JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117, B11208, doi:10.1029/2012JB009469, 2012
Understanding volcano hydrothermal unrest from geodetic observations: Insights from numerical modeling and application to White Island volcano, New Zealand Nicolas Fournier1 and Lauriane Chardot1,2,3 Received 19 May 2012; revised 26 August 2012; accepted 3 October 2012; published 17 November 2012.
[1] In this work we assess how volcano geodetic observations can be used to gain insights into hydrothermal system dynamics. We designed a range of numerical models of hydrothermal unrest and associated ground deformation caused by the thermo–poro–elastic response of the substratum. Throughout an episode of unrest, ground deformation is consistently first controlled by the poroelastic response of the substratum to pore pressure increase near the injection area. Later, thermal expansion may become the dominant process if the injection is sustained. We inverted these synthetic geodetic data using simple conventional pressure source models and compared the retrieved source characteristics with that of the synthetic hydrothermal systems. Simple pressure source models can reproduce well ground deformation caused by pore–pressure increase at depth. Most importantly, the pressure source’s depth retrieved from the inversions corresponds to those of the area of injection of the hot magmatic fluids into the hydrothermal system. When the thermoelastic contribution to ground deformation becomes significant through time, simple point or spherical finite sources cannot reproduce the ground deformation signal. This allows one to determine whether observed ground deformation events due to hydrothermal unrest are distinct episodes of unrest and injection at depth, or whether one may correspond to the late, thermally-controlled phase of a previous event. Finally we applied this strategy to White Island volcano, New Zealand, to gain insights into the processes driving the last two episodes of ground uplift. Citation: Fournier, N., and L. Chardot (2012), Understanding volcano hydrothermal unrest from geodetic observations: Insights from numerical modeling and application to White Island volcano, New Zealand, J. Geophys. Res., 117, B11208, doi:10.1029/2012JB009469.
1. Introduction [2] Measuring volcano ground surface deformation is one of the major techniques used in volcano monitoring [Dzurisin, 2003; Vasco et al., 1988]. The inversion of the geodetic data generally yields fundamental insights into the location, size and overpressure of the pressure source responsible for the observed ground deformation. This is particularly true when the source of deformation is thought to be magmatic in origin, whether it is a substantial magma reservoir [Battaglia and Vasco, 2006; Chang et al., 2010] or part of the feeding system (e.g., dyke or sill) [Bonaccorso and Davis, 1999; Fukushima et al., 2005; Marchetti et al., 2009]. In many cases, 1
GNS Science, Wairakei Research Centre, Taupo, New Zealand. EOST, Université de Strasbourg, Strasbourg, France. 3 Now at Department of Geological Sciences, University of Canterbury, Christchurch, New Zealand. 2
Corresponding author: Nicolas Fournier, GNS Science, Wairakei Research Centre, Private Bag 2000, Taupo 3352, New Zealand. (
[email protected]) Published in 2012 by the American Geophysical Union.
however, the observed ground deformation is suspected to be driven by hydrothermal system processes [Battaglia et al., 2006; Bonaccorso et al., 2010; D’Auria et al., 2011; Gambino and Guglielmino, 2008; Gottsmann et al., 2006; Mossop and Segall, 1999; Rinaldi et al., 2010, 2011; Todesco, 2009; Todesco et al., 2004]. Although the underlying processes differ drastically between magmatic and hydrothermal processes, the types of models employed for the inversions are often similar: point source analytical formulations [Bonaccorso and Davis, 1999; Fialko et al., 2001; McTigue, 1987; Mogi, 1958; Okada, 1985] or more sophisticated finite numerical models of ground deformation [Battaglia and Vasco, 2006; Cayol and Cornet, 1997; Fukushima et al., 2005; Peltier et al., 2009a]. Modeled sources generally represent a pressurized cavity of varying shape, size and location, generally embedded in an elastic medium, or more rarely in an elasto–plastic or visco– elastic medium [Bonafede and Ferrari, 2009]. Approximating a magmatic source to a pressurized cavity or a tensional crack is sensible and the source characteristics retrieved from the inversion correspond to physical tangibles (e.g., volume of magma entering the reservoir). However, what do these inversion results represent when hydrothermal processes are
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Figure 1. (left) Conceptual diagram (not to scale) of magmatic–hydrothermal interactions (e.g., fluid migration) and resulting ground deformation due to hydrothermal unrest. (right) Geophysical observables (e.g., ground deformation) in this case and the information derived from their inversion (e.g., location, size and overpressure of a simplified pressure–source). responsible for ground deformation (Figure 1)? Ground surface deformation caused by hydrothermal activity is driven by processes involving the poroelastic and thermal response of a permeable medium to hydrothermal fluid flow. To what degree can conventional cavity–type numerical models then be used to constrain the source parameters when hydrothermal system dynamics control ground deformation? And more importantly, what useful information can be retrieved when inverting hydrothermally-driven geodetic signals with these widely-used techniques? [3] Ideally, to answer these questions, one could use well– constrained hydrothermal systems producing ground deformation and compare the geodetic inversion results with these known characteristics. In reality, though, our understanding of volcano hydrothermal systems (e.g., reasonably accurate dimensions, pressure and temperature distribution through time) is generally – if not always – poorly -constrained. It then becomes extremely difficult to assess whether the pressure source characteristics retrieved from the inversion of geodetic observations accurately depict the hydrothermal system dynamics. An alternative consists in simulating hydrothermal system dynamics and associated ground deformation. These synthetic geodetic data can then be inverted for the source characteristics which, in turn, are to be compared with the dimensions, location and characteristics of the simulated hydrothermal system. [4] In this paper, we address these questions by first simulating ground deformation due to hydrothermal systems using multiphase, multicomponent fluid and heat flow models and thermo–poro–elastic models. Secondly, we invert the synthetic deformation signal with simple analytical and numerical models. We then compare the inversion results with the known hydrothermal source characteristics from the synthetic models and discuss what information can be retrieved by inverting hydrothermally-driven ground deformation data with simple, widely-used pressure source models. Finally, we revisit recent observed deformation episodes at White Island volcano, New Zealand, in the light
of this work, and draw some conclusions about how our results can be used in real–life case studies.
2. Method Overview [5] The initial step of this study consists in producing a range of synthetic, hydrothermal system–related ground deformation signal. Hydrothermal system dynamics have been extensively modeled at various volcanoes [Christenson et al., 2010; Hurwitz et al., 2007; Hutnak et al., 2009; Ingebritsen et al., 2010; Rinaldi et al., 2010, 2011; Todesco, 2009; Todesco et al., 2010]. These simulations involve multiphase and multicomponent heat and fluid flow in a permeable medium. We followed the same strategy and designed 4 models of various dimensions and characteristics, using the Integral Finite Differences (IFD) TOUGH2 modeling code [Pruess, 2004]. The output from the TOUGH2 models (pressure and temperature distribution through time) is then input into the thermo–poro–elastic Finite Element Method (FEM) code BIOT2 [Hsieh, 1996] to compute ground displacement through time, as in Hurwitz et al. [2007] and Hutnak et al. [2009]. It must be noted here that the coupling between fluid–flow and thermo– poro–elastic response is one–way (i.e., deformation of the porous/permable medium does not affect fluid flow). Finally, the synthetic ground velocities are inverted for sources parameters using a Neighborhood Algorithm method (N.A.) [Fukushima et al., 2005; Sambridge, 1999a] with both analytical [Mogi, 1958] and finite, numerical [Cayol and Cornet, 1997] formulations. The overall strategy is pictured in Figure 2.
3. Hydrothermal System Modeling [6] Volcanic hydrothermal systems characteristics (e.g., dimensions, fluids properties and dynamics) vary greatly from one volcano to the other. Similarly, hydrothermal unrest episodes can differ drastically in duration and amplitude, depending on the volcano or the studied time period. It is therefore unreasonable to attempt a fit–for–all approach
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approximated as a point source, which is consistent with the injection of magmatic fluids at the base of a hydrothermal system through a fracture, as the source of hydrothermal unrest. [11] 4. The fluids are multicomponent (H2O and CO2) and multiphase (liquid and gas). [12] 5. The fluids are injected at a constant rate throughout the simulation period. [13] The base model (1) is a reproduction of one of the models by Hutnak et al. [2009] and depicts hydrothermal system dynamics for a large caldera system (50 5 km, radius and depth respectively). Because volcanoes and associated hydrothermal systems’ dimensions span across several orders of magnitude (i.e., O(102–104) m), we tested the influence of the size of the modeled system on the simulations results. Model 2 (intermediate, 5 1.7 km) was designed with smaller dimensions and same injection characteristics (i.e., injection rate and temperature). Model 3 (intermediate, 5 1.7 km) has the same dimensions as model 2 but a lower injection rate to test the effect of injection rate on our results. Finally, model 4 (small, 5 0.5 km) has smaller dimensions and lower injection temperature. Dimensions and injection characteristics for the three models are summarized in Table 1.
Figure 2. (top) Flowchart showing the different steps used for simulating hydrothermal models and calculating the deformation that they induce and (bottom) the methods for retrieving each model characteristics from the synthetic surface displacements. with a generic model. All models are thus deliberately kept simple but bear important characteristics common to most known hydrothermal systems. [7] The hydrothermal fluid–flow modeling strategy is based on previous, well–documented work [Christenson et al., 2010; Hurwitz et al., 2007; Hutnak et al., 2009; Rinaldi et al., 2010; Todesco, 2009; Todesco et al., 2010]. Most of these studies emphasize the importance of accounting for the presence of CO2 in the injected fluid, hence the choice of a multicomponent approach (vs. H2O only as in earlier works [Hurwitz et al., 2007]). Parameters common to all our models are summarized below: [8] 1. The models are 2D axi–symmetrical with a flat topography. [9] 2. The modeling domain is homogeneous with isotropic material properties: permeability (1015 m2), porosity (0.1), shear modulus (1 GPa), drained Poisson ratio (0.25), rock grain density (2700 kg m3), thermal conductivity (2.8 W m1 C1) and expansion coefficient (105 C1), and rock grain specific heat (1000 J kg1 C1). [10] 3. Hot fluids are injected at the base and center of the modeling domain. The injection area of hot–fluids is
3.1. Heat and Fluid–Flow [14] Heat and fluid–flow modeling was conducted using the TOUGH2 code [Pruess, 2004] with the EOS2 module. It allows simulations of nonisothermal flows of multicomponent, multiphase fluids in multidimensional porous and fractured media. The reader is directed to Christenson et al. [2010], Hurwitz et al. [2007], Hutnak et al. [2009], Rinaldi et al. [2010], Todesco [2009], and Todesco et al. [2010] and references therein for extensive details of the TOUGH2 modeling for volcanic hydrothermal systems. [15] Boundary conditions are imposed at the ground surface (fixed temperature and pressure of 10 C and 0.1 MPa respectively in our case), outer edge and at the center of the model (symmetry axis). The lower boundary represents the base of the hydrothermal system: it is impermeable, apart from the injection point where fluids are injected into the domain, and has constant basal heat flux (0.1 W m2 in our case). Initial conditions in the domain are hydrostatic pressure and linear vertical thermal gradient between top and bottom boundaries, as in Hurwitz et al. [2007] and Hutnak et al. [2009]. [16] The main output from TOUGH2 used in this study is the spatio–temporal distribution of pore pressure and temperature in the modeling domain. Table 1. TOUGH2 Models Parameters: Domain Dimensions, Injection Depths, Durations and Rates, and Fluid Temperaturea
Model 1 2 3 4
Large caldera Intermediate Intermediate Small
Inject. Inject. Radius Depth Duration Temperature (km) (km) (kyr) ( C) 50 5 5 5
5 1.7 1.7 0.5
22.5 10 10 10
350 350 350 250
Inject. Rate H2 O (t d1)
CO2 (t d1)
10 103 10 103 1 103 10 103
500 500 50 500
a Note that the injection rate is held constant for all models but model 3, for which a 10-fold smaller rate is tested. Fluids enthalpy for model input is derived from the injection temperatures (350 C for the large and intermediate models, and 250 C for the small model).
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3.2. Synthetic Ground Deformation [17] The TOUGH2–derived pore pressure and temperature distribution through time is input into the BIOT2 code to compute the thermo–poro–elastic response of the substratum. BIOT2 solves equations essentially based on poroelastic formulations, and extended for thermal expansion. [18] The governing equations ((1) and (2)) for linear poroelasticity [Verruijt, 1969, p. 342; see Hsieh, 1996] are: d dh ðr:uÞ þ rf gnb dt dt
ð1Þ
m rðr:uÞ rf grh ¼ 0 1 2n
ð2Þ
Kr2 h ¼
mr2 u þ
with K the hydraulic conductivity, h the change in hydraulic head, u the displacement of the skeletal matrix, n the porosity, [rf g] and b the specific weight and compressibility of fluid respectively. m and n are the shear modulus and Poisson’s ratio of the skeletal matrix. [19] As detailed in Hurwitz et al. [2007], pore pressure replaces the hydraulic head term in the original, hydrogeology–oriented, formulations (equation (2)). BIOT2 integrates the pore–pressure change [ p p0] and computes the poroelastic deformation of the medium using the following formulation: mr2 u þ
m rðr:uÞ rð p p0 Þ ¼ 0: 1 2n
ð3Þ
[20] Formulations for linear thermoelasticity bear strong similarities with the aforementioned poroelastic formulations [Norris, 1999]. Poroelasticity can therefore be conveniently extended to thermo–poro–elasticity by extending the pressure term [r(p p0)] in equation (3) to: 2mð1 þ n Þa r ð p p0 Þ þ ðT T 0 Þ 3ð1 2n Þ
ð4Þ
where a is the coefficient of volumetric thermal expansion of the saturated porous medium and [T T0] the temperature change. Combining equations (3) and (4), one obtains the final thermo–poro–elastic equation (5) which is solved by BIOT2 (see Hurwitz et al. [2007] for more details): m rðr:uÞ rðp p0 Þ 1 2n 2mð1 þ n Þa rðT T0 Þ ¼ 0 3ð1 2n Þ
mr2 u þ
ð5Þ
ð1þn Þ where 2m 3ð12n Þ is the drained bulk modulus, with n the drained Poisson’s ratio. All external boundaries are set as fixed (i.e. zero displacement throughout the simulations), with the exception of the ground surface (i.e., free). As highlighted by Hurwitz et al. [2007], there are some limitations to the coupling between TOUGH2 and BIOT2. First, and as mentioned previously, it is a one–way coupling only (from TOUGH2 to BIOT2); i.e., the change in strain amplitude and distribution calculated with BIOT2 has no effect on permeability, porosity and fluid flow. Secondly, while medium heterogeneity and complex geometries can be introduced in TOUGH2, BIOT2 cannot currently handle varying rheology
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(i.e., elastic modulii and thermal expansivity). Bearing in mind these limitations, the TOUGH2/BIOT2 coupling proved extremely useful for assessing the mechanical effects of key hydrothermal system dynamics parameters (e.g., pore– pressure and temperature) on the porous/permeable substratum [Hurwitz et al., 2007; Hutnak et al., 2009]. [21] The final output from BIOT2 used here is ground surface displacement through time at each top–surface node of the 2D axi–symmetrical computational mesh [Hurwitz et al., 2007; Hutnak et al., 2009]. These synthetic displacements are then converted to 3D and used as input for the 3D inversions described below.
4. Inversions of Synthetic Ground Deformation [22] The synthetic ground deformation generated above with the coupled TOUGH2/BIOT2 models spans a wide range of timescales (i.e., O(102–104) yr). Conversely, geodetic time series recorded at volcanoes (e.g., GPS, leveling) generally do not extend beyond several decades at most and may only represent a small observational window into longer, significant deformation events lasting 1–100’s yr. Attempting to invert synthetic cumulative displacement occurring over 100’s or 1000’s yr is therefore inadequate if one wants to relate modeled data to real, observed volcano geodetic signals. As a result, we chose to convert the synthetic displacements (e.g., mm) to velocities (e.g., mm yr1) to allow comparison with real–life observations (e.g., ground velocity derived from GPS data). For each model, we selected time windows for which the ground velocity was essentially constant. The number of studied time periods thus varies with the models, depending on the temporal evolution of the ground surface velocity field for each one of them. It must be noted that while using velocities instead of displacements allows a more direct and flexible comparison between the results from this modeling work and real–life geodetic data, it has a drawback: the uncertainty in velocities calculated from real data tends to decrease when computed over longer periods of time (e.g., years versus weeks). As a result, it is difficult to introduce a meaningful, generic level of white noise in our synthetic velocities to better mimic real– life observations because this noise is strongly dependent on the duration over which the velocities are computed. Hence, we did not introduce noise in the synthetic velocities. This implies that the inversion misfits for our theoretical models are likely to be smaller than that for inversions in real case studies. [23] The spatial density of ground surface nodes far exceeds that of any volcano geodetic network so we downsampled the number of points at the surface to better mimic real–life networks. Still, the resulting number of discrete surface data points (i.e., “synthetic stations”) corresponds to an ideal case scenario at any given volcano, and “network” density for the inversion remains greater than for most actual volcano geodetic networks. [24] The inversion of the synthetic ground velocities is carried out using the Neighborhood Algorithm method (N.A.) [Fukushima et al., 2005; Sambridge, 1999a]. This Monte Carlo inversion method essentially seeks to minimize a misfit function between modeled and observed ground displacements and the ensemble of retrieved source parameters is subsequently evaluated using a probability density
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function. Extensive details about this technique can be found in Fukushima et al. [2005] and Sambridge [1999a, 1999b]. [25] The N.A. inversion is run for both analytical and numerical formulations to ensure consistency of the inversion scheme throughout the various formulations. Sought output from the inversions is generally pressure sources’ location (latitude, longitude and depth), overpressure and size. Note that because the synthetic ground velocities were computed using a 2D axi–symmetrical modeling strategy, we fixed the source horizontal location to limit computational needs. This implies that the underlying assumption for the data inversion is that the source horizontal location is known. This, of course, is generally not the case in natural situations. However, whenever a symmetrical ground deformation field is observed, the source horizontal location can be estimated with reasonable accuracy, provided there is no significant elastic heterogeneity of the deforming medium or topographic effect. Note that we tested the effect of fixing the source location in the inversions by including the source’s horizontal location in the sought parameters. The results always pointed to the source’s actual location within a few 10’s m and did not measurably change the values for the other parameters (i.e., source depth, radius and overpressure) nor the inversion cost. We are therefore confident that fixing the source horizontal location for the inversions did not impact measurably on the results. Finally, the elastic properties were set to fit that of the BIOT2 modeling (shear modulus m of 1 GPa and Poisson ratio n of 0.25). Further work could include running the inversions either with a range of elastic properties or keeping the shear modulus as a parameter to be solved for during the inversion. In real–case studies of volcano deformation, though, these parameters are usually reasonably well constrained using prior information such as Vp/Vs ratio or experimental data on local rock properties. We therefore opted to keep the elastic properties as a constant for the inversion and note that any difference between the stated and actual values would only affect the retrieved overpressure, not the inferred 3D location of the pressure source. 4.1. Analytical Formulations [26] A variety of analytical formulations of ground displacement due to a pressurized point source is available in the literature. Yet, because of its simplicity, none is more widely used than the Mogi source formulation [Mogi, 1958], whether as the sole modeling approach or as a preliminary step to more sophisticated modeling strategies. Formulations exist for poroelastic point sources [Wang, 2000]. However, as noted by Lu et al. [2002], the distinction between a Mogi and a poroelastic source is virtually impossible, based solely on geodetic observations. For these reasons, we focus here on the use of a Mogi point source for geodetic inversion using analytical formulations. [27] The expression for a tension-sphere source in a homogeneous half-space in a cartesian system [Lu et al., 2002] can be represented as: ui ðx1 x1′ ; x2 x2′ ; x3 x3′ Þ ¼ CM
xi xi′ R3
ð6Þ
with xi the location of the point of interest at the free surface (x1, x2, x3 the easting, northing and elevation respectively, with
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x3 = 0). Similarly, xi′ is the location of the source with x1′ , x2′ and x3′ the easting, northing and the depth (x′3 positive) of the source respectively. CM is a combination of material properties and source strength and R is the distance between the source and the point of interest at the ground surface. [28] Reformulating these equations for x0, y0 and d (source easting, northing and depth respectively) and a flat free surface grid with nodes of coordinates (x,y,z with z = 0), 3D modeled displacements u at the nodes (in meters) can be rewritten as: 2 3 C ðx x0 Þ 1 4 M uðx; y; zÞ ¼ 3 CM ðy y0 Þ 5 R CM d
ð7Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where R ¼ ðx x0 Þ2 þ ðy y0 Þ2 þ d 2 . [29] In the case of a Mogi source [Mogi, 1958] CM ¼ DPM ð1 n Þ
a3M ð1 n Þð1 þ n Þ ¼ DVM 2pð1 2n Þ m
ð8Þ
with n the Poisson’s ratio, aM the source radius and DVM the volume change inside the spherical source (e.g., volume of magma entering the reservoir). [30] Note the non-unicity of the results due to the intrinsic link between the spherical source radius aM and the overpressure DPM (i.e., great pressure in a small source cannot be distinguished from a low pressure in a big source) [Cayol and Cornet, 1997]. One can therefore only assume reasonable values for the amount of material (e.g., magma) entering the reservoir at depth (or use realistic source dimensions). 4.2. Numerical Models [31] In this study, we use the 3D Mixed Boundary Element Method (MBEM) by Cayol and Cornet [1997] to model ground displacement due to a finite pressure source. It combines the Direct and the Displacement Continuity methods to analyze deformation in an elastic, homogeneous and isotropic medium. Unlike FEM models, it doesn’t require computationally demanding re–meshing of the modeling domain between iterations. It is therefore particularly well– suited to inverse problems and has been used in numerous previous studies [Beauducel et al., 2004; Cayol and Cornet, 1998; Cayol et al., 2000; Fukushima et al., 2005; Green et al., 2006; Peltier et al., 2008, 2009a, 2009b]. Another advantage of this technique is that it doesn’t consider infinite stresses at the corners and edges. Stress and displacements can thus be calculated everywhere in the modeling domain, including areas near the boundaries, without the pitfall of edge effects. We refer the reader to Cayol and Cornet [1997, and references therein] for more extensive details about the MBEM technique.
5. Results 5.1. Synthetic Hydrothermal System Models [32] The most relevant output from TOUGH2 for this work is pore–pressure and temperature distribution through time within the modeling domain. A representative example is shown in Figure 3 and bears characteristics common to all models and previous studies. As mentioned by Hurwitz et al.
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Figure 3. Example of temporal evolution of (top) pore pressure and (bottom) temperature in the TOUGH2 models (e.g., caldera model at early (1’s years) and later stages (100–1000’s years); note that this plot is a close–up of the first 3 km from the injection point, while the model’s horizontal dimension is 50 km). Through time, pore pressure first accumulates near the injection point and then get redistributed into the model’s domain, with a size reduction of the pressurized zone near the injection point. Conversely, the zone of high temperature expands through time, with the focus remaining the injection point. [2007] and Hutnak et al. [2009], pore–pressure increases significantly at – or near – the onset of the simulation, while the temperature increase remains limited. Through time, pore– pressure generally decreases near the injection point and gets redistributed as fluids migrate more evenly throughout the domain, while the temperature increase tends to affect the domain more widely. In order to assess the time-varying relative contribution of poroelasticity and thermoelasticity to
ground deformation, we computed for each model the ground deformation due to the pore–pressure effect only. This was achieved using an unrealistic low thermal expansion coefficient (a in equation (5)) in BIOT2, hence effectively inhibiting thermal expansion in the models. We compared the results of these pore–pressure–only models to those due to the combined effect of both pore–pressure and thermal expansion. The results of these tests for each model (Table 1) are shown in
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Figure 4. Temporal evolution of the ground surface displacement atop the injection point for all TOUGH2/BIOT2 synthetic models. Bottom plots for each model span over the whole simulation period. Top plots for each model close in on the onset of the simulation. The numbered greyed areas are periods for which velocity is broadly constant (i.e., linear displacement) and used for the inversions. Velocities were calculated using the start and end point of each red segment. The test simulation with inhibited thermal expansion (i.e., poroelastic response only) is shown with dashed lines. Figure 4. The most important result is that, regardless of the scale of the domain and the hot fluids injection rate or temperature, the same pattern can be observed: ground deformation is first dominated by pore–pressure increase near the injection point. From the onset, this period lasts for 20 years for the caldera model, 3–4 years for the intermediate models, and 10 months for the small model. In our simple models with continuous injection of fluids throughout the simulations, the correlation coefficient, R2 = 0.99 between the duration of the pore–pressure dominated deformation period and the depth
of fluids injection (Table 2). As a rule of thumb, the length of the time period for which pore–pressure dominates is therefore directly proportional to the injection depth. After that period of time, the contribution of thermal expansion to ground deformation progressively increases through time – while the pore– pressure effect decreases – until it largely dominates the ground deformation processes. We note that for a given injection rate, the duration of the poro–elastic phase is controlled by the permeability and dimensions of the models: the greater the distance between the injection point and the models
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Table 2. Periods Used for Each Model’s Inversiona Synthetic TOUGH2/BIOT2 Models Model Caldera Intermediate Intermediate (Low injection) Small
Inversion Best-Fits: Mogi (M) and Finite ( f )
Period
Start
End
Effect (P, T)
Zinj (m)
ZM (m)
Zf (m)
dPM (MPa yr1)
dPf (MPa yr1)
RM (m)
Rf (m)
costM (%)
costf (%)
1 2 3 1 2 1 2 1 2 3 4 5 6 7 8
0 day 175 yr 4500 yr 0 day 25 yr 0 day 200 yr 0 day 4 mth 8 mth 2.3 yr 3.5 yr 5.5 yr 35 yr 250 yr
20 yr 3000 yr 7500 yr 4 yr 1,000 yr 3 yr 5000 yr 2 mth 7 mth 10 mth 2.8 yr 5 yr 13 yr 60 yr 1000 yr
P P+T T P P+T P T P P P P+T P+T P+T P+T P+T
5000 5000 5000 1700 1700 1700 1700 500 500 500 500 500 500 500 500
4884 4064 7604 1592 1401 1536 729 400 581 632 1483 366 615 1625 5929
5886 3062 2516 1703 1508 1542 1069 526 566 948 1651 936 606 1508 9410
28 12 75 77 23 48 100 79 41 92 23 25 90 14 11
24 67 83 41 3 69 3 45 24 35 43 22 9 23 38
356 109 106 255 77 145 35 254 321 215 240 63 67 89 91
435 60 62 335 159 194 159 340 355 385 211 125 143 74 77
0.3 29.2 37.5 0.3 1.2 0.3 12.5 0.5 0.5 0.5 4.5 13.3 1.3 67.5 87.5
0.8 25.0 13.5 0.4 1.2 0.3 15.0 1.0 0.3 2.5 4.6 35.6 1.2 67.6 87.5
a
Zinj is the injection depth in TOUGH2. For the inversions, M and f subscripts correspond to Mogi and finite models respectively. Z, dP and R are the source depth, overpressure and radius, and cost is the inversion cost.
open boundaries (or the lower the permeability), the longer it takes for the fluids to reach the boundaries. Once the fluids reach these open boundaries (e.g., steady–state fluid–flow exiting the hydrothermal system via cracks in natural systems), and provided that the injection rate remains constant, pressure will progressively begin to decrease in the system. 5.2. Inversion of Synthetic Signal [33] Ground velocities for various representative time periods for each model were inverted using both analytical point source and finite formulations of a spherical pressure source, as detailed in section 4. Information about each modeled period and the inversion best–fits sources parameters are summarized in Table 2. Profiles of synthetic horizontal and vertical ground velocities for synthetic models and inversions best–fits are shown in Figures 5 and 6. Note that the last indicated period for all models corresponds to a plateauing of the ground deformation, hence extremely small ground velocity (i.e., ≪1 mm yr1). Because we aim at keeping this modeling effort in phase with the scale of real– life, observable data, we did not use these periods for the inversions, as ground deformation may not be detectable. 5.2.1. Inversions Fit [34] A measure of the fit between the synthetic velocities and the velocities for each best–fit model is provided as a cost parameter in percent (Table 2) (see Fukushima et al. [2005] for full details). The smaller the cost, the better the fit for each inversion. Our results show that for all models, the inversion fit is best (cost
