the layered slab, with evidence for both high- and low-velocity layers near the top of the slab (possibly involving the eclogitic crust) and the existence of velocity
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contrasts within the slab that may be associated with double layers of seismicity detected in many regions. Imaging internal slab structure is also of interest for detecting the position of phase boundaries in the slab (key temperature indicators) as well as possible metastable depression of such boundaries (e.g., Solomon and U, 1975; Roecker, 1985; Iidaka and Suetsugu, 1992; Collier and Helffrich, 1997; Koper et al., 1998; Flannagan and Shearer, 1998b). As indicated earlier, there are con¯icting results on the nature of major phaseboundary de¯ections inside the slab, and a thin wedge of metastable olivine has not been resolved. Diffraction and defocusing effects have been used to bound slab velocity gradients in many studies (e.g., Sleep, 1973; Cormier, 1989; Weber, 1990; Sekiguchi, 1992; Silver and Chan, 1986; Vidale, 1987; Gaherty et al., 1991; Vidale et al., 1991), but computational limitations and the dif®culties of accounting for wave-propagation effects on amplitudes and waveforms have limited the contribution of such studies.
4.7 Upwellings and Plumes Seismic methods intrinsically image downwelling highvelocity structures like slabs better than hot, upwelling lowvelocity structures for two reasons: slabs often have deep focus earthquake sources in the cold downwelling that provide improved raypath coverage of the surrounding structures, whereas hot upwellings tend to have only shallow activity; and wave propagation through hot, low seismic velocity regions involves signi®cant wave front healing, attenuation, and diffraction effects that obscure the travel-time signature. Nonetheless, regions of expected upwelling beneath major volcanic centers have been the target of many tomographic investigations, for the purpose of ascertaining the size and geometry of the zone of partial melting. Crustal structures beneath volcanic centers are described in Chapter 25 by McNutt and Chapter 26 by Benz et al., and only mantle features are considered here. Global tomography provides limited resolution of presumed upwelling regions at this point, in part due to the spatially localized nature of most upwellings. The best-imaged regions are the large-scale features associated with the midocean ridge system. Surface wave and long-period body wave tomography indicate that low velocity material underlies almost all of the midocean ridge system on scale-lengths that can be resolved even in models with only 1000 km scale resolution (e.g., Zhang and Tanimoto, 1991; Su and Dziewonski, 1997; Trampert and Woodhouse, 1996; EkstroÈm et al., 1997; Boschi and Dziewonski, 1999; Ritsema et al., 1999). The depth extent of the low-velocity region under ridges is less-well resolved, with some studies indicating concentration of low-velocity material in the upper 100 km (e.g., Zhang and Tanimoto, 1991, 1992), but the more compelling case being that low-velocity material extends down to at least 250 km below fast-spreading ridges such as the Paci®c
The Earth's Interior
rise (e.g., Su et al., 1992; Su and Dziewonski, 1997). Global P-wave tomography models typically have poor sampling of midocean ridge systems, and little vertical resolution of upper mantle structure, in contrast to their resolution of downwellings. The lack of nearby stations causes strong trade-offs between mantle structure and source parameters for near-ridge events. The existence of low velocity material at depths down to 400 km beneath ridges is strongly supported by bodywave analysis of SS, SSS and SSSS phases (e.g., Graves and Helmberger, 1988; Grand et al., 1997). However, transition zone discontinuities beneath the Paci®c rise do not appear to have anomalous depths as might be expected if thermal anomalies extend through to the lower mantle (e.g., Shen et al., 1998; Lee and Grand, 1996). The prevailing notion is that most midocean ridge upwellings are relatively passive in nature, with partial melting occurring as a result of pressure reduction as material rises super-adiabatically into the ridge. Acute heterogeneity and concentrations of low-velocity upwellings are imaged in the upper mantle wedge above subducting slabs, with the best detail being provided by regional-scale tomographic inversions (e.g., Zhao et al., 1992, 1994, 1995, 1997). The low velocity regions are so pronounced that they likely involve signi®cant partial melting, which is thought to be the result of lowering of the melting temperature due to the presence of volatiles released from the subducting slab. Upwellings are also inferred from lowvelocity structure found below continental rift zones such as the East African rift. These appear to extend deep into the upper mantle as well, with low velocity P and S anomalies as deep as 350 km (e.g., Su and Dziewonski, 1997; Ritsema et al., 1998). Deep structures that may correspond to frozen-in plume features have also been imaged by tomography under South America (Van Decar et al., 1995). There has also been great interest in studying the structure under major hotspots such as Iceland, Yellowstone, and Hawaii. Global surface wave tomography has not resolved the 100±200 scale structures of relevance, but there is some suggestion that many large hotspots are underlain by lowvelocity material in the upper 200 km of the mantle (Zhang and Tanimoto, 1991). Tomographic inversion of P-wave arrival anomalies suggests that low velocities extend to at least 400 km depths below Iceland as a large cylindrical structure with a radius of about 150 km (Tryggvason et al., 1983; Wolfe et al., 1997). Shear-wave anomalies in this structure are as large as 4% whereas P-wave anomalies are 2%. This requires temperature anomalies of on the order of 200±300 C. Shen et al. (1998) examine topography of the 410 and 660-km discontinuities beneath Iceland as indicated by Pds conversions in receiver functions, and ®nd that the transition zone is about 20 km thinner than average, which they interpret as evidence for a lower mantle origin of the thermal upwelling. Similar de¯ections of the transition zone discontinuities are observed along the Yellowstone hotspot track (e.g., Dueker, and Sheehan, 1997), although the
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primary low velocity features imaged by tomography are concentrated in the range 50±200 km beneath the Snake River Plain (Dueker and Humphreys, 1990; Saltzer and Humphreys, 1997). Travel-time anomalies for P waves beneath other hotspots have been interpreted as being caused by plumes extending through the transition zone (Nataf and VanDecar, 1993).
4.8 Laterally Varying Anisotropy The average upper mantle velocity structure can be characterized as transversely isotropic, as described above. A model like PREM provides a ®rst-order ®t to global Love and Rayleigh wave dispersion observations, as well as equivalent toroidal and spheroidal eigenfrequencies. However, the very nature of anisotropy, involving large-scale alignments of intrinsically anisotropic minerals such as olivine, systems of oriented cracks, or sheared fabrics or lamellae, is such that lateral variations in anisotropic properties are expected throughout the crust and upper mantle. This is actually found to be the case, with lateral variations in the anisotropic structure of the lithosphere and asthenosphere for both continental and oceanic regions having been imaged by a variety of body-wave and surface-wave methods. Global and plate-scale tomographic inversions of surface wave dispersion measurements have incorporated anisotropic structure either in the reference model (by using PREM), or explicitly in the parameterization of the model (e.g., Nataf et al., 1984, 1986; Nishimura and Forsyth, 1989; Montagner and Tanimoto, 1990, 1991; EkstroÈm and Dziewonski, 1998). EkstroÈm and Dziewonski (1998) demonstrate convincingly that the contributions to surface-wave travel times from anisotropy variations are signi®cant, and allowance for spatial variations in anisotropy is both justi®ed and necessary. EkstroÈm and Dziewonski (1998) ®nd that the radially varying transverse isotropy of PREM is a good average model for both oceanic and continental regions, even when there are substantial baseline shifts in the average velocities. The main exception is the central Paci®c plate where there are strong geographical variations in radial anisotropy, with maximum anisotropy differences being much stronger than in PREM around 150 km deep. It appears that actual anisotropy in the Paci®c plate is not simply transverse isotropy, but azimuthal anisotropy (which causes wave speed to vary with azimuth, not just polarization), but mapping of azimuthal anisotropy is still rather poorly constrained (e.g., Nishimura and Forsyth, 1988, 1989; Montager and Tanimoto, 1991; EkstroÈm and Dziewonski, 1988). As constraints on the geometry and variations in anisotropy improve, it will be possible to relate the anisotropic observations to models of shear ¯ow that induce lattice preferred orientations (LPO) or fabrics in the upper mantle lithosphere and asthenosphere (e.g., Tanimoto and Anderson, 1984; Montagner, 1994).
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Continental observations of seismic anisotropy have primarily involved body-wave measurements of shear-wave splitting and azimuthal Pn travel times, although surface-wave observations in the continents do support the existence of upper mantle anisotropy (e.g., Gaherty et al., 1996). Silver (1996) and Savage (1999) review the observations of upper mantle anisotropy and the basic hypotheses for interpreting anisotropy as a result of either frozen or actively supported fabrics in the rocks. The most extensively analyzed phases have been SKS phases, which traverse the core as a P phase, and hence have a known initial polarization at the core±mantle boundary on their path to the surface. Vinnik et al. (1984, 1989, 1992), Kind et al. (1985) and Silver and Chan (1988, 1991) established methods for analyzing the splitting of SKS signals to determine the orientation and magnitude of azimuthal anisotropy, typically under the assumption of a horizontal symmetry axis for hexagonal crystals. A large number of analyses of S and SKS splitting to determine receiver and source-side anisotropic structure have ensued (see Savage, 1999 for many references), demonstrating that the Earth's lithosphere has extensive azimuthal anisotropy, sometimes with large-scale coherence, and sometimes with small-scale regional variations. The rapid variations that are sometimes observed require that the anisotropy be concentrated in the shallow mantle, but the magnitude of splitting (values as large as 2±3 sec have been observed) requires that the anisotropy be as strong as 2.5±3% over the upper 250 km of the mantle. Analysis of splitting for earthquakes at different depths suggest anisotropy of 0.5±2% for the mantle above and below slabs and up to 5% within slabs (e.g., Shih et al., 1991; Kaneshima and Silver, 1995; Fouch and Fischer, 1996; Hiramatsu et al., 1997). Splitting generally does not increase with source depth for events deeper than 400 km (e.g., Kaneshima and Silver, 1995; Fouch and Fischer, 1996; Fischer and Wiens, 1996), however, there is limited evidence for transition zone anisotropy in converted phases (Vinnik and Kind, 1993; Vinnik and Montagner, 1996) and from modeling body-wave and normal-mode observations (Montagner and Kennett, 1996). As yet, there is not a fully satisfying reconciliation of the global model of transverse isotropy provided by PREM and the extensive observations of laterally varying azimuthal anisotropy provided by body-wave studies. It appears that the mantle requires a more general parameterization than transverse isotropy, but the data feeding into global tomographic inversions and reference Earth models are not yet suf®cient to constrain the complete anisotropic orientation.
4.9 Attenuation The foregoing discussion has emphasized elastic properties of the crust and mantle, primarily constrained by elastic wave travel times. However, the Earth is not perfectly elastic, and seismic waves of all types undergo anelastic attenuation as
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they propagate. This results in amplitude decay at a rate exceeding that caused by geometric spreading, along with slight dependence of seismic velocity on frequency, or dispersion. In general, the mechanisms that cause anelastic losses are thermally activated microscale processes such as dislocation motions and grain boundary interactions (see Anderson, 1967b; Minster, 1980; Minster and Anderson, 1981). One of the primary goals of studying attenuation is to constrain thermal structure inside the planet. The details of microscale processes that cause attenuation are not resolvable with seismic waves, which intrinsically average large volumes, so phenomenological models are used to account for the macroscopic effects of anelasticity (see Lay and Wallace, 1995). The most common parametrization is in the form of the quality factor, Q, de®ned as the inverse of the fractional loss of energy, E, per cycle of oscillation: 1/Q E/2E. As Q increases, the attenuation is smaller, and for in®nite Q, the elastic solutions are retrieved. Attenuation quality factors can be de®ned for all types of seismic waves, with the corresponding value depending on the speci®c path through the Earth, the sense of particle motion involved in the wave, and the frequency of the vibration. Suitably designed experiments have allowed Q values to be estimated for body waves and surface waves for more than four decades (e.g., Sato, 1958; Bath and Lopez, 1962; Anderson, 1963; Press, 1964; Anderson and Archambeau, 1964; Anderson and Kovach, 1964; Ben-Menahem, 1965). Generally, P- wave quality factors (Q ) are higher than S-wave quality factors (Q ) (see Fig. 3), and it is believed that most intrinsic attenuation is related to shear processes associated with lattice defects and grain boundaries (for a Poisson solid with all losses due to shearing mechanisms, Q 9/4Q ) (e.g., Anderson et al., 1965). Observationally, Q for seismic waves in the mantle is not strongly dependent on frequency over the band 0.001±0.2 Hz, with typical Q values of 100±500 or so, but at higher frequency the attenuation is lower, and Q increases with frequency. The existence of attenuation modi®es the equations of motion for Earth materials from those for pure linear elasticity. However, for the moderate Q values found in the Earth, good approximations of the solution for the full viscoelastic equations can be obtained by perturbation of the elastic solutions with effective attenuation operators (see Lay and Wallace, 1995). For example, the amplitude spectrum for a propagating P or S wave is modi®ed by a term like: A(f) Aoe( ft* ), where Z ds
3 t
f v
sQ
s, f s
with s being a variable along the path, v(s) being the velocity encountered on the path, and Q(s, f) being the spatially and frequency varying attenuation factor. The ®nite Q encountered by a seismic wave, even if it is approximately constant over
The Earth's Interior
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a frequency band, results in frequency dependence of seismic wave velocity, with higher frequencies sensing an unrelaxed effective modulus and having higher velocities than lower frequencies, which sense a relaxed effective modulus (e.g., Futterman, 1962; Jeffreys, 1965; Liu et al., 1976; Kanamori and Anderson, 1977; Anderson et al., 1976). The frequency dependence of physical mechanisms that cause attenuation is usually treated using the standard linear solid model, for which each physical mechanism in¯uences a characteristic frequency band de®ned by a Debye peak, and a propagating wave encounters a distribution of distinct mechanisms that superimpose to produce an effective absorption band over a range of frequencies. The systematic variation of elastic velocities with frequency is observed in the Earth, and must be accounted for in order to reconcile Earth models based on short-period body waves with those based on long-period normal modes (e.g., Hart et al., 1977; Montagner and Kennett, 1996). The PREM model, which has a radially varying constant Q structure, thus has explicitly frequency dependent seismic velocities (Dziewonski and Anderson, 1981). There have been extensive measurements of attenuation for globally sampling data sets of surface waves and free oscillations (e.g., Kanamori, 1970; Anderson and Hart, 1978; Sailor and Dziewonski, 1978; Nakanishi, 1979; Dziewonski and Anderson, 1981; Masters and Gilbert, 1983; Smith and Masters, 1989; Roult et al., 1990; Romanowicz, 1990; Widmer et al., 1991; Durek et al., 1993; Romanowicz, 1995; Durek and EkstroÈm, 1996). Average Q models for the upper mantle are shown in Figure 15. The lithosphere is relatively high Q, but there are Q values of 60±70 in the vicinity of the low velocity zone, which suggests a connection between partial melting and strong attenuation. The Q of the lower mantle is much higher (Fig. 3), thus most attenuation is believed to take place along the upper mantle portion of wave paths. The more recent of the global studies have produced
600
QR19 QL6
500
PREM
400 Q
QM1
300
low resolution (up to degree 6) tomographic models of aspherical attenuation that show a negative correlation with models of shear velocity variations as would be expected for temperature effects (e.g. Durek et al., 1993; Romanowicz, 1995). Relatively low Q values are found in the upper mantle under the Paci®c and under Eastern Africa. In general, there are higher Q regions underlying most continental areas than underlying oceanic regions (e.g., Dziewonski and Steim, 1983; Romanowicz, 1995). The lateral variations in attenuation are particularly important to account for when inferring thermal anomalies from seismic tomography, because the dispersive effect in low Q regions, which tend to be hot and low seismic velocity, accentuates the velocity anomaly for a given thermal heterogeneity (e.g, Karato, 1993). The tomographic inversions for attenuation are complicated by the need for correcting for focusing and defocusing effects of velocity heterogeneity, and it is likely that joint inversions for velocity structure and attenuation structure will be pursued in the future. Higher spatial resolution measurements of attenuation for body and surface waves indicate that Q varies laterally by an order of magnitude, especially in the upper mantle. This means that the average radial Q model for PREM, which has an average value of Q 128 in the upper 400 km of the mantle, is only useful for normal modes and long-path surface waves, which involve extensive lateral averaging. For body waves in the period range 30±1 sec, average values of t * are 1 0.5 sec for P waves and 4 2 sec for S waves, whereas at shorter periods of 1±0.1 sec the t * values may decrease to 0.1 or 0.2 sec on speci®c paths (e.g., Sipkin and Jordan, 1980; Der et al., 1980; Taylor et al., 1986; Chan and Der, 1989; Flanagan and Wiens, 1990; Sheehan and Solomon, 1992; Ding and Grand, 1993; Bhattacharyya et al., 1996; and many more). The exponential form of the t * operator still means that high frequencies are strongly attenuated on paths through the mantle. The lateral variations in attenuation beneath continental areas have been of particular importance for nuclear explosion monitoring, with estimates of explosion yields trading off directly with estimates of the seismic attenuation of the high frequency P waves from explosions. This has prompted extensive work on the variation and frequency dependence of attenuation for periods near 1 sec (see discussions by Bache, 1985; Burger et al., 1987). Overall, models for attenuation in the mantle remain relatively primitive, but ®rst-order mapping of the structure has been achieved.
200
5. Lower Mantle
100 0 0
100 200 300 400 500 600 700 Depth (km)
FIGURE 15 Spherically averaged Q models for the upper mantle from various studies of surface wave and normal mode attenuation (from Romanowicz, 1995).
The lower mantle extends from 800 to 2890 km deep, where the Earth's primary internal compositional contrast exists at the core±mantle boundary. For most of this depth range, the structure appears to be relatively uniform, free of major radially symmetric boundaries, and quite plausibly composed of uniform composition of (Mg0.9 Fe0.1)SiO3 perovskite, with
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km sec–1; g cm–3
670 Discontinuity
P Velocity Extremal bounds
11.0
D⬙
P
S Velocity
7.0
Density
3.0 600
1200
1800 Depth (km)
2400
3000
FIGURE 16 Variation of seismic velocities and density through the lower mantle for model PREM, along with extremal bounds that indicate the con®dence interval for spherically averaged models based on travel-time data. The D00 region is the lowermost 200 km of the lower mantle overlying the core±mantle boundary (CMB) (from Lay, 1989).
(Mg, Fe)O and minor additional components such as SiO2stishovite and calcium perovskite. No major phase changes in these primary components are expected over the pressure range of the lower mantle. Seismic velocity models for the lower mantle (Fig. 16) differ very little from the classical models of Gutenberg and Jeffreys except near the 660 km discontinuity and at the base of the mantle, largely because the travel-time curves for P and S waves are remarkably free of complexity in the range of 30±100 degrees and therefore provide tight constraints on the structure (Fig. 1). Nonetheless, there have been substantial contributions to our understanding of mantle dynamics and chemical evolution as a result of detailed studies of lower mantle structure, and vigorous research is being pursued to map out small aspherical structures as well as detailed structure of the base of the transition zone and in the lowermost 200 km of the lower mantle, which Bullen (1949) identi®ed as an inhomogeneous zone and labeled the D00 region.
5.1 Radially Symmetric Structure/ Discontinuities The average lower-mantle properties have been determined by both classical arrival time inversion and by normal mode analysis, with the latter re®ning early estimates of the density structure that had been based on velocity±density systematics, integral constraints on Earth's mass and moment of inertia, and integration of seismic velocity models using the Adams± Williamson equation (Adams and Williamson, 1923). Global observations of body wave travel times, measurements of slopes of the travel-time curves by seismic array analyses, and
measurements of normal-mode eigenfrequencies proliferated in the 1960s to 1980s, with many radially symmetric Earth models for the lower mantle being produced (e.g., Chinnery and ToksoÈz, 1967; Hales et al., 1968; Herrin, 1968; Johnson, 1969; Hales and Roberts, 1970; Randall, 1971; Jordan and Anderson, 1974; Gilbert and Dziewonski, 1975; Dziewonski et al., 1975; Sengupta and Julian, 1978; Uhrhammer, 1978; Dziewonski and Anderson, 1981; Kennett and Engdahl, 1991; Morelli and Dziewonski, 1993). Although the lower mantle variations among these models are less than 1%, there is still great importance in having an accurate reference model both for earthquake location procedures and for use as a background model in tomographic analyses (reference model structures are often optimized in the very process of producing a tomographic model). Thus, efforts to improve the average lower mantle parameters continue, with increasing quantities of data and variety of phase types being incorporated into the analysis (Masters et al., 1999). All of these average lower mantle models have smooth velocity gradients with no signi®cant structures other than reductions of velocity gradients in the D00 region, as in the PREM model (Fig. 16). The small variations between lower mantle radial velocity models have still received much attention because any departure from homogeneity (as expected for self-compression of uniform composition material) would have major implications for possible chemical layering or phase changes. P and S velocities throughout the lower mantle above the D00 region are bounded to within about 0.1 km sec 1 in terms of an average model (e.g., Lee and Johnson, 1984). This tight bound (Fig. 16) is consistent with the ®nding by Burdick and Powell (1980), that small features in ray parameter estimates from seismic arrays tend to vary azimuthally, and are not globally representative, with on average very smooth structure in the lower mantle being preferred as an average model. There have been observations of re¯ections and converted phases from a velocity or impedance contrast near 900 km depth near subduction zones (e.g., Revenaugh and Jordan, 1991; Kawakatsu and Niu, 1994), but this appears to be a strongly laterally varying structure (Shearer, 1993), and may be associated with steeply dipping mantle heterogeneities (Niu and Kawakatsu, 1997; Kaneshima and Helffrich, 1998; Vinnik et al., 1998; Castle and Creager, 1999). At this time there is no compelling evidence for signi®cant laterally extensive layering of the lower mantle except near the top of the D00 region. The lower mantle has relatively high Q values for seismic waves (see Fig. 3), and mapping any lateral variations is very dif®cult due to the strong regional variations in the upper mantle. Normal modes and averaged body-wave attenuation measurements place some constraints on the average Q values, but it is possible to satisfy most data with extremely simple models (e.g., Dziewonski and Anderson, 1981; Masters and Gilbert, 1983). Although there is some evidence for a low Q zone at the base of the mantle, this is not well
The Earth's Interior
resolved because of strong trade-offs with velocity gradients in the D00 region.
5.2 D00 The existence of the Earth's magnetic ®eld, caused by ongoing thermochemical convection and an associated geodynamo in the conducting iron alloy core, requires that heat is ¯uxing from the core into the mantle. While estimates of the total heat budget of the mantle indicate that heating from below comprises only 10±30% of the total mantle heat ¯ux (the balance is from residual internal heat and radioactive decay in the mantle), a thermal boundary layer should exist at the base of the mantle, with a rapid increase in temperature across a conductive boundary layer. Like the Earth's other major thermal boundary layer in the lithosphere, the boundary layer at the base of the mantle is likely to be undergoing strong lateral and vertical ¯ow, as upwellings produced by thermal boundary layer instabilities drain hot material from the boundary layer and downwellings replace it with cooler material. As a hot, low viscosity boundary layer, it is likely that there is much more small-scale structure in the dynamical regime than is found in the relatively stiff lithosphere. It is generally accepted that heterogeneity within the thermal boundary layer is partially responsible for the inhomogeneity detected by Dahm (1934) and con®rmed by Bullen (1949) as well as for the reduced seismic velocity gradients in the region found in some of the average Earth models (e.g., Stacey and Loper, 1983; Lay and Helmberger, 1983; Doorbos et al., 1986; Loper and Lay, 1995). However, the juxtaposition of the boundary layer adjacent to the largest density contrast in the Earth (the density jump across the core±mantle boundary is larger than that at the surface of the Earth) heightens the probability that there is also chemical heterogeneity in the D00 region, caused by either density-strati®ed residue from the Earth's core formation process, ongoing chemical differentiation of the mantle, or even chemical reactions between the core and mantle (e.g., Lay, 1989; Knittle and Jeanloz, 1989; Goarant et al., 1992; Jeanloz, 1993; Manga and Jeanloz, 1996). Because of its importance for unraveling the thermal and chemical processes in the mantle many seismological studies have characterized the structure of the D00 region (see the survey papers in Gurnis et al., 1998, and reviews by Loper and Lay, 1995; Weber et al., 1996; Lay et al., 1998; Garnero, 2000). The existence of the great velocity reductions across the core±mantle boundary (CMB) causes seismic wave energy to diffract into the geometric shadow zone at distances greater than 100 . Waves diffracted along the core are sensitive to the absolute velocities and the velocity gradients in the D00 region, and have long been studied to constrain average and laterally varying structure (e.g., Alexander and Phinney, 1966; Sacks, 1966; Bolt et al., 1970, Mondt, 1977; Doornbos and Mondt, 1979; Mula and MuÈller, 1980; Wysession and Okal, 1989; Wysession et al., 1992; Valenzuela and Wysession, 1998, and
853
many more). These studies demonstrate that no single velocity structure suf®ciently characterizes D00 everywhere, and that in some cases there are strong negative velocity gradients in D00 while in other places there are near-zero or positive velocity gradients. There are also changes in the relative perturbation of P and S velocities that are likely due to mineralogical or textural origin (e.g., Wysession et al., 1999). These phases involve extensive lateral averaging of what appears to be a region rich in small-scale structure, but they provide important input into large-scale tomographic models for D00 because of their extensive spatial coverage (e.g., Kuo and Wu, 1997; Kuo et al., 2000; Castle et al., 2000). Both P- and S-velocity structure have velocity discontinuities, or zones of rapid velocity increase over depth ranges of no more than 30±50 km, at many locations near the top of the D00 region (the top of D00 is not precisely de®ned, and many take it to correspond to either where there is a discontinuity or the onset of a change in velocity gradient, which may be from 50 to 350 km above the CMB). The velocity increases are detected by re¯ections and triplications, which arrive ahead of the core-re¯ected PcP and ScS phases (e.g., Wright and Lyons, 1975; Lay and Helmberger, 1983; Wright et al., 1985; Young and Lay, 1987, 1990; Gaherty and Lay, 1992; Weber and Davis, 1990; Houard and Nataf, 1993; Weber, 1993; Kendall and Shearer, 1994; Kendall and Nangini, 1996; Ding and Helmberger, 1997; Thomas and Weber, 1997; Kohler et al., 1997; Reasoner and Revenaugh, 1999; and many others reviewed by Wysession et al., 1998). The re¯ector varies in depth by several hundred kilometers (e.g., Kendall and Shearer, 1994), and appears to have short wavelength lateral variations of on the order of 100 km that may produce scattering rather than simple re¯ections (e.g., Weber, 1993; Kruger et al., 1995; Lay et al., 1997; Scherbaum et al., 1997; Yamada and Nakanishi, 1998; Freybourger et al., 1999; Emery et al., 1999). It has been argued that the discontinuities are actually globally extensive, caused by a phase change, with lateral variations in depth and strength (velocity increases vary from 1 to 3%) being the result of lateral temperature variations and interactions with upwelling and downwelling ¯ow (e.g., Nataf and Houard, 1993; Sidorin et al., 1998, 1999). Others have questioned whether there is a ®rst-order discontinuity or simply scattering from strong velocity heterogeneities as imaged in long-wavelength tomography models (e.g., Liu et al., 1998). The latter possibility requires large ad hoc increases in the magnitude of the tomographic heterogeneities, and does not appear to be a viable explanation for the broadband reflections that are observed. However, thin high or low velocity lamella models may ®t some P-wave observations (Weber, 1994; Thomas et al., 1998; Freybourger et al., 1999). Thus, at present, the interpretation of the D00 discontinuity is uncertain, and work continues on characterizing this structure and its dynamical signi®cance. Of particular importance will be determination of whether there is any density increase in D00
854
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that might represent a chemical change or phase change, either of which could strongly affect the dynamics of the boundary layer (e.g., Sleep, 1988; Kellogg, 1997; Montague et al., 1998; Hansen and Yuen, 1988; Tackley, 1999). The large-scale variations in D00 imaged by seismic tomography have surprising predominant degree 2 and 3 spherical harmonic components (e.g., Su et al., 1994; Li and Romanowicz, 1996; Masters et al., 1996; Dziewonski et al., 1996; Kuo and Wu, 1997; Liu and Dziewonski, 1998; Kuo et al., 2000). These models show consistent high shear velocities rimming the Paci®c plate, with low velocities beneath the central Paci®c and the southeastern Atlantic and southern Africa. This geometry produces a correlation between areas of slab subduction over the past several hundred million years (e.g., Lithgow-Bertelloni and Richards, 1998) and fast regions of D00 , which could result if slabs sink to the base of the mantle and retain enough thermal anomaly to produce high seismic velocities. Similarly, the low-velocity regions of D00 are generally below hotspot regions at the surface, suggesting that D00 upwellings may penetrate all the way to the Earth's surface. This will be discussed further below. Small-scale variations in D00 , with about 1% heterogeneities on scale-lengths of about 10 km are also present. This was ®rst established by interpretation of short-period precursors to PKP phases (e.g., Cleary and Haddon, 1972; Haddon and Cleary, 1974; Doornbos, 1976; Bataille and FlatteÂ, 1988; Bataille et al., 1990; Hedlin et al., 1997; Cormier, 1999). It has generally been believed that the levels of heterogeneity increase in D00 relative to the overlying mantle, but there is weak evidence that small-scale structure in D00 is not distinctive (e.g., Hedlin et al., 1997). It is clear that some of
the strongest scattering, involving much larger velocity heterogeneities, does arise within D00 (Vidale and Hedlin, 1998; Wen and Helmberger, 1998), and this is likely associated with an intermittent thin layer of partial melt that causes an ultralow velocity zone (ULVZ) just above the CMB. The bandwidth of the signals used in scattering analyses controls the sensitivity to scatterers of different dimensions, and analysis of broadband data indicates a rich spectrum of scattering scalelengths in D00 . Evidence for an ULVZ at the base of the mantle was ®rst presented by Garnero et al. (1993) and Silver and Bina (1993). A layer from a few to tens of kilometers thick with as much as 10% P velocity reduction and 30% S velocity reduction is found in some regions of the lower mantle (Fig. 17), with the primary evidence (see Garnero et al., 1998 for a review) being delayed SPdiff KS phases (e.g., Garnero and Helmberger, 1995, 1998; Helmberger et al., 1998) and the shape of precursors to PcP re¯ections (e.g., Mori and Helmberger, 1995; Revenaugh and Meyer, 1997). The strong velocity reductions tend to be most easily explained by partial melting (Williams and Garnero, 1996), suggesting that some component of the mantle is exceeding its solidus at the hottest temperatures of the thermal boundary layer. There is fairly strong correlation between locations of ULVZ patches and slower than average shear velocities in D00 and the overlying lower mantle, which is suggestive of a relationship between partial melting in D00 and large-scale upwellings (e.g., Williams et al,, 1998). There is presently extensive effort to map and interpret the ULVZ feature, as it potentially has signi®cant implications for chemistry and dynamics of D00 (Garnero, 1999).
FIGURE 17 Mollweide projection of Earth showing the ULVZ distribution at the base of the mantle. Light shading corresponds to the Fresnel zone regions where a ULVZ has been detected. Dark regions are where no ULVZ has been detected. No shading corresponds to no coverage. Black-®lled circles are hot spot locations (where there is ULVZ coverage), scaled to buoyancy ¯ux estimates. Crosses are location of calculated lower mantle density anomalies due to subducted material (From Garnero et al., 1998).
The Earth's Interior
Given the complexity of structure at all scales in D00 , it is not surprising that uncertainty remains as to whether there is any topography on the core±mantle boundary itself. Long wavelength topography of the CMB was proposed by Creager and Jordan (1986) and Morelli and Dziewonski (1987) based on studies of bulletin PcP and PKP arrival times, but it has been demonstrated that allowing for strong heterogeneity in D00 and the limited resolution of the available data make CMB topography models very uncertain (e.g., Doornbos and Hilton, 1989; Rodgers and Wahr, 1993; Pulliam and Stark, 1993; Obayashi and Fukao, 1997; Garcia and Souriau, 2000). As models for the entire mantle improve, this may prove to be a solvable problem, and it is a critical one, for it plays a major role in estimating the extent of mechanical coupling between the core and mantle. For imaging shorter-wavelength topography of the CMB, the primary approach has involved travel-time ¯uctuations and precursors to underside re¯ections of internal core reverberations (PKKP). These phases provide an upper bound of about 100 m topography on 10 km scale lengths (e.g., Doornbos, 1974, 1980; Chang and Cleary, 1978; Bataille and FlatteÂ, 1988; Earle and Shearer, 1997, 1998). Although the bulk of the lower mantle does not appear to have large-scale organized anisotropy, the D00 region has been shown to have extensive regions where shear-wave splitting occurs (see review by Lay et al., 1998a, b). Observations of splitting for ScS phases have been made for several decades (e.g., Mitchell and Helmberger, 1973; Lay and Helmberger, 1983b), but observations of diffracted waves convincingly demonstrated that anisotropy is present in D00 (e.g., Vinnik et al., 1991, 1995, 1998; Lay and Young, 1991; Kendall and Silver, 1996; Matzel et al., 1996; Garnero and Lay, 1997; Ritsema et al., 1998; Russell et al., 1998). These observations have prompted increased consideration of the anisotropic crystallography of high pressure phases likely to be present in the lower mantle along with what deformation mechanisms are likely to control the formation of fabrics (e.g., Stixrude, 1998; Karato, 1998). At this time, there are substantial uncertainties in the nature of the anisotropy and its cause. In many places it appears that transverse isotropy with a vertical symmetry axis is consistent with the data (producing earlier SH arrivals than SV arrivals), but there are also clear observations of azimuthal anisotropy, and thus far it has only been possible to characterize the horizontal component of the symmetry axis. Strong shear ¯ows in the boundary layer may induce lattice preferred orientation of the anisotropic lower mantle minerals, but it is not clear why this would not also hold for the overlying lower mantle. Sheared inclusions of chemical heterogeneities and pockets of partial melt may also play a role in generating the seismic anisotropy. As observational and laboratory constraints improve, it is likely that modeling anisotropy in D00 will provide an important constraint on the thermal and dynamical regime in the boundary layer.
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5.3 Aspherical Lower Mantle Structure One of the earliest fundamental contributions of global seismic tomography was the demonstration that large-scale structure exists in the lower mantle and that this unexpected con®guration of deep heterogeneity can account for previously unexplained long-wavelength features in the Earth's geoid (e.g., Dziewonski et al., 1977; Clayton and Comer, 1983; Dziewonski, 1984; Hager et al., 1985). This required improved understanding of how mantle heterogeneities induce ¯ow and de¯ection of boundaries that affect the geoid (Hager, 1984; Richards and Hager, 1984). Although the early low resolution tomographic models for the lower mantle, which have relatively strong spherical harmonic components from degrees 2 to 5, have proved remarkably successful in accounting for the long wavelength geoid (see review by Hager and Richards, 1989), there has been continuing debate about the spectrum of lower mantle heterogeneity. Are the long-wavelength patterns the result of spatial distribution of smaller scale features such as slabs embedded in the lower mantle? If so, then the long wavelength distribution of heterogeneity in the lower mantle is more a consequence of the last few hundred million years of surface tectonics than a fundamental aspect of the lower mantle. Similarly, if the long wavelength patterns in surface hotspots re¯ect features rising from the core±mantle boundary, then the distribution of D00 boundary layer instabilities may contribute to the present long-wavelength structure of the deep mantle. These are still open questions to a large extent, but there is signi®cant convergence in deep-mantle tomographic shear velocity models of the current generation (e.g., Masters et al., 1996; Li and Romanowicz, 1996; Grand et al., 1997; Liu and Dziewonski, 1998; Ritsema et al., 1999), all of which have substantial long wavelength heterogeneities. The same is true for largescale P velocity models, although the level of agreement between models is not currently as strong (e.g., van der Hilst and Karason, 1999; Bijwaard and Spakman, 1999). The presence of large-scale lower-mantle features enables formulation of simultaneous or iterative inversions for dynamical features such as the geoid and dynamic topography, and this has become a new area of research (e.g., Hager et al., 1985; Hager and Clayton, 1989; Dziewonski et al., 1993; Phipps Morgan and Shearer, 1993; Forte et al., 1993, 1994). The primary additional parameter that is constrained in such geodynamic models is the viscosity structure, and it is generally found in geoid inversions as well as contemporary studies of glacial rebound analyses that the viscosity of the lower mantle is one to two orders of magnitude higher on average than that of the average upper mantle (e.g., Mitrovica and ForteÂ, 1997; Lambeck and Johnston, 1998). As the resolution of lower mantle structure improves with each new generation of global tomographic model, it has become clear that there are signi®cant intermediate scale features in the lower mantle. This had been deduced for
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localized regions quite early by array studies or analyses of differential travel times for phase pairs sensitive to lower mantle structure (e.g., Jordan and Lynn, 1974; Lay, 1983), but the geometry and lateral extent of such features was not resolved until tomographic models emerged. Recent high resolution S-velocity (e.g., Grand, 1994; Grand et al., 1997) and P-velocity (van der Hilst et al., 1997) models resolve a high velocity tabular structure extending vertically beneath North America and South America and a similar elongate body beneath southern Eurasia, both of which extend to at least 1300±1800 km depth (Fig. 18). These are interpreted as relatively cold, sinking slab material that has penetrated into the lower mantle as the Americas moved westward and as the Tethys Sea closed, respectively. The midmantle seismic velocity near 1300 km depth is thus dominated by elongate tabular high-velocity features, and it is likely that these contribute signi®cantly to the strong long-wavelength patterns in spherical harmonic models that have lower resolution (see corresponding features in the models discussed by Dziewonski et al., 1993). Below about 1800 km depth, tomographic models show less coherence and tabular structures are not clearly imaged (e.g., Grand et al., 1997). Instead, the models become dominated by large horizontally extensive regions of high and low velocity with strong degree 2 and 3 patterns dominating in D00 , as noted above. The large-scale low-velocity regions below
the Central Paci®c and Eastern Atlantic/Southern Africa do appear to extend upward above the D00 region into the lower mantle. These have been identi®ed as ``superplumes,'' given that their scale greatly exceeds that expected for isolated D00 boundary layer instabilities, and Dziewonski et al. (1993) call them the ``Equatorial Paci®c Plume Group'' and the ``Great African Plume,'' respectively. Attention has focused on large low velocity features in the lower mantle as possible deep roots of plume upwellings. Ritsema et al. (1998) ®nd that velocity anomalies in the structure under southern Africa involves 3% shear velocity anomalies and strong lateral gradients, both of which are more pronounced than in the model of Grand et al. (1997). Even stronger anomalies are reported in the D00 region below the southeastern Atlantic, with as much as 10% S-velocity reductions in a 300 km thick layer (Wen et al., 2000). Ritsema et al. (1999) presented a new S-velocity model in which a low velocity region extends from the core±mantle boundary under the southeastern Atlantic Ocean continuously into the upper mantle beneath eastern Africa. They do not ®nd a low shear velocity zone in the lower mantle beneath Iceland, but Bijwaard and Spakman (1999) present a P velocity image with low velocity under Iceland all the way to the core±mantle boundary. Goes et al. (1999) ®nd a low P-velocity structure beneath Europe from 660 to 2000 km depth which they invoke as the source of small plumes in the upper mantle associated with volcanism in
Layer: 10 1200. 1400. km
Perturbation [%] –0.50
0
0.50
FIGURE 18 Horizontal section through a tomographic model of P-wave velocity structure near 1300 km in the lower mantle, obtained by inversion of ISC arrival times after careful processing for depth determination. Solid dark area correspond to high velocities, with two major coherent features that correspond to tabular structures extending vertically below southern Asia and eastern North America. These are inferred to be subducted slab material that has penetrated into the lower mantle (from van der Hilst et al., 1997).
The Earth's Interior
6. Core The core comprises about 31.5% of the Earth's mass, and the density is such that the only plausible composition is primarily iron. The contrasts in density and viscosity between the lower mantle and the outer core are comparable to those found at the surface of Earth between air and rock and between ocean water and rock, respectively. This is a staggering thought, to step across the core±mantle boundary from ultradense silicates and oxides to relatively superdense iron alloy that has viscosity close to that of water. This profound chemical change was seismically detected early in the 20th century, and many studies have sought to constrain the properties of the molten outer core and the solid inner core. Much of the effort has been motivated
by the recognition that a geodynamo resides within the core, producing and sustaining the Earth's magnetic ®eld. The geodynamo involves turbulent ¯ow of the outer core alloy, geometrically constrained by the planet's rotation and the presence of the inner core, with the heterogeneous structure of the base of the mantle producing a variable heat ¯ow boundary condition on the system. A brief summary of principal ®ndings is presented here, with many additional details provided elsewhere (Chapter 56 by song; Jacobs, 1987; Song, 1997; Creager, 2000).
6.1 Radially Averaged Structure Average velocity and density structures for the core are shown in Figure 19, with smoothly increasing velocities in the outer and inner cores and ®nite shear velocity only in the inner core. The mean velocities of the outer core are tightly constrained by the well-de®ned travel-time branches of PKP and SKS phases (Fig. 1), and once again, the classic models of Jeffreys and Gutenberg (Fig. 2) are very similar to contemporary models for the outer core. The outermost portion of the outer core is best constrained by SKS and SKnS phases, which have continuous turning points just below the CMB because the P velocity of the outer core is higher than the S velocity at the base of the mantle (e.g., Hales and
Pressure (GPa) 200 300
100 15 Gravity (m sec–2)
Vp y Densit (V p) locity nal ve io s s pre
Density (mg m–3)
10
Velocity (km sec–1)
Europe. Smaller-scale plume or slab features may also exist in the lower mantle, that are below the current resolution of seismic tomography. Innovative methods of scattering analysis or array imaging may prove to be the only means by which to constrain such structures (e.g., Ji and Nataf, 1998, Tilmann et al., 1998; Tibuleac and Herrin, 1999). While the lower mantle appears not to have internal layering, it has been proposed that the downward transition in heterogeneity pattern from a midmantle dominated by slablike structures to a deep mantle dominated by large-scale high and low velocity features is caused by compositional strati®cation. In this model (see Kellogg et al., 1999; van der Hilst and KaÂrason, 1999), the lowermost mantle is compositionally distinct, being composed of undifferentiated, ``primordial'' mantle material which is the source of isotopic anomalies sampled by major hotspot plumes. Downwelling slabs can depress the chemical boundary by hundreds of kilometers, de¯ecting it from a depth of around 2000 km. The postulated chemical boundary is not a strong re¯ector, and does not give rise to coherent features in the radially averaged mantle model. The density increase of the deep layer could be due to enrichment in iron or silica, which have competing effects on the velocity structure. This is a highly speculative model, but can at least reconcile the current observations of the deep mantle seismic structure with geochemical observations. Signi®cant improvement of our understanding of the lower mantle will come with reliable determination of density heterogeneity directly from simultaneous inversion of normal modes and gravity observations. A ®rst step in this direction has been presented by Ishii and Tromp (1999). Although also very preliminary, this study found that highdensity material is piled up in regions of uplift beneath the Paci®c and Africa, which would require a signi®cant chemical heterogeneity contribution to offset the thermal anomaly of the upwellings. Until the models improve it may even be premature to associate low velocities with upwellings, for chemical heterogeneity may indeed be very important in the deep mantle.
857
Com
Vs
Gravity
5 D⬙ Lower mantle 0 2000
Outer core (Vs =0)
4000 Depth (km)
N–S Eq. Inner core Shear velocity (Vs)
6000
FIGURE 19 Seismologically measured density (bold solid curve), and compressional (Vp) and shear (Vs) elastic wave velocities in km sec 1 (thin lines) through the core and lowermost mantle shown as functions of depth and corresponding pressure. Extremal bounds on the Vp pro®le through the core are included for comparison. The difference between the polar (N-S) and equatorial (Eq.) compressional velocities through the inner core are indicated by dotted lines. Heterogeneity in the D 0 region is illustrated by variations in Vp and Vs pro®les. (Reproduced with permission, from Jeanloz, 1990, # Annual Review Inc.)
858
Roberts, 1971). Studies of SKS-S, SKKS-SKS and SKKKS-SKS differential times have raised the possibility that a thin region with reduced velocity gradient exists in the outermost 50±100 km of the core (e.g., Hales and Roberts, 1971; Lay and Young, 1990; Souriau and Poupinet, 1991; Garnero et al., 1993; Tanaka and Hamaguchi, 1993, Garnero and Lay, 1998). The issue is still open, but it is clear that if there is any coreside boundary layer it is very subtle and likely to involve only 0.5±1.0% anomalies in a thin layer. Jeffreys and Bolt interpreted precursors to PKP phases in terms of complex inner core±outer core transition models, but these phases are now interpreted as the result of scattered phases from D00 , and much simpler models of this transition near 5150 km depth are preferred. Generally, global average Earth models have smooth outer core velocity gradients right down to the inner core boundary, consistent with selfcompression of the outer core alloy, however, several studies have suggested the presence of a transition zone with reduced gradients just above the boundary (e.g., Souriau and Poupinet, 1991; Song and Helmberger, 1992;). The contrasts at the boundary are best constrained using waveform modeling of re¯ections and diffractions, with recent studies preferring simple models (e.g., Cummins and Johnson, 1988; Shearer and Masters, 1990; Song and Helmberger, 1995). The P and S velocities are almost constant within the inner core on average. The S velocity, ®rst constrained by normal mode modeling (e.g., Dziewonski and Gilbert, 1971) is around 3.6 km sec 1. Direct observation of body waves that traverse the inner core as shear waves has been very dif®cult, but some candidates have been reported (e.g., Julian et al., 1972; Okal and Cansi, 1998; Deuss et al., 2000). The density of the inner core appears to be several percent lower than the density of pure iron, indicating the presence of some lighter elements (Jephcoat and Olson, 1987), whereas the outer core is about 10% less dense than pure iron (Masters and Shearer, 1990), with the light alloying component probably being H, C, S, O, Mg, and/or Si. The outer core has a very high Q value, from 3000 to 10 000, and short-period seismic energy can travel great distances, including multiple underside re¯ections from the core±mantle boundary, with little anelastic attenuation (e.g., Engdahl, 1968; Adams, 1972; Cormier and Richards, 1973; Tanaka and Hamaguchi, 1996). However, the inner core has low Q , on the order of 200±360, which strongly attenuates short-period phases that penetrate into it (e.g., Doornbos, 1974, 1983; Cormier, 1981; Choy and Cormier, 1983; Bhattacharyya et al., 1993; Song and Helmberger, 1995a). The attenuation of short-period signals may in part be caused by scattering rather than intrinsic attenuation (e.g., Cormier et al., 1998; Vidale and Earle, 2000) because normal modes do not require very low Q values (e.g. Widmer et al., 1991). The inner core indeed displays signi®cant heterogeneity and seismic anisotropy, whereas there is no convincing evidence for either in the outer core.
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6.2 Anisotropy and Heterogeneity of the Inner Core Both body waves and normal modes indicate that the inner core is heterogeneous and anisotropic in its structure. Observations of anomalously split normal modes (e.g., Masters and Gilbert, 1981) and patterns in PKIKP arrival times (Poupinet et al., 1983) laid the foundation for the ®rst studies to propose the presence of anisotropy in the inner core (Woodhouse et al., 1986; Morelli et al., 1986). Although alternate models of aspherical structure in the outer core have been considered, there is now consensus that inner core structure can account for the normal mode (e.g., Tromp, 1993, 1995) and PKIKP data (e.g. Song, 1997; Creager, 1999). The latter phases travel 5±6 sec faster along the spin axis than across the equatorial plane (e.g., Creager, 1992; Song and Helmberger, 1993, 1995b, 1998; Vinnik et al., 1994; Shearer, 1994; Su and Dziewonski, 1995; McSweeney et al., 1997; Creager, 1999; see the reviews by Song, 1997 and Creager, 2000). The PKIKP data have established that there are largescale lateral heterogeneities in the inner core associated with the anisotropy, with hemispherical patterns that extend all the way to the center of the Earth (e.g., Tanaka and Hamaguchi, 1997; Creager, 1999). The western hemisphere is 2±4% anisotropic on average. The anisotropy may be the result of crystal alignment induced by magnetic ®elds, convection, crystallization processes, or other effects not yet understood. Some of the structural complexity may also be associated with radial layering of the inner core (e.g., Song and Helmberger, 1998), but mapping out the surprising complexity of the inner core is still underway.
6.3 Rotation Rate of the Inner Core The existence of heterogeneity and anisotropy within the inner core of the Earth allows a test of the stability of such patterns over time. This is of interest because it is uncertain whether the rotation of the inner core is locked to that of the mantle, and models for the geodynamo predict that there may be some differential rotation due to torques applied to the inner core. Song and Richards (1996) observed temporal variation in PKIKP-PKP differential times for observations on a path near the fast direction along the spin axis, with about 0.3 s change over 30 years. Assuming symmetry of the anisotropic fabric in the inner core, they inferred a 1.1 y 1 eastward (faster) relative rotation of the inner core. Su et al. (1996) used a lower quality data set with better spatial distribution, and inferred a 3 y 1 relative rotation rate. Subsequent work has extended the high quality data set, along with discarding the inadequate assumption of symmetry of the anisotropic pattern and allowing for small-scale structure in the inner core or near D00 that may enhance or reduce the rate of change of differential time measurements (e.g., Creager, 1997; Souriau et al., 1997; Laske and Masters, 1999; Souriau and
The Earth's Interior
Poupinet, 2000; Poupinet et al., 2000; Song and Li, 2000; Song, 2000; Vidale et al., 2000). The more recent studies, reviewed by Creager (2000), suggest an inner core differential rotation rate of 0.2 to 0.6 y 1, with some evidence favoring no relative rotation, but the evidence for relative rotation at a rate of about 0.2 y 1 is quite compelling. More discussion of this topic is found in Chapter 56 by song.
7. Conclusions This summary of basic attributes of the Earth's interior determined by seismology has only scratched the surface of the detailed knowledge acquired over the past century, and no overview of this length could begin to do full justice to the vast literature and many contributors who have played important roles in building this knowledge. However, this is a good starting point for delving into the topic, and the many references provide multiple pathways to the full body of seismological information. It should be clear that during the past century many ®rst-order questions about the interior have been resolved, and there is good general consensus on basic issues of layering of the planet. However, there are many fundamental questions that remain open, and progress in the future will build upon the foundations described in this text. It is generally accepted that future advances will come from a combination of advances in wave propagation theory, development of new waveform inversion methods (and computing capabilities), increases in high quality seismic data acquired on multiple scales around the world, and by introduction of creative strategies for solving seismological problems. Equally well accepted is the notion that seismologists must increase their interactions and communications with mineral physicists and geodynamicists, building new interdisciplinary approaches to parameterizing and constraining structures and processes in the Earth's interior. The next century will see profound advances in our understanding, of that we can be assured, but all seismologists should study and contemplate the achievements of the many seismologists who contributed to the great ®rst century of exploring the Earth's interior.
Acknowledgments This research was supported by NSF grants EAR 9418643.
References (abridged set; see Editor's Note below) Aki, K. and P.G. Richards (1980). ``Quantitative Seismology Theory and Methods,'' Vol. I, W. H. Freeman, San Francisco, 557 pp.
859 Anderson, D.L. (1963). Recent evidence concerning the structure and composition of the Earth's mantle. Phys. Chem. Earth 6, 1±129. Burbach, G.V. and C. Frohlich (1986). Intermediate and deep seismicity and lateral structure of subducted lithosphere in the circumPaci®c region. Rev. Geophys. Space Phys. 24, 833±874. Dahm, C.G. (1934). A study of dilatational wave velocity in the Earth as a function of depth, based on a comparison of the P, P 0 , and PcP phases. Ph.D. dissertation, St. Louis University, St. Louis, MO. Dziewonski, A.M. and D.L. Anderson (1981). Preliminary reference Earth model. Phys. Earth Planet. Inter. 25, 297±356. Ewing, W.M., W.S. Jardetzky, and F. Press (1957). ``Elastic Waves in Layered Media,'' McGraw-Hill Book, Company, New York, 380 pp. Garnero, E.J. (2000). Heterogeneity of the lowermost mantle. Annu. Rev. Earth Planet. Sci. 28, 509±537. Gilbert, F. and A.M. Dziewonski (1975). An application of normal mode theory to the retrieval of structural parameters and source mechanisms from seismic spectra, Philos. Trans. R. Soc. London, Ser. A 278, 187±269. Gurnis, M., M.E. Wysession, K. Knittle, and B.A. Buffett (Eds) (1998). ``The Core-Mantle Boundary Region,'' American Geophysical Union, Washington, DC, 334 pp. Gutenberg, B. (1959). ``Physics of the Earth's Interior,'' Academic Press, New York. Herrin, E. (1968). Introduction to ``1968 Seismological Tables for P-phases,'' Bull. Seismol. Soc. Am. 58, 1193±1195. Isacks, B. and P. Molnar (1971). Distribution of stresses in the descending lithosphere from a global survey of focal mechanism solutions of mantle earthquakes Rev. Geophys. Space Phys. 9, 103±174. Jacobs, J.A. (1987). ``The Earth's Core,'' Academic Press, San Diego, 413 pp. Jeffreys, H. and K.E. Bullen (1940). ``Seismological Tables,'' British Association for the Advancement of science London 50 pp. Kanamori, H. and D.L. Anderson (1977). Importance of physical dispersion in surface-wave and free oscillation problems, Review, Rev. Geophys. Space Phys. 15, 105±112. Kennett, B.L.N. and E.R. Engdahl (1991). Travel times for global earthquake location and phase identi®cation, Geophys. J. Int. 105, 429±465. Kirby, S.H., S. Stein, E.A. Okal, and D.C. Rubie (1996). Metastable mantle phase transformations and deep earthquakes in subducting oceanic lithosphere. Rev. Geophys. Space Phys. 34, 261±306. Lay, T. (1996). ``Structure and Fate of Subducting Slabs,'' Academic Press, San Diego, 185 pp. Lay, T. and T.C. Wallace (1995). ``Modern Global Seismology,'' Academic Press, San Diego, 521 pp. Lithow-Bertelloni, C. and M.A. Richards (1998). The dynamics of Cenozoic and Mesozoic plate motions. Rev. Geophys. Space Phys. 36, 27±78. Loper, D.E. and T. Lay (1995). The core±mantle boundary region. J. Geophys. Res. 100, 6397±6420. Nolet, G. (Ed.) (1987). ``Seismic Tomography with Applications in Global Seismology and Exploration Geophysics,'' D. Reidel, Dordrecht, 386 pp. Ringwood, A.E. (1975). ``Composition and Petrology of the Earth's Mantle,'' McGraw-Hill, New York, 618 pp.
860 Ritzwoller, M.H. and E.M. Lavely (1995). 3D seismic models of the Earth's mantle. Rev. Geophys. Space Phys. 33, 1±66. Romanowicz, B. (1991). Seismic tomography of the Earth's mantle. Annu. Rev. Earth Planet. Sci. 19, 77±99. Savage, M.K. (1999). Seismic anisotropy and mantle deformation: What have we learned from shear wave splitting? Rev. Geophys. Space Phys. 37, 65±106. Silver, P.G. (1996). Seismic anisotropy beneath the continents: Probing the depths of geology. Annu. Rev. Earth Planet. Sci. 24, 385±432. Silver, P., R.W. Carlson, and P. Olson (1988). Deep slabs, geochemical heterogeneity and the large-scale structure of mantle convection: investigation of an enduring paradox Annu. Rev. Earth Planet. Sci. 16, 477±541.
Lay Song, X. (1997). Anisotropy of the Earth's inner core Rev. Geophys. Space Phys. 35, 297±313. Thurber, C.H. and K. Aki (1987). 3D seismic imaging. Annu. Rev. Earth Planet. Sci. 15, 115±139.
Editor's Note A list of complete references cited in this Chapter is given on the attached Handbook CD, under directory \ 51Lay. See also the next ®ve chapters.
