Sep 10, 2000 - Margin (SIGMA), was conducted along the southeast Greenland margin jointly ... element, 8460 cubic inch air gun array fired every-50 m (20 s).
JOURNAL OF GEOPHYSICAL
RESEARCH, VOL. 105, NO. B9, PAGES 21,591-21,614, SEPTEMBER 10, 2000
Crustal structure of the southeastGreenland margin from joint refraction and reflection seismictomography J.Korenaga, •'2W. S.Holbrook, 3G. M. Kent,4P.B. Kelemen, 2R. S.Detrick 2, H.-C.Larsen, sJ.R. Hopper, sandT. Dahl-Jensen s Abstract. We presentresultsfrom a combinedmultichannelseismicreflection(MCS) andwideangleonshore/offshore seismicexperimentconductedin 1996 acrossthe southeast Greenland continentalmargin.A new seismictomographicmethodis developedto jointly invertrefraction andreflectiontravel timesfor a two-dimensional velocitystructure.We employa hybridraytracingschemebasedon the graphmethodandthe localray-bendingrefinementto efficiently obtainan accurateforwardsolution,andwe employsmoothingandoptionaldampingconstraints to regularizean iterativeinversion.We invert 2318 Pg and 2078 PmP travel timesto constructa compressional velocitymodelfor the 350-km-longtransect,anda long-wavelengthstructurewith stronglateralheterogeneityis recovered,including(1) -30-km-thick, undeformedcontinental crustwith a velocityof 6.0 to 7.0 km/s nearthe landwardend, (2) 30- to 15-km-thickigneous crustwithin a 150-km-wide continent-oceantransitionzone, and (3) 15- to 9-km-thick oceanic crusttowardthe seawardend.The thicknessof the igneousuppercrustcharacterized by a highvelocitygradientalsovariesfrom 6 km withinthetransitionzoneto -3 km seaward.The bottom half of the lower crustgenerallyhasa velocityhigherthan7.0 km/s,reachinga maximumof 7.2 to 7.5 km/s at the Moho. A nonlinearMonte Carlo uncertaintyanalysisis performedto estimate the a posteriorimodelvariance,showingthatmostvelocityanddepthnodesarewell determined with onestandarddeviationof 0.05-0.10 km/s and0.25-1.5 km, respectively.Despitesignificant variationin crustalthickness,the meanvelocityof the igneouscrust,which servesas a proxyfor the bulk crustalcomposition, is surprisingly constant(-7.0 km/s)alongthe transect.On the basis of a mantlemeltingmodelincorporating the effectof activemantleupwelling,thisvelocitythicknessrelationshipis usedto constrainthe mantlemeltingprocessduringthe breakupof GreenlandandEurope.Our resultis consistentwith a nearlyconstantmantlepotential temperatureof 1270-1340øCthroughouttherifting but with a rapidtransitionin the styleof mantleupwelling,from vigorousactiveupwellingduringthe initial rifting phaseto passive upwellingin the later phase. 1. Introduction
Rifted continental margins are often associated with voluminousigneousactivity as inferred from seawarddipping Igneous crust emplaced at a rifted continentalmargin is the reflectors(SDRs), which were proposedto originatein subaerial integratedproductof the melting of an upwellingmantleduring eruptions[Hinz, 1981;Mutter et al., 1982],aslaterconfirmedby continentalbreakup.Its thicknessis often taken as a goodproxy deep-seadrilling [Robertset al., 1984; Eldholm et al., 1989; for the total melt volume producedupon rifting, whereasits Larsen et al., 1994]. Deep seismicstudieshave revealedthick seismicvelocityreflectsthe originalmelt composition [e.g., sequences of maficigneouscrustbelowSDRson severalmargins White and McKenzie, 1989; Kelemen and Holbrook, 1995]. [e.g., White et al., 1987; Mutter et al., 1988;Holbrook and Becausethe mantle melting processis highly sensitiveto the Kelemen, 1993]; the thicknessof suchigneouscrust can be as temperature and composition of the mantle as well as its muchas severaltimesthat of normaloceaniccrust,indicating upwelling rate [e.g., McKenzie and Bickle, 1988; Kinzler and someunusualconditionin mantlemelting, suchas higher-thanGrove, 1992; Langmuir et al., 1992], the crustalseismicstructure normalpotentialtemperature and/orrapidmantleupwelling.The of a rifted margin is one of the primary sourcesof information southeastGreenland margin, which was formed during the regardingmantledynamicsin therifting period. opening of the North Atlantic around 60 Ma [Srivastavaand Tapscott,1986], is one of thesevolcanicrifted margins;SDRs have beenmappedover2000 km alongthe entiremargin[Larsen 1Department of Earth, Atmospheric,and PlanetarySciences, andJakobsd6ttir,1988],andthecrustalstructure of theconjugate Massachusetts Instituteof Technology,Cambridge. 2Department of Geology andGeophysics, Woods HoleOceanographicmargin [White et al., 1987; Mutter and Zehnder, 1988; Barton Institution, Woods Hole, Massachusetts. and White, 1997a] suggeststhe existenceof similarly thick 3Department of GeologyandGeophysics, University of Wyoming, igneouscrustbeneaththe SDRs.Becauseof its proximityto the Laramie,Wyoming. 4Institute of Geophysics andPlanetary Physics, Scripps Institution of Icelandhotspot,it hasbeenproposedthat a mantleplumeplayed Oceanography,SanDiego, California. a major role in the formation of this volcanic margin [e.g., 5Danish Lithosphere Centre, Copenhagen, Denmark. Richards et al., 1989; White and McKenzie, 1989; Hill et al., 1992; Coffin and Eldholm, 1994; Barton and White, 1997a], but Copyright2000 by AmericanGeophysical Union. Papernumber2000JB900188. 0148-0227/00/2000JB 900188 $09.00
the paucity of high-qualityseismicdata in this region has preventeda full understanding of the influenceof a mantleplume on continentalrifting magmatism. 21,591
21,592
KORENAGA ET AL.: REFRACTION AND REFLECTION TOMOGRAPHY
70øN
•OøN Greenland
60øN
60øN
Figure1. Locationof the 1996 SIGMA seismicexperiment. Circlesdenotelocationof onshoreandoffshore seismicinstruments. (a) Bathymetrywith 500-m contourinterval.(b) Magneticanomalywith positiveanomaly shaded.
To investigatethe influence of the Iceland hotspot on the opening of the North Atlantic, an extensive deep seismic experiment, the 1996 Seismic Investigation of the Greenland Margin (SIGMA), was conductedalong the southeastGreenland margin jointly by Woods Hole Oceanographic Institution (WHOI) and the Danish LithosphereCentre. Four transectswere located at latitudes of approximately68øN, 66øN, 63øN, and 59øN to systematicallysample the structureof the margin at increasing distance from the Greenland-Iceland Ridge, the presumedIceland hotspottrack (Figure 1). This paperfocuseson results from transect 2, whose data comprise -300 km of multichannel seismic reflection data and coincidentwide-angle
alwaysa seriousconcernfor reflectiontomography, andwe show a simple and practicalway to investigatethe ambiguityusing depthkernelweighting.The uncertaintyof a velocitymodelis alsoestimated by a nonlinearMonteCarloapproach. The crustal structure of the volcanic continental margin, which exhibits
stronglateralheterogeneity bothin velocityandcrustalthickness, is shownto be fully resolvedwith high modelfidelity, and we discuss its geologicalandgeophysical implications.
2. Data Acquisition and Processing
The seismicdata on transect2 of the SIGMA experimentwere acquired in September 1996 aboard R/V Maurice Ewing. eightonshoreSeismometers, coveringfromthe Greenland coast Multichannelseismic(MCS) profilingwas conductedusinga 20throughthe continentalshelf to the deep-wateroceanbasin at element,8460 cubicinch air gun array fired every-50 m (20 s) magnetic anomaly chron 19. Unlike the two transectsto the and a 4.0-km hydrophonestreamerwith 160 channels.Widesouth,linear marine magneticanomaliesare not observedon the angle data were recorded on 10 WHOI ocean bottom northwestern part of transect 2 (Figure lb), suggesting a hydrophones(OBH), eight U.S. Geological Survey (USGS) significant deviation from normal seafloor spreading.Owing to ocean bottom seismometers(OBS), and eight on-land seismic its proximity to the hotspot track, the extent of rifting-to- recordersfrom the Programfor the Array SeismicStudiesof the spreadingmagmatismon this transectis critical to assessthe Continental Lithosphere (PASSCAL), deployed along the transect(Figure2). We will hereafterrefer to model distance possibleeffectsof a mantleplume. from a pointlocated-5 km In this paper, we develop a joint refraction and reflection alongthe transect,whichis measured tomographicmethodto invert wide-angletravel time data for a northwest of the most landward seismometer, ST 9. The total compressional velocity field. The forward travel time calculation model distance of transect 2 is 350 km. takes a hybrid approach;a graph-theoreticalmethodis used to ensurea global optimization,followedby ray-bendingrefinement 2.1. Multichannel Seismic Data to achievethe desiredaccuracy.The inversionwith a fine model Shot gatherswere recordedat a samplingintervalof 4 ms. parameterizationis regularized by smoothnessconstraintson both velocity and reflector nodes.Velocity-depth ambiguity is Streamer group spacing was 25 m, which gives a common
refraction
and reflection
data recorded on 17 ocean bottom and
KORENAGA
ET AL.: REFRACTION
66øN
65øN
64øN
36øW
34øW
32øW
30øW
Figure 2. Configurationof transect2 seismicexperiment.Circles and triangles denote ocean bottom instruments and onshore seismicrecorders,respectively.Bathymetrycontoursare drawn at 500-m interval.
AND REFLECTION
TOMOGRAPHY
21,593
becauseof a differential move-out betweenprimary reflections andwater multiples. To correctly relocate reflectors in the depth section and collapse diffraction hyperbolae due to rough reflector topography,poststackdepthmigrationwas performedusingthe split-stepmigrationalgorithm[Stoffaet al., 1990]. The velocity model based on the wide-angle data was used again for the crustal section in the migration. Except for several migration artifactsoriginatingin missingdata spotson the landwardside, the overall quality of the migrated image is good, clearly depictingthe sedimentarylayers,the basementtopography,and the intrabasement SDR sequence(Figure3). Sedimentarylayers start to appear at km 113 and gradually thicken seaward, reaching a maximum thicknessof-1.5 km aroundthe shelf break. The deep-wateroceanbasin is covered with Seaw•d D1 in Reflectors ":,..•;..•'S
90
100
0 1••.....•• ••....•. .......
110
a8
. ...4-.'. :i~': '...•....,....
'•.'•.•.
120
130
a4
140
150
160
170
180
190
200
210
220
310
320
330
340
350
17
..•..•.'..i
.,;, ..:,•.,',,, .... '.....;.;• •'?..•.. ... ß..•h,,,.• •, •'•'-"" - '•'•'•'• Seaward Dipping Reflectors,. :,v..:t,'. ',:,,,,. '•,• ':•:&" g•;'.'. 190
200
210
220
230
240
250
260
2?0
280
290
300
Model Distance [km] Figure 3. Depth-migratedsectionof multichannelseismicreflectionprofile. Coherencefiltering, automaticgain correction,and trace normalizationwere applied.Locationsof oceanbottominstrumentsare also shownby solid circles.
The refractionphasethroughthe crystallinecrust,Pg, is observedon all the instruments. The patternof the Pg arrival variessignificantlyfromdeep-water instruments to shallow-water and on-landinstruments, indicatinga stronglateralvariationin the crustalstructure alongthe transect. The maximumrangeof thePg arrivalsincreases from-70 km in deepwaterto -150 km alongtheinnercontinental shelf,indicating landward thickening of the high-velocity gradient upper crust. The near-offset asymmetryobservedin Pg arrivals on OBH 20 (Figure4g) suggests a sharptransition in theshallowuppercrustalvelocityat km-80 becauseof the nearly flat basementand absenceof sediment coveraroundthe instrument. The apparent velocityof
small to confidentlyresolvecausativegeologicalstructure.Being a later arrival, the PmP phasetendsto be obscuredby sourcegeneratednoise,and it is alsosometimesdifficult to distinguishit from midcrustal reflections and their multiples. The selfconsistentidentificationof the PmP phasewas made possibleby confirming reciprocity among a number of different sourcereceiver pairs. For the on-land stations,however, reciprocity cannotbe confirmed owing to the lack of land sources,and we reliedon the phasecorrelationamongthe closelylocatedstations. Refractionand reflectiontravel times were pickedmanually,and we assigneda picking error of half a periodof the first cycle of an arrival, varied from 50 to 100 ms, to each pickedtravel time. first arrivals rarely exceeds7.0 km/s, so we do not have clear Note that this criterion of assigninga picking error resultedin observation of refraction phasethroughtheshallowuppermantle, generally smaller data uncertainty than that used by W. S. Pn, in this seismicexperiment.The absenceof Pn phaseis Holbrook et al. (Mantle thermal structureand melting processes commonin volcanicrifted margins[e.g.,Holbrooket al., 1994a, during continental breakup in the North Atlantic, submittedto 1994b], and this may be becauseof high lowermostcrustal Earth and PlanetaryScienceLetters,2000, hereinafterreferredto velocitieswith possiblecumulatesincreasing downward,which as Holbrooket al., submittedmanuscript,2000). The new picking causes a broadtransition in P wavevelocityintothemantle. errorsare usedin this studybecausewe realizedthat the previous
The reflectionphasefromthecrust-mantle boundary, PmP,is estimate was less consistent and often too conservative. observedon mostof the instruments with variablequality.The smallestoffsetwherePmP arrivalscan be recognizedranges 3. Joint Refraction and Reflection Tomography from -20 km in the deep ocean basin to 60-80 km on the continental shelf, and most of the PmP arrivals can be traced to
mergewith the Pg arrivals.Severalminor midcrustalreflections
arealsoobserved on someinstruments, butwe do notattemptto modelthembecause thenumberof suchobservations appears too
3.1. Model
Parameterization
A two-dimensional velocity model is parameterizedas a shearedmesh hanging beneath the seafloor and land surface
KORENAGA
ET AL.: REFRACTION
[Toomey et al., 1994; Van Avendonk et al., 1998]. Bilinear interpolationis used in each parallelogram-shaped grid cell, so the velocity field is continuouseverywhere.Nodal spacingcan be variable both in the horizontal and the vertical directions, and it
shouldbe much finer than expectedvelocity variationsto avoid any bias introducedby a coarseparameterization.A fine mesh is alsoimportantto obtainaccurategraphtheoreticalsolutions.The sheared mesh representation allows accurate travel time calculationin the presenceof large topographicvariations,with much smaller computationalresourcesthan a rectangulargrid used in some previous tomographicstudies [e.g., White and Clowes,1990; Zhang and Toks6z,1998]. A reflector is representedas an array of linear segments, whosenodal spacingis independentof that usedin the velocity grid. The horizontalcoordinateof reflectornodesis fixed so that each node has only one degree of freedom in the vertical direction. Currently, only one reflector is supported in our method, which we used to model the PmP phase.Although the
(a)
300
5
,
TOMOGRAPHY
21,595
velocity discontinuity at the Moho is fundamental for the generationof the PmP phase, we do not explicitly treat this discontinuityin our modeling. Instead, we choseto employ a floating reflectorformulationso that a reflectordepthis updated freely withoutchangingadjacentvelocitynodes. 3.2. Forward
Problem
The accurateand efficient calculationof travel timesand ray paths is essential in seismic tomography. With a sampling interval of 10 ms and an averagespacingof a few hundredmeters in a velocity grid, our targetaccuracyis 1 ms in travel timesand 100 m in ray path positions.We employ a hybrid methodbased on the graphmethodand the ray-bendingmethod,similar to the one developed by Papazachos and Nolet [1997] and Van Avendonket al. [1998], becauseit is probably most efficient in termsof both memory and computationtime. The graphmethod, also known as the shortest path method, was developed in
(b)
Distance [km] 250
AND REFLECTION
Distance [km] 200
350
250
31
5
,q
,E'
5
5
• o lO
•
30
'
0
100
200
Distance [km]
• o 1OBH2411 12130
300
'
0
I
100
"
IOBH191
,
' ' ,
200
300
Distance [km]
Figure 4. Examplesof wide-angleseismicdataare plottedafter rangegain correction,with picked(solidcircle with pick error)andpredicted(opencircle)traveltimesfor Pg andPmP phases.Synthetictraveltimesarebasedon the velocitymodelpresented in Plate3a, andcorresponding ray pathsare alsoplottedat the bottom.(a) OBH 24, (b) OBH 19, (c) OBS A4, (d) OBS C4, (e) OBS C3, (f) OBH 25, (g) OBH 20, (h) ST 18, and (i) ST 15. The 70-s shotdata are shownfor most of the deep-waterand on-landinstruments. For the USGS OBS data we showthe hydrophone component, whichhasbetterqualitythanthegeophone components. Completedataplottingis given by Korenaga[2000].
21,596
KORENAGA ET AL.' REFRACTION AND REFLECTION TOMOGRAPHY
[urn]qldoo
[s] O'œ/x-om!&
[s] O'œ/x-omkL
[up4]qldo(I
[s] 0'œ/x-omkL
[s] 0'œ/x-omkL
KORENAGA ET AL.: REFRACTION AND REFLECTION TOMOGRAPHY
[ur•] •t•do(I [s] 0'L/X-O•!•L
[s] 0'L/X-O•!•L
[uP4]qldo(I [s] 0'L/X-O•!•
[s] 0'L/X-Om!•L
21,597
21,598
KORENAGA ET AL.: REFRACTION AND REFLECTION TOMOGRAPHY
(h)
(g)
Distance [km]
Distance [km]
1•0
•o
200
_
,
150
J
.
:•I,.,•'.' :•fl•,,.
,., ',,I,,: '•.'•,,
, , ,
...,.,,•[]q•doo
KORENAGA ET AL.: REFRACTION
foundin otherseismictransects on NorthAtlanticmargins[White et al., 1987;Mutter and Zehnder,1988], which are higherthan 7.2 krn/sfor mostof the lower crust.The thickness of the upper crustreducesto -3 km for the oceaniccrust.Thoughthis part of the crust is thinnest along the transect,it is still thicker than
AND REFLECTION TOMOGRAPHY
21,605
inversions[e.g., Zhang and Toksiiz,1998], we conducttwo types of analyses:(1) resolution tests using syntheticdata and (2) a nonlinear Monte Carlo uncertainty analysis. In the resolution testswe calculate syntheticdata for a perturbedvelocity model with the same sources and receivers as in the actual observation,
normal oceanic crust with 6 to 7 km thickness [White et al.,
add random noise of 100 ms to the synthetic data, and invert them with an initial unperturbedmodel to see how well given perturbationsare recovered.Thoughnot comprehensive, this is a observed near the Moho from km 260 to 300. succinctand computationallyinexpensiveway to demonstratethe To examine the sensitivityto startingmodels,we conducted resolving power of the available ray coverage. In the first anotherset of inversionswith a different startingmodel. The resolutiontest we perturbedvelocity nodeswith 5% positive and secondstartingmodelwasconstructed by hanginga 1-D average negative anomalies of a 140-km wavelength aligned in the crustal velocity profile calculated from Plate l a beneath the midcrust (Figure 10a). Good recovery was obtained for the basement,and the initial Moho was set flat at 25 km deep seaward half of the model (Figure 10b). Despite a significant (Plate 2a). The initial RMS travel time misfit exceeded 800 ms deteriorationtoward the landwardend, the resultsuggeststhat the withZ2 of 136.1,butoutlierswithnormalized residuals >5 after ray coverageof our data is sufficientto resolvethe continentthe first iterationare only 2.3% of all data,indicatinga minorrole oceanboundaryaroundkm 100. The recoveredanomaliestend to of outlier removal. Damping was applied to retain average be laterally stretched,resultingfrom our conservativechoiceof slowness and depth perturbations below 3% and 9%, the horizontal correlationlength. In the secondresolutiontest, respectively.After the first two iterations,dampingwasno longer only the reflectornodeswere perturbedwith a 1.5-km amplitude required, and all the travel time residualswere within the cutoff and a 100-km wavelength(Figure 10c). The perturbedMoho was threshold. After 10 iterations the RMS travel time misfit reduced well recoveredfor km 50 to 100 and km 150 to 330. The parts to 78 mswithZ2of 1.01(Plate2b).Thoughthedetailsdiffer,the that were not recoveredcorrectly,suchas km 100 to 150 and near main key structural features observed in Plate lb remain the the model ends, are indeed poorly sampledby PmP (Figure 9). same. These features include the overall variation in crustal The unrecovered reflector perturbations leak into velocity thickness, the thickeningof the high-velocity-gradient uppercrust perturbationsabove the reflector, but their amplitude is only from the seaward end to the continental shelf, and its sudden -0.5%, being consistent with the negligible velocity-depth thinningnear the coastline. The crustalvelocity structurefrom ambiguityindicatedin Figure 8. km 170 to 330, includingthe small-scalehigh-velocityanomaly The uncertaintyof the seismicvelocity is fundamentalfor the in the lower crust around km 280, is almost identical between the reliableinterpretationof crustalcomposition.The only practical two models,indicatingthat this part of the modelis well resolved way to estimatethe model uncertaintyfor a large-scale,nonlinear and virtually independentof startingmodels.An increasein the inversion such as our tomographyis the Monte Carlo method lower crustal velocity at km 100 to 150 is also found in the [e.g., Tarantola and Valette, 1982; Tarantola, 1987]. By secondmodel,thoughits overallvelocityis lower.A majorityof invertingdatawith randomerrorswith randominitial models,we can construct a number of Monte Carlo realizations, with which the continentalcrust seemsto require an averagevelocity of -6.5 km/s with an almostlinear velocity gradient,as found in the a posteriorimodelcovariancematrix is estimatedas
1992]. Its velocity is still higherthan7.0 krn/sin the bottomhalf of the lower crust, and a prominenthigh-velocityanomalyis
both models. These close similarities between the two models
satisfactorilydemonstrate the robustness of the resolvedvelocity
½=I[p- E(p)]. [p-E(p)]Tap(p)dp, (10)
structure.
To investigatethe degreeof velocity-depthambiguityin our inversion,we repeatedthe inversionwith the startingmodelof Plate l a, using two different values,0.01 and 100, for depth kernel weighting.The inversionsolutionsafter 10 iterationsare shownin Figure8 alongwith the solutionfor equalweighting. The travel time misfits for the three models are very similar. Sincethereis no major differencefoundamongthesemodels,we conclude that our inversion solution does not suffer from serious
velocity-depth ambiguity, given the relatively wide spatial correlationthat we employedin the smoothingconstraints. We will thusemploythe equalweightingof the velocityanddepth kernelsin all the followinginversions. 4.2. Resolutionand Accuracy
where p is the solutionvectorof the realizations,E(p) is the a
posteriori expectation of p, and C•p(p)is the a posteriori marginal density function [Tarantola and Valette, 1982]. By assumingthat all N realizations have the same probability, we may approximatethe abovedefinitionas [Matarese,1993]
---• [pi-E(p)]-[pi - E(p)] T,
(11)
.__
where Pi is the solutionof the ith realization.Zhangand Toks6z [1998] noted that modeling data errors with Gaussianerrorsfor absolutetravel timesis unrealisticin light of the natureof travel time picking, and they suggestedusing commonshoterrors(or commonreceiver errors in the caseof marine experiments)and travel time gradienterrors.We thusrandomizeddata by adding the following two error componentsto the originaldata:random common receiver errors with a maximum amplitude of 50 ms,
The ray coverage in themodelcanbe concisely represented by the derivativeweightsum(DWS) [Toomeyand Foulger,1989], whichis the column-sum vectorof the Fr6chetvelocitykernel. and random travel time errors with the same maximum The DWS for our velocitymodelis shownin Figure9, asa crude amplitude.The small-amplitudetravel time errorshave virtually measureof the linear sensitivityin our inversion.The lower crust at km 30 to 130 is sparsely coveredby reflections alone,implying lowerresolutionthantheotherpartsof themodel. Because the DWS does not provide any quantitative informationregardingthe resolutionand accuracyof the model and because nonlinear sensitivity is important for iterative
the same function as the travel time gradient errors used by Zhang and Toksiiz[ 1998]. The highly correlatednatureof travel time pick errors can be taken into account by this data randomization.Random initial velocity modelswere preparedby hanging random 1-D crustal velocity profiles beneath the basement. A two-layer crustal model was used to generate
21,606
KORENAGA
ET AL.: REFRACTION
AND REFLECTION
TOMOGRAPHY
(a) w=0.01
10
•
15
• •
20 25
•
30 0
50
100
150
200
250
300
350
50
100
150
200
250
300
350
(b) w=l
lO 15 20 25 30
0
(c) w= 100
_•• .......................................... •ir'"-"•.--:.--'-----'• -•- '........... .... •--•• .l::: 15 '• o
20 25
•
30 0
50
•00
•50
200
250
300
350
Distance [km]
1.50
4.50
6.75
7.00
7.25
7.50
Velocity [km/s] Figure8. Testof velocity-depth ambiguity usingdifferentweighting of thedepthkernel.Initialmodelis shownin Platel a and 10 iterationswereapplied.(a) w=0.01,(b) w=l (sameas Platelb), and(c) w=100. RMS traveltime misfitsare78, 77, and77 ms,respectively.
..
5 ...
===================== ..... :::.::: .... .::::•.: .. %:..:::•.....:•:i:•...:::.::::!•.•:•......•ii•:...::::s::•:..:•i•iid:.•::•.i......:•!: ..
•i?•?•i'•iii •=•.?.':i..".:;!Si ....... •!•::•!ii:ii{,:i"-:.:;:::::•:---:--'i::;i•:•.: ":'---::.:7....•11•iiO'.':'•-'-=':-•--'•}i-17{•:•i•i•i:i:':'7 '-:.. ' '............. :•:i• .
•
......... '::"5•i:i'..::-' '"::":':•:-: '"
25 30 50
100
150
200
250
300
350
Distance [km]
lO
:' I
i
50
300
Derivative Weight Sum Figure 9. Derivativeweightsumin thecaseof thesolutionshownin Platelb.
KORENAGA
ET AL.: REFRACTION
AND REFLECTION
TOMOGRAPHY
21,607
(a) Model A: Input 0
.--
1
•-•
15
•
20
•
25
•
30 0
50
100
150
200
250
300
350
(b) Model A: Recovery(after 4 iterations)
L•1 •
20
•
30
•
2':::%•" ....... ............ fi/'"•"'"%•"••••'•'••••'•••••• :::::::::::::::::::::::: .......... ,:::•,•:.::•, •,•,,:•,,•2•m ,•-:•, ...
35
, , , 0
• .... 50
• .... 100
• .... 150
• ....
• ....
• .... 200
• .... 250
300
350
(c) Model B: Input 0
•
15
o 25 !i
:..,--•;½.
½h 30 35
.... 0
• .... 50
1O0
150
• .... 200
• .... 250
I .... 300
350
(d) Model B: Recovery(after 4 iterations)
• o
•
........... "'•-•--•-----'-*••i:'* "''-'-*'-"--4• a.......
.--::.----,,,. ,• ---.•.
25
30 •*'"'•'"""':•::' '"'•'":'•••:'•"'"" ........ 35
.... 0
• ....
i ....
• ....
50
i .... 200
• .... 250
i .... 300
350
Distance [km]
Velocity Perturbation[%] Figure 10. Resolutiontests.Referencevelocity model is the sameas in Plate l a. We use the samesourceand receiverlocationsfor synthetictravel time calculation,and randomnoiseof 100 ms was addedto syntheticdata prior to inversion.(a) True model perturbationconsistingfive alternating5% velocity anomalies.(b) Recovery obtainedafter four iterations.Almost no changeis observedfor reflector depths.(c) Model reflector (solid) constructed by adding1.5-kmperturbation with 100-kmwavelengthto the referencereflector(dashed).(d) Starting from the referencereflector,goodrecoveryobtainedfor mostpartswith smallleakinginto velocityperturbations.
random 1-D profiles; there are five controllingparameterssuch as top, midcrustal, and bottom velocities and upper and lower crustalthicknesses,and their possiblevariationswere chosenso to cover a wide rangeof 1-D crustalvelocity profiles(Figure 11). The RMS amplitude of this initial velocity randomizationwith respectto a typical Monte Carlo ensemble(e.g., Plate 2b) is -5%. Initial reflector depthswere uniform and randomly set between 20 and 30 km, independentlywith initial crustalvelocityprofiles.
normalized Z 2 to-1.0. Using100realizations, the final crustal
With this degreeof modelperturbations, normalizedZ 2 was
Using the Monte Carlo ensembles, one can estimate the uncertaintyof an averagedquantity by applying the averaging operation to each ensemble and then calculating the variance
generally higher than 100, with an RMS travel time misfit >800 ms. On average, 10 iterations were required to reduce
velocity model as well as the a posteriorimodel variancewere calculated(Plate 3). The standarddeviationof the velocity nodes is lowest (