Using shear wave amplitude patterns to detect metastable ... - CiteSeerX

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. B6, 10.1029/2001JB000608, 2002

Using shear wave amplitude patterns to detect metastable olivine in subducted slabs Kris L. Pankow,1 Quentin Williams, and Thorne Lay Center for the Study of Imaging and Dynamics of the Earth, Institute of Geophysics and Planetary Physics, and Earth Sciences Department, University of California, Santa Cruz, California, USA Received 9 May 2001; revised 31 December 2001; accepted 4 January 2002; published 7 June 2002.

[1] Olivine within the lowest temperature regions of subducting oceanic lithosphere may persist metastably to depths well below the equilibrium phase boundary for transformation to b phase. This may produce a tapering low seismic velocity wedge within the slab in the transition zone; transformational faulting of such metastable olivine has been proposed as a possible explanation of deep earthquakes. Detecting seismic velocity structure associated with metastable olivine within a slab using seismic wave arrival time information alone has proven problematic. Motivated by previous two-dimensional numerical calculations for upgoing and downgoing seismic waves, a three-dimensional Gaussian beam method is used to assess whether the azimuthally varying teleseismic amplitude signature produced by a slab with an internal wedge of metastable olivine is distinguishable from that for a slab with equilibrium transitions. Five slab velocity structures are considered: a thermal model with horizontal phase transitions at the same depths as in ambient mantle, two models incorporating equilibrium transitions within the slab, and two models with tongues of metastable olivine. A depth- and temperaturedependent thermal conductivity term and the effect of the latent heat of transformation of olivine to b phase are included in the thermal modeling. Three-dimensional dynamic ray tracing and Gaussian beam summation are performed for events located at different depths and lateral positions for each of the slab models. For sources near 400 km depth the presence of low-velocity metastable olivine produces relatively complex azimuthal shear wave amplitude patterns compared to thermal and equilibrium models. Comparison with observed amplitudes for four events in the Kurile slab indicates that allowing for internal slab velocity complexity in the transition zone provides better agreement with observations than simple thermal and equilibrium slab models. This indicates that careful modeling of teleseismic shear wave amplitude patterns may have the resolution to detect INDEX TERMS: 7203 and characterize the presence of metastable olivine in deep slabs. Seismology: Body wave propagation; 7207 Seismology: Core and mantle; 8120 Tectonophysics: Dynamics of lithosphere and mantle—general; KEYWORDS: subducting slabs, metastable olivine, mantle convection, phase changes, three-dimensional wave propagation, deep earthquakes

1. Introduction [2] The primary seismic velocity characteristics of a subducting slab are produced by its downwelling thermal anomaly. Subducting oceanic lithosphere can be as much as 1000C colder than the surrounding mantle [Minear and Tokso¨z, 1970]. As a general rule, seismic waves travel faster through relatively cold material, with shear waves being particularly sensitive to temperature. Thus, to first-order, seismic models of slabs are expected to involve 3 – 10% high-velocity tabular shapes, depending on the precise thermal structure and the scaling of P and S velocity with temperature (see Lay [1997] for a review of observed 1 Now at Seismographic Station, University of Utah, Salt Lake City, Utah, USA.

Copyright 2002 by the American Geophysical Union. 0148-0227/02/2001JB000608$09.00

average slab velocity anomalies). However, slabs are thermally neither uniform nor symmetric objects. The thermal structure is expected to vary across the width of the slab, with the largest thermal anomaly being concentrated in the upper 50 km. The thermal structure is further complicated by entrained flow in the surrounding mantle, partial melting in the wedge above the slab, and along-dip variations in lithospheric age. [3] In addition to the thermal anomaly the slab is chemically differentiated. For example, for oceanic lithosphere derived from a pyrolite mantle [Ringwood, 1982], one expects a sequence of layers involving basaltic/gabbroic crust, residual harzburgite, residual lherzolite, and slightly depleted pyrolite. Each of these layers has slightly different phase equilibria and resulting seismic velocities as the lithosphere sinks into the mantle [cf. Ringwood, 1982; Bina et al., 2001]. Seismic wave conversions from internal boundaries in the slab indicate that this internal layering

ESE 2 - 1

ESE 2 - 2

PANKOW ET AL.: DETECTING METASTABLE OLIVINE IN DEEP SLABS

Figure 1. Olivine(a)-b phase, b-g, and g-perovskite phase diagram used in this study. The light shaded lines indicate the equilibrium boundaries, while the solid lines denote kinetic boundaries. The kinetic boundaries are for 1% and 99% conversion to b phase contour lines. The thick shaded lines represent the cold geotherms for each of the models displayed in Figure 2. The lettered curves correspond to Figures 2a – 2d. can involve significant contrasts in properties [cf. Lay, 1997; Collier et al., 2001]. The combination of thermal structure and compositional layering leads to complicated dehydration scenarios and phase changes that may occur at different depths in each layer due to differences in mineralogy [cf. Vacher et al., 1999; Bina et al., 2001]. For earthquake sources located within the slab, both P and S waves should encounter a complex velocity structure that imparts a ‘‘slab signal’’ to the upgoing and downgoing wave fields. In general, long paths within the slab are likely to have early arrival times compared to paths that quickly exit the slab, and this provides the information used in tomographic imaging and arrival time residual sphere analysis of deep slab structure. The complex, likely anisotropic, velocity structure also affects the amplitudes and waveforms of P and S waves [e.g., Cormier, 1989; Iidaka and Obara, 1997; Koper and Wiens, 2000; Pankow and Lay, 2002; Vidale, 1987; Vidale et al., 1991; Weber, 1990; Kendall and Thomson, 1993], with sensitivity that differs from that for arrival times. [4] As pressure and temperature in the slab increase with depth, some phase changes take place that have large seismic velocity effects. There are two competing hypotheses about the phase boundaries within subducting slabs: either the minerals in the slab transform to their high-pressure phases under equilibrium conditions, or some of the transformations are kinetically inhibited [cf. Mosenfelder et al., 2001]. Each hypothesis predicts a distinct seismic velocity structure, allowing tests to be devised to evaluate model predictions. To date, predictions about the behavior of phase transitions within the

slab have been based largely on thermodynamic and kinetic arguments coupled with mineral physics data and have yet to be unequivocally supported by direct seismic observation. [5] One such phase transition, metastable olivine transforming to its high-pressure phases of either b or g spinel, has been proposed to nucleate shear instabilities, thus generating deep earthquakes [e.g., Green and Burnley, 1989; Green et al., 1990; Kirby et al., 1996; Green and Houston, 1995]. Under equilibrium conditions the olivine to b phase transition occurs at shallower depths in the cold slab than the 410-km depth typical of ambient mantle. If the transition is kinetically inhibited, a wedge of metastable olivine may penetrate below 410 km, producing a lowvelocity tongue of material bounded by a cutoff, or critical, isotherm. Transformational faulting on the margins of this wedge could produce a deep double seismic zone [e.g., Wiens et al., 1993; Iidaka and Furukawa, 1994]. If it can be shown that metastable olivine is not present in deep slabs, then the association of deep earthquakes with transitions of olivine is precluded. Whether or not earthquakes are associated with the phase transformation, the presence of metastable olivine in the slab would reduce the slab’s negative buoyancy in the transition zone [e.g., Schubert et al., 1975; Goto et al., 1987; Daessler and Yuen, 1993; Schmeling et al., 1999; Bina et al., 2001], affecting the driving forces of subduction. [6] The P wave arrival time signature associated with a tongue of metastable olivine in a slab has been examined in several studies. Contradictory results have been found as to whether olivine persists metastably or undergoes its equilibrium transformation above 400 km depth within the slab. Iidaka and Suetsugu [1992] found evidence supporting the presence of depressed metastable olivine for the Izu-Bonin subduction zone, while Solomon and U [1975] and Roecker [1985] found evidence for an elevated, equilibrium phase boundary for the Tonga and Izu-Bonin slabs. Collier and Helffrich [1997] detect underside P reflections indicating an elevated ‘‘410’’ within the Izu slab, compatible with an equilibrium model, although it is interesting to note that comparable shallow depths of the 410 are found at reflection points outside of the Izu, Japan, and Kurile slabs [Collier et al., 2001]. In the most comprehensive study to date, using an array of ocean bottom seismometers above the Tonga slab and a three-dimensional finite difference algorithm, Koper et al. [1998] conclude that the upgoing P wave arrival times can be equally fit by an elevated equilibrium boundary or a depressed metastable boundary. Vacher et al. [1999] constructed theoretical slab models that contained a suite of major slab minerals and their associated phase changes. By examining arrival times for stations directly above the slab, they concluded that a slab model of pure olivine produces results that are quite similar to a slab with full mineralogic stratification and that highly accurate source locations and precise knowledge of the three-dimensional structure outside the slab region are prerequisites for studying the detailed internal structure of slabs with arrival times. [7] The necessary step of locating all deep events in a simplified Earth model removes degree 0 and degree 1 terms from arrival time residuals [Jordan, 1977], and this projects much of the arrival time signal associated with any meta-


ESE 2 - 3

Figure 2. Cross sections of the four models generated for this study. Perturbations in shear velocity are shown. (a and b) Tongues of metastable olivine. (c and d) Calculated for equilibrium transition. The numbered circles correspond to the locations of the 10 events for which synthetics were calculated. See color version of this figure at back of this issue. stable wedge geometry into event mislocation, making it extremely difficult to identify a metastable wedge contribution to the residual arrival times [Koper et al., 1998]. This effect is particularly acute if a limited range of ray paths is considered, such as just downgoing phases. Arrival time anomalies also accumulate along the entire path length, not

just within the slab. The arrival time anomalies accumulated in the heterogeneous mantle outside the slab can be very large and must be accurately removed [Schwartz et al. 1991a, 1991b; Gaherty et al., 1991; Ding and Grand, 1994; Pankow and Lay, 1999], but this is a very complex process that is not easily validated.

ESE 2 - 4


Table 1. Slab Parameters for the Four Models

Model Model Model Model

A B C D

Velocity, cm yr1

Dip

Slab Age, Myr

Number of Time Steps

12 10 6 10

60 60 60 60

150 120 50 120

415 377 208 377

[8] While arrival time information alone usually yields ambiguous results, waveforms may also be used to distinguish between equilibrium and metastable slab models. In contrast to the average slab path anomaly sensed by arrival times, waveform data are sensitive to detailed lateral gradients within the slab [Cormier, 1989; Engdahl et al., 1988; Vidale, 1987; Vidale et al., 1991; Weber, 1990]. Distant path corrections do not appear to be particularly large for teleseismic S waves, although source radiation corrections are significant [Pankow and Lay, 2002; hereinafter referred to as PL]. Vidale et al. [1991] used a two-dimensional finite difference scheme to generate synthetic seismograms for waves that propagate downdip through a metastable olivine tongue, finding significant distortion of the wave pulse when compared to waves that traveled through purely thermal and equilibrium phase boundary models. They noted the importance of event location within the slab and that the best source depth for sensing the presence of metastable olivine is near 400 km. Unfortunately, this depth lies near a minimum in the distribution of slab seismicity. Koper and Wiens [2000] also computed synthetics for twodimensional models, evaluating the regional upgoing wave field from deep events. They found that any low-velocity metastable olivine tongue should act as a waveguide producing a coda after P and S arrivals. They did not observe such codas in recordings made above deep events in Tonga. There are relatively few opportunities to examine seismic observations for slabs in the quasi-two-dimensional updip or downdip geometries for the requisite large range of takeoff angles needed to characterize slab effects, but the work of Vidale et al. [1991] and Koper and Wiens [2000] motivates consideration of full three-dimensional amplitude and waveform effects. The details of waveform shape are strongly influenced by source rupture complexity, receiver structure, and other propagation effects, so it would be particularly useful if direct phase amplitudes could be used to constrain internal slab structure. The main challenges in processing amplitudes are focal mechanism correction, sensitivity of source location relative to the slab velocity gradient, and the difficulty of generating synthetics for three-dimensional slab structures [PL]. [9] We calculate teleseismic distributions of S and ScS amplitude anomalies for five different slab models using a three-dimensional Gaussian beam method. The slab models are generated by first calculating the thermal field for a set of parameters for a simplified petrological slab model. The temperature field is then combined with either an equilibrium phase diagram or a kinetic phase diagram for olivine to determine a velocity model. We then compute and examine the distribution of focusing and defocusing in the resulting teleseismic amplitude patterns in order to find any characteristic signatures that might be used to distinguish between different slab models. We conclude with a preliminary

Grid Spacing, km x 5.8 5.8 5.8 5.8

z 10 10 10 10

examination of teleseismic S wave data from events in the Kurile subduction zone to see if such signatures are evident.

2. Models [10] We constructed five different shear velocity models using four different thermal structures, which intersect the equilibrium and kinetic phase boundaries as shown in Figure 1. For each velocity model we calculate a thermal structure, then use either an equilibrium or kinetic phase diagram for the olivine to b phase transition, interpolate the appropriate depth- and position-dependent phase assemblage and thus derive the seismic velocity structure. We consider two equilibrium models and two kinetic models (Figures 1 and 2). The fifth model is a thermal structure with the phase transitions constrained to occur at the same depth as in ambient mantle. The details of the models are given below, with the input parameters for the different models and stages of modeling given in Tables 1 – 3. 2.1. Thermal Models [11] We generate realistic thermal models with the finite difference code originally developed by N. H. Sleep [Tokso¨z et al., 1973], appropriate for a cooling half-space model. The input slab characteristics and grid spacing are given in Table 1. For all models we assumed a specific heat of 1.036 103 J kg1 K1, a lithosphere basal temperatures for the halfspace of 1450C, density of the lithosphere of 3222 kg m3, coefficient of thermal expansion 2.6 105, and a lithosphere basal heat flux of 50 mW m2. We modified the code to account for depth-dependent thermal conductivity for the half-space model. Thermal conductivity is both a pressureand temperature-dependent parameter, and we incorporate each of these dependences sequentially in our modeling. This is motivated by the strong dependence of the slab thermal structure, and thus the inferred phase assemblage, on the values of thermal conductivity at depth [Hauck et al., 1999]. In the first stage of our modeling, we interpolate the

Table 2. Kinetic Parameters Used to Calculate Phase Boundaries Parameter Strain energy/unit volume, erg cm3 Characteristic pressure, GPa Grain size radius, cm Characteristic temperature, K Activation volume of oxygen lattice diffusion, erg atom1 GPa1 Number of nucleation sites, cm3 Surface energy/unit volume, erg cm2 Thickness of interface, cm Shape factor for volume Fractional volume change of olivine-spinel a

From Wu et al. [1993].

Value 6.0 108 26.9 0.5 773.15a 1.3 1013 6.1 1022 200 2.5 108 4p/3 0.074

ESE 2 - 5

PANKOW ET AL.: DETECTING METASTABLE OLIVINE IN DEEP SLABS Table 3. Elastic Parameters for the Mantle Mineralsa Mineral

r, g cm3

KS, GPa

dKS /dT, GPa K1

dKS /dP

G, GPa

dG/dT, GPa K1

dG/dP

Olivine b phase g phase Perovskite

3.222 3.472 3.548 4.108b

129 174 184 266c

0.016 0.018 0.017 0.031

5.1 4.9 4.8 3.9c

82 114 119 153

0.013 0.014 0.014 0.028

1.8 1.8 1.8 2.0

a With r density; KS adiabatic bulk modulus; G shear modulus; dKS /dP and dG/dP pressure derivatives of the moduli; dKS/dT and dG/dT temperature derivatives of the moduli. Except where indicated, values are from Duffy and Anderson [1989]. b From Wang et al. [1994]. c From Knittle and Jeanloz [1987].

thermal conductivity using values from a standard compilation as a function of depth [Stacey, 1992]. This has the effect of broadening slab isotherms relative to a constant value of thermal conductivity. In the second stage, we allow the thermal conductivity to change as a function of temperature at each time step in the calculation. This changes the shape of the isotherms inside the slab and causes the minimum temperature of the slab to be increased relative to that produced using a constant thermal conductivity [e.g., Hauck et al., 1999]. Figure 3 demonstrates the significant effect on slab temperatures resulting from the variable conductivity. The stability of the variable conductivity calculation was checked by examining the contoured thermal structure at each step, ensuring smooth convergence. [12] The value of the temperature derivative of thermal conductivity (dK/dT ) in the second stage turns out to be crucial in maintaining metastable olivine within the slab. This value influences the ability of the slab to remain cold enough to support metastability and thus the depth extent of metastable olivine. Metastable olivine is expected to only occur below a depth-dependent critical temperature [e.g., Sung and Burns, 1976a, 1976b]. Varying dK/dT can change the penetration depth of the critical temperature (typically 500 –600C) by 100 km (Figure 4). In this study, we use a value of dK/dT = 2.42 W mK2 [Kanamori et al., 1968; Hofmeister, 1999]. However, this value is not very well constrained, and we examine the general sensitivity to dK/dT of our results for the deepest penetration of the 600C isotherm (Figure 4). For a critical temperature of 600C [Sung and Burns, 1976a, 1976b], a 50 dipping slab must be older than 90 Myr and must subduct at a rate of at least 10 cm yr1 to allow the 600C isotherm to reach below 500 km depth. If the slab is 70 Myr old, it must subduct at a rate >14 cm yr1 to achieve a comparable depth to the 600C isotherm. For lithosphere subducting at a dip of 75 and 10 cm yr1, the slab must be close to 85 Myr old in order to get the 600C isotherm below 500 km. For comparison, to achieve the same depth, a 70-Myr-old slab with this dip must subduct at >12 cm yr1. These trade-offs are diagrammed in Figure 4. Using these results for dK/dT = 2.42 W mK2, we expect only the Tonga subduction zone to meet the requirements for large volumes of metastable olivine to be present at depth [Jarrard, 1986; DeMets et al., 1994]. This is not to say that metastable olivine does not exist in other regions, but in most cases it appears unlikely that it penetrates to great depth, unless viscoelastic effects are important in determining the rate of transformation of olivine to b phase [Liu et al., 1998]. Our result is compatible with the calculations of Devaux et al. [1997] and Mosenfelder et al. [2001] in predicting relatively small volumes of metastable

olivine in most slabs. The results depend strongly on the choice of dK/dT. We have also considered simplified halfspace lithospheric cooling models, lacking a leveling off of thermal structure with age for lithosphere older than 70–

Figure 3. Slab temperatures for a half-space model with (a) a constant thermal conductivity of 3.14 W mK1 everywhere and (b) a temperature-dependent thermal conductivity obtained by a two-step calculation procedure. Low temperatures in the slab do not persist to as large a depth in the latter model.

ESE 2 - 6


Figure 4. Contours showing the maximum penetration depth of the 600C isotherm given variations in slab parameters such as convergence rate, age, dip, and variation in the temperature dependence of the thermal conductivity (dK/dT ). The slab dips 50 in Figures 4a and 4b, and it dips 75 for Figures 4c and 4d. The convergence rate for Figures 4a and 4c is 10 cm yr1, and the age for Figures 4b and 4d is 70 Ma.

80 Myr, as proposed, for example, by Stein and Stein [1992]. This effect would also work to further reduce the amount of metastable olivine that may exist in various slabs. As our goal is to assess whether the internal slab structure associated with a metastable tongue of olivine produces seismically observable effects, we do not seek the most conservative thermal model. 2.2. Phase Transitions [13] The lithology of subducting slabs involves a basaltic crust overlying a harzburgite layer, a lherzolite layer, and a

slightly depleted pyrolite layer. Each layer has varying amounts of olivine and other minerals, but olivine makes up the majority of all the layers except the crust. As shown by Vacher et al. [1999], a pure olivine slab is not seismically distinguishable from a more complicated model in terms of integrated travel time effects. This is due to the seismic velocities of the pyroxene and garnet components of the slab offsetting one another, producing an aggregate velocity that is essentially identical to that of pure olivine. We therefore model the slab as pure olivine up to the highpressure phase boundary with b phase. At this depth we


assume that 70% of the slab (the olivine component) transforms to b phase and the remaining 30% is assumed to be present as one third orthopyroxene and two thirds garnet. This mixture matches the observed velocity jump at the 410 km discontinuity in PREM [Dziewonski and Anderson, 1981]. This algorithm thus is likely to accurately represent the seismic velocities of the subducted slab, although some estimates of the velocity contrast at the seismic discontinuity are weaker than in PREM [e.g., Collier et al., 2001]. We neglect the high-pressure transformation of pyroxene to garnet, but this is unlikely to produce large velocity perturbations, as pyroxene is not notably abundant in the subcrustal portion of the slab. Other minerals exist in the slab that might undergo metastable transitions (i.e., enstatite to ilmenite [Hogrefe et al., 1994]). However, in this study, we concentrate on the behavior of the olivine system, which volumetrically dominates the slab’s composition and thus its seismic velocity signature. [14] To model the presence of phase transitions, we take three different approaches. In the first set of models we calculate equilibrium phase transitions (Figure 1) for olivine to b phase [Akaogi et al., 1989], for b phase to g-spinel [Akaogi et al., 1989], and for g-spinel to perovskite + magnesiowu¨site using the estimated Clapeyron slopes of these transitions [e.g., Vacher et al., 1998]. The depths to these transitions closely match the observed seismic discontinuities at 410, 520, and 670 km in the ambient mantle. The equilibrium transitions in cold slabs are elevated by up to 80 km for the olivine to b phase transition and depressed by up to 40 km for the g-spinel to perovskite + magnesiowu¨site phase transition (Figures 2c and 2d). The elevated olivine to b phase equilibrium boundary in the slab juxtaposes high-velocity, dense b phase in the slab with olivine in the hotter surrounding mantle, and thus this zone of the slab model has seismically high velocity. The equilibrium spinel to perovskite + magnesiowu¨site transition, on the other hand, juxtaposes low-velocity spinel in the slab model next to dense perovskite + magnesiowu¨site in the surrounding normal mantle. This change in mineralogy has the effect of canceling the thermal effect on seismic velocities, and thus the deep portion of the slab model is seismically indistinguishable from or even slightly slower in velocity than ambient mantle. [15] In the kinetic models, olivine remains metastably within the slab until a critical temperature is reached. We follow the general approach of Sung and Burns [1976a, 1976b] in calculating the kinetic phase diagram. Table 2 lists the input parameters in our kinetic modeling: these closely follow those of Daessler and Yuen [1996]. For the slab environment we assume that nucleation occurs on grain surfaces: Such heterogeneous nucleation tends to produce the lowest critical temperature for the transformation. The critical temperature is set at 500C in accord with experimental results [Wu et al., 1993]. The resulting phase diagram (Figure 1) closely matches that of Daessler and Yuen [1996], who used a more complete numerical solution for the thermokinetic coupling of the olivine to b phase transition. We also have quite good agreement with the calculations of Mosenfelder et al. [2001], with very modest tongues of metastable olivine being produced for all but the highest subduction rates. We note the implicit assumption of a constant growth rate of the high-pressure phase at a given

ESE 2 - 7

pressure and temperature may be flawed and that the rate of viscoelastic relaxation may be important in controlling the growth of b phase [Liu et al., 1998]. However, this effect is not readily quantified, and we simply observe that assumption of a constant growth rate likely provides a minimum estimate of the amount of metastable olivine within a subducting slab. [16] As the metastable olivine approaches the spinel to perovskite + magnesiowu¨site transition, we force any metastable olivine to transform directly to perovskite + magnesiowu¨site. This reflects the fact that spinel is not stable at these pressures and temperatures and also is motivated by straightforward buoyancy arguments. Although the relative magnitude of buoyancy stresses to internal stresses within the subducting slab is controversial [Bina, 1997; Devaux et al., 2000], large amounts of less dense metastable olivine are unlikely to be readily pushed into the much denser perovskite-dominated material of the lower mantle. [17] The last model type is a purely thermal model with phase transitions that depend only on pressure. The olivine to b phase transition is imposed to occur at 410 km, the b-g spinel transition occurs at 520 km, and the spinel to perovskite + magnesiowu¨site transition occurs at 670 km. Although this model is somewhat unrealistic, it serves two purposes. First, it provides an intermediate model with which to compare the equilibrium and kinetic models. Second, if the ray paths only graze the boundary of the metastable wedge or if the wedge penetrates only by depths of several tens of kilometers, the seismic results would look very much like this simple thermal model. 2.3. Calculating Velocities [18] Along with our calculation of the kinetic and equilibrium phase diagrams, we calculate the bulk modulus and rigidity as a function of percent transformation to high-pressure phases using Voigt-Reuss-Hill averaging [Watt et al., 1976] for each pressure and temperature. The pressure and temperature derivatives are given in Table 3. The values used are in accord with those used in modeling stress fields in subducting slabs [e.g., Devaux, et al., 2000]. To obtain the velocity at each point in the grid, we combine the thermal models with the appropriate phase information as a function of pressure and temperature and then include the effect of the latent heat of the olivine to b phase and b phase to g-spinel transitions [Rubie and Ross, 1994]. [19] The slab velocity structure is defined relative to a background mantle structure given by the 1-s PREM shear wave model [Dziewonski and Anderson, 1981]. We use the grid from the thermal calculation as the model space, calculating a seismic velocity at each point. This was done by interpolating the bulk modulus and rigidity as a function of pressure and temperature at each grid point. For the slab these values are calculated in the downdip direction, so that the effects of latent heat can be included in the velocity calculations. We use 135C [Rubie and Ross, 1994] as the total temperature added through latent heat effects for both the a-b and b-g transformations. Thus, if a grid point changes phase from olivine to a fraction of spinel, it transfers that fraction of the latent heat to the grid point below it. The seismic velocity at the

ESE 2 - 8


tracing are plotted on ray maps, which indicate the endpoint of each ray in geographical coordinates on a lower hemisphere projection (Figures 6a and 6b). The calculations of teleseismic SH amplitudes by the Gaussian beam method are plotted on amplitude residual spheres (Figure 6c) [Davies and McKenzie, 1969]. The ray map may be interpreted as a ray intensity map; the more rays intersecting a given surface element, the larger the resulting amplitude. However, some strongly deflected rays carry little amplitude, and some rays near caustics will have large amplitudes, effects accounted for when computing the finite frequency synthetics. The amplitude residual sphere displays the amplitude difference from the overall mean, which is effectively geometric spreading in the PREM model; focusing causes positive residuals. In general, the peak amplitudes correspond closely to ray density, although variations are not as pronounced as ray density might suggest near caustics. [22] Gaussian beams are calculated by an integral superposition of all rays passing within a specified region around the receiver with the amplitudes of the rays weighted such Figure 5. Orthographic projection centered on the northwestern Pacific region. The heavy line near the center is where the theoretical slab was placed in the Earth. The triangles are WWSSN stations were amplitudes are calculated. Note that stations at azimuths out the backside of the slab are found in the central Pacific and South America. lower point is then calculated for a state warmer than the initial thermal model.

3. Calculating Seismic Body Wave Amplitudes [20] The two-dimensional theoretical velocity models are expanded laterally to three dimensions with a geometry generally appropriate for the Kurile subduction zone (Figure 5). We use a constant radius of curvature for the model compatible with the general arc geometry but do not introduce all known geometric complexities for the Kurile slab as we focus on sensitivity to gross internal slab structure. We locate 10 sources near the middle of this structure so as to avoid complications from rays exiting the lateral terminations of the slab (Figure 5). The sources span the slab both laterally and in depth; three sources transect the slab at 200 km depth, three more transect the slab at 400 km, two are located near the top of the slab at 300 and 350 km, and two sources bound the metastable region near 450 and 500 km depth (Figure 2). [21] From each of these 10 source locations we shoot S and ScS rays using three-dimensional dynamic ray tracing [Cerveny and Hron, 1980; Cerveny 1985a, 1985b; Cerveny and Psencik, 1979] and then sum the rays using a threedimensional Gaussian beam method [Cerveny, 1985a, 1985b]. We interpolate the velocity model with cubic splines to provide stable ray path calculations. This is similar to the approach of Sekiguchi [1992] and PL. We compute synthetic horizontally polarized SH displacements with a 10-s width Gaussian wavelet source function, checking each waveform to ensure convergence of the beam sum and stability of the waveform. Results of the dynamic ray

Figure 6. Examples of (a and b) ray maps and (c) an amplitude residual sphere. For the ray maps, the endpoints of each ray are plotted in geographical coordinates as a function of takeoff angle and azimuth. Figure 6a is the ray map for the S phase shot through model D from event 6, with the circumference of the plot corresponding to a takeoff angle of 60. Figure 6b is the ScS phase, with the circumference of the plot corresponding to a takeoff angle of 25, which is for the central portion of Figure 6a. Figure 6c shows corresponding S and ScS logarithmic amplitude residuals plotted with the circumference of the plot corresponding to a takeoff angle of 60. The squares are defocused regions, the octagons are focused regions, and the large pluses denote stations where a stable beam could not be formed. Note where there is a uniform distribution of rays the amplitude residuals are uniform and where there are a limited number of rays stable residuals cannot be formed.


ESE 2 - 9

that the amplitude profile in the plane perpendicular to the central ray has a Gaussian distribution. Rays that have amplitudes more than 0.001 of the largest value are included. The main benefit of the Gaussian beam method over dynamic ray tracing is that the existence conditions for Gaussian beams [Cerveny and Psencik, 1983] ensure more accurate amplitude calculations at caustics and in shadow zones (singularities are suppressed), but there are limitations in the accuracy. [23] Special attention must be paid to the beam parameter in order to compute accurate seismograms [Weber, 1988]. This parameter specifies the width and phase construction of each Gaussian beam. We use the parameterization for the beam width suggested by Cerveny [1985b] and Sekiguchi [1992]. To further improve the accuracy of the summation, if the travel time anomaly calculated using Gaussian beams is larger than 15 s, the station is assigned a default amplitude. This generally occurs in regions with very sparse ray sampling, and some ray contributions may have been missed. In this way, unstable results, which tend to overestimate the defocusing effect, are not allowed to skew the overall mean. PL provide further discussion of the stability and limitations of the Gaussian beam method for this application.

4. Results [24] We use the purely thermal model with constant phase boundary depths as a reference with which to compare the other models. The predominant feature in calculations for the thermal model is the degree one pattern in the lower hemisphere SH amplitude residuals (Figure 7), with low amplitudes in the northwestern quadrant. This arises from paths to stations in the downdip direction (toward the northwest) being defocused while paths to stations at azimuths opposite the dip have very little amplitude perturbation. This is a typical pattern for a simple thermal slab, as found by PL. As the source depth increases, the intensity and extent of downdip defocusing decreases, and in the opposite azimuth to the dip the station residuals remain uniform. It is notable that the teleseismic slab effects primarily involve defocusing; very little strong focusing is predicted by these models, apart from some northerly azimuths. This contrasts with the data measured by PL, which show significant regions of coherent focusing for events above 500 km depth toward the north and northwest. [25] We compare the four models with more realistic phase boundaries to the reference thermal model and each other (Figure 8). The sources at 200 km in depth (numbers 1, 2, 3) show some significant differences, which correspond to the strength of the low-velocity tongue within the slab (strongest for model A, Figure 8a; weaker for model B, Figure 8b; and missing for models C and D, Figures 8c and 8d). Note that there are zones of strong focusing toward the north and west for the nonequilibrium models, whereas much smoother patterns of defocusing are predicted for the equilibrium models. The latter are largely indistinguishable from the thermal model for the sources at 200 km depth. For all of the kinetic and equilibrium models, stations at azimuths opposite the dip direction have relatively uniform residuals, similar to the reference model. Position within the slab has a strong affect on the patterns for the nonequili-

Figure 7. Logarithmic amplitude residuals calculated for the purely thermal model. The symbols are the same as in Figure 6c. Note the degree one pattern and the uniform distribution of residuals to the south and southeast. The numbers on the left of each plot correspond to the event numbers in Figure 2.

ESE 2 - 10


Figure 8. The Gaussian beam logarithmic amplitude residuals result for the four theoretical models in Figure 2: (a) model A in Figure 2a, (b) model B in Figure 2b, (c) model C in Figure 2c, and (d) model D in Figure 2d. The numbers on the left correspond to the event numbers in Figure 2, while the source depth is indicated on the right. The symbols are the same as in Figure 6c.


Figure 8. (continued)

ESE 2 - 11

ESE 2 - 12


brium models, which makes it hard to uniquely constrain internal slab structure. [26] For slightly deeper sources near 300 km depth (events 4 and 5 in Figure 8), the amplitude residual patterns are strongly influenced by the elevated portions of the olivine to b phase transition within the slab. The patterns are augmented with respect to the thermal model reference. The residuals for model D (Figure 8d) show fairly uniform patterns in the direction opposite to the dip. However, rays from event 4 traveling through Model C (Figure 8c) are defocused around the elevated b phase, causing some pattern out the back of the slab. Both nonequilibrium models show some relative focusing at this azimuth. Event 5 is deep enough not to have complicated interactions with the elevated boundary, and a uniform distribution of amplitude residuals is found at azimuths opposite the dip direction. [27] On the basis of two-dimensional full waveform calculations, Vidale et al. [1991] pointed out that sources near 400 km should be the most diagnostic when looking for metastable olivine. Sources at this depth most efficiently channel seismic wave energy into the low-velocity tongue, producing caustics and diffractions. This conclusion is supported by our three-dimensional synthetics, as shown in Figure 8, events 6, 7, and 8. For the sources in the two equilibrium models, there is a consistent band of defocusing toward the northwest that matches the patterns predicted for the thermal model. A narrow fringe of focused arrivals toward the northwest is seen for events near the upper side of the slab. The nonequilibrium models are distinctive, with stronger amplitude variations and coherent bands of focusing and defocusing in the downdip direction, especially if the source is located above the low-velocity feature (source 6). For the latter case, there are also rather strong variations out the backside of the slab. For model B (Figure 8b) the pattern in the southeastern quadrant is scattered for source 6 and approaches the pattern seen in the thermal model for source 8 (where the event is seaward of the low-velocity layer). As waves propagate through the low-velocity region, the wave field becomes highly distorted over a wide range of azimuths, extending out the backside of the slab. [28] Ray termination plots are shown in Figure 9 to demonstrate this variation. When the downgoing waves do not interact with the low-velocity region, the ray patterns are more uniform. This distorted ray pattern is also evident, although to a lesser degree, for the deeper events (events 9 and 10 in Figures 8 and 9) where waves traveling out the backside of the slab pass through the lower extension of the metastable olivine tongue. For these deeper event locations the equilibrium models continue to mimic the thermal model. These calculations suggest that teleseismic SH wave amplitude data may provide a means for testing for the presence of low-velocity metastable olivine within slabs in the transition zone: The overall variations are stronger, discrete bands of focusing in the downdip direction are observed, and there is variability out the backside of the slab for sources located near the top of the slab.

5. Discussion [29] Amplitude residual spheres provide a promising approach to characterizing internal slab structure, especially low-velocity regions such as a metastable olivine tongue.

Figure 9. Ray maps for the S phase shot through (left) model C and (right) model B. The existence of metastable olivine in model B severely distorts the rays exiting to the southeast (opposite the slab dip). The numbers correspond to the event numbers in Figure 2. The takeoff angle corresponding to the circumference of the circle is 60.

The overall pattern of amplitudes for sources from 200 to 500 km may prove useful, but the greatest sensitivity is for events near 400 km depth. Downdip focusing and out the back of the slab amplitude variations are key features to seek, recognizing that position of the source within the slab plays an important role on the predicted pattern of residuals. Differential amplitude residual spheres for nearby events with very precise relative locations might prove particularly useful, as this can eliminate the distant propagation effects and isolate near-source interactions.


Figure 10. Logarithmic amplitude residual spheres for four events from the Kurile subduction zone: (a) 21 June 1978, depth of 404 km, (b) 10 July 1976, depth of 415 km, (c) 5 September 1970, depth of 583 km, and (d) 29 January 1971, depth of 544 km. The data have been corrected to an isotropic source and distant path corrections have been applied [PL]. Squares denote regions of defocusing, and octagons denote regions of focusing. The takeoff angle corresponding to the circumference of the circle is 60.

[30] When we examine actual long-period (5 –15 s) firstpeak SH wave amplitude data from sources near 400 km depth in the Kurile slab (Figures 10a and 10b), we observe significant focusing toward the northwest, with substantial variations at azimuths out the back of the slab. These data, from World Wide Standardized Seismic Network (WWSSN) and Canadian Seismic Network (CSN) observations, have been corrected for the effects of source radiation pattern, geometric spreading, and near-receiver effects. The various corrections applied to these data are discussed in detail by PL, along with the relative advantages of using long-period SH data. While the corrections are based on reasonable procedures, they are clearly imperfect, and some of the amplitude fluctuations seen in the data are the result of inadequate corrections, instrument fluctuations, digitization and rotation errors, and measurement errors. However, the corrected amplitude patterns do display some coherent patterns that appear to be near-source effects. [31] PL were able to match some aspects of these patterns by locating the sources in the uppermost portion of purely thermal slab models, but these provided poor fits to the travel times and did not predict the variation at azimuths toward the southeast. The introduction of a low-velocity layer within the slab yields a more complex pattern of amplitudes, which may improve the fit toward the southeast, along with facilitating the explanation of focusing toward

ESE 2 - 13

the northwest. For events above 200 km depth, PL failed to match the strong focusing observed toward the north, and they were forced to locate the sources deep within the slab structure to avoid strong downdip defocusing. The calculations in Figure 8 for sources at 200 km indicate that better fits can be obtained with models containing metastable olivine slab structure. For events below 500 km depth (see Figures 10c and 10d), PL again found it difficult to match focusing toward the northwest, but this is a predicted effect for the nonequilibrium models in Figure 8 (events 9 and 10). We do not try to optimize the source location and slab model to match the data in this paper, as a larger data set, ideally incorporating higher-quality digital data, is needed, but qualitatively, the slab models with metastable tongues of olivine appear closer to the data than the equilibrium models for source locations widely distributed in the slab. [32] PL encountered several other difficulties that may be ameliorated by introducing a low-velocity layer within the Kurile slab. The models based on amplitude modeling tend to underpredict arrival time anomalies for the same events. It may be possible to reconcile the amplitude and travel times studies by invoking a low-velocity metastable olivine layer within faster slab material. A more complex slab structure, with strong internal velocity gradients that were not included in the thermal models, provides a means by which to model amplitudes and travel times. An additional difficulty with the previous study is that no change in geometry or velocity contrast of simple thermal slab models could produce the observed variations in focusing and defocusing to the south and southeast. Again, internal slab structure widens the affected azimuthal range and qualitatively improves the match to the data. [33] A conclusive demonstration of the presence of metastable olivine within a subducting slab awaits detailed modeling of data for a specific slab geometry, but this study has demonstrated the potential of using shear wave amplitude patterns as the key attribute to match. The addition of complexity to thermal slab models is certainly motivated by our understanding of slab phase equilibria, but there is sufficient uncertainty in thermal structure, in mineral kinetics on the large-scale of a slab, and in the role of volatiles in the slab to raise questions about any particular model. Improving the fit to data by more complex models must be assessed in the context of degrees of freedom of the model complexity for convincing resolution of slab internal structure to be achieved. The major obstacle to progress is the challenge of correcting data for wave propagation effects far removed from the slab to ensure that scatter is not misinterpreted as slab signal.

6. Conclusions [34] Given the results of this study, efforts to model teleseismic amplitude patterns to constrain slab structure need to consider petrological and thermal complexity of the slab, including the possibility of kinetically inhibited phase transitions in the cold slab interior. What was initially considered scatter in either arrival time or amplitude data is likely to be partly due to three-dimensional effects produced by interaction with internal slab structure. By

ESE 2 - 14


modeling the data assuming only thermal slab structure or by smoothing the data in an effort to be consistent with the thermal model assumption we may be drawn to incorrect conclusions. We have shown that shear wave amplitude residuals from sources within slabs provide a means to detect and constrain the presence of metastable olivine. Downdip focusing produced by the quasi-waveguide properties of the low-velocity tongue of olivine produces distinctive patterns from those for simple thermal slab models with equilibrium phase boundaries: (1) in the direction opposite the slab dip, a broad region of variable focusing and defocusing is generated and (2) focusing downdip produces larger amplitudes than is possible with a thermal model. [35] Although shear wave amplitude patterns offer a promising approach to establishing the presence of metastable olivine within subducting slabs, there are practical difficulties to using amplitudes in this fashion. First, earthquakes near the most diagnostic depth of 400 km occur infrequently. Second, amplitude patterns are always rather scattered and noisy, and a large number of observations must be obtained for each event in order to establish the overall pattern characteristic of a particular slab structure. Third, the data must be processed to remove distant propagation and receiver effects and accurate source radiation pattern corrections must be made. Finally, the complete three-dimensional slab structure must be accounted for, with consideration of the sensitivity of the positioning of the source within the slab velocity gradients. If these problems are overcome, consideration of the three-dimensional amplitude patterns from intermediate and deep focus earthquakes may establish whether metastable olivine is present within a slab. [36] Acknowledgments. We thank Shoji Sekiguchi for providing his dynamic ray tracing and Gaussian beam codes and for extensive documentation and testing of these codes on our computers. John Vidale and Doug Wiens provided helpful reviews of the manuscript. We also thank Justin Revenaugh and Ru-Shan Wu for providing computer time. This research was supported by NSF grants EAR-9418643 and EAR-9350220. Contribution 452 of the Center for the Study of Imaging and Dynamics of the Earth.

References Akaogi, M., E. Ito, and A. Navrotsky, Olivine-modified spinel-spinel transitions in the system Mg2SiO4-Fe2SiO4: Calorimetric measurements, thermochemical calculation, and geophysical application, J. Geophys. Res., 94, 15,671 – 15,685, 1989. Bina, C. R., Patterns of deep seismicity reflect buoyancy stresses due to phase transitions, Geophys. Res. Lett., 24, 3301 – 3304, 1997. Bina, C. R., S. Stein, F. C. Marton, and E. M. Van Ark, Implications of slab mineralogy for subduction dynamics, Phys. Earth Planet. Inter., 127, 5166, 2001. Cerveny, V., Gaussian beam synthetic seismograms, J. Geophys., 58, 44 – 72, 1985a. Cerveny, V., The application of ray tracing to the numerical modeling of seismic wavefields in complex structures, in Handbook of Geophysical Exploration Section I, Seismic Exploration, vol. 15, edited by S. Treitel and K. Helbig, pp. 1 – 124, Geophys. Press, London, 1985b. Cerveny, V., and F. Hron, The ray series method and dynamic ray tracing system for three-dimensional inhomogeneous media, Bull. Seismol. Soc. Am., 70, 47 – 77, 1980. Cerveny, V., and I. Psencik, Ray amplitudes of seismic body waves in laterally inhomogeneous media, Geophys. J. R. Astron. Soc., 57, 91 – 106, 1979. Cerveny, V., and I. Psencik, Gaussian beams and paraxial ray approximation in three-dimensional elastic inhomogeneous media, J. Geophys., 53, 1 – 15, 1983.

Collier, J. D., and G. R. Helffrich, Topography of the ‘‘410’’ and ‘‘660’’ km seismic discontinuities in the Izu-Bonin subduction zone, Geophys. Res. Lett., 24, 1535 – 1538, 1997. Collier, J. D., G. R. Helffrich, and B. J. Woods, Seismic discontinuities and subduction zones, Phys. Earth Planet. Inter., 127, 35 – 49, 2001. Cormier, V. F., Slab diffraction of S waves, J. Geophys. Res., 94, 3006 – 3024, 1989. Daessler, R., and D. A. Yuen, The effects of phase transition kinetics on subducting slabs, Geophys. Res. Lett., 20, 2603 – 2606, 1993. Daessler, R., and D. A. Yuen, The metastable olivine wedge in fast subducting slabs: Constraints from thermo-kinetic coupling, Earth Planet. Sci. Lett., 137, 109 – 118, 1996. Davies, D., and D. P. McKenzie, Seismic travel-time residuals and plates, Geophys J. R. Astron. Soc., 18, 51 – 63, 1969. DeMets, C., R. G. Gordon, D. F. Argus, and S. Stein, Effects of recent revisions to the geomagnetical reversal time scale on estimates of current plate motions, Geophys. Res. Lett., 21, 2191 – 2194, 1994. Devaux, J. P., G. Schubert, and C. Anderson, Formation of a metastable olivine wedge in a descending slab, J. Geophys. Res., 102, 24,627 – 24,637, 1997. Devaux, J. P., L. Fleitout, G. Schubert, and C. Anderson, Stresses in a subducting slab in the presence of a metastable olivine wedge, J. Geophys. Res., 105, 13,365 – 13,373, 2000. Ding, X.-Y., and S. P. Grand, Seismic structure of the deep Kurile subduction zone, J. Geophys. Res., 99, 23,767 – 23,786, 1994. Duffy, T. S., and D. L. Anderson, Seismic velocities in mantle minerals and the mineralogy of the upper mantle, J. Geophys. Res., 94, 1895 – 1912, 1989. Dziewonski, A. M., and D. L. Anderson, Preliminary reference Earth model, Phys. Earth Planet. Inter., 25, 297 – 356, 1981. Engdahl, E. R., J. E. Vidale, and V. F. Cormier, Wave propagation in subducted lithospheric slabs, Proceedings of the 6th Course: Digital Seismology and Fine Modeling of the Lithosphere, pp. 139 – 155, Plenum, New York, 1988. Gaherty, J. B., T. Lay, and J. E. Vidale, Investigation of deep slab structure using long-period S waves, J. Geophys. Res., 96, 16,349 – 16,367, 1991. Goto, K., Z. Suzuki, and H. Hamaguchi, Stress distribution due to olivinespinel phase transition in descending plate and deep focus earthquakes, J. Geophys. Res., 92, 13,811 – 13,820, 1987. Green, H. W., II, and P. C. Burnley, A new self-organizing mechanism for deep earthquakes, Nature, 341, 733 – 737, 1989. Green, H. W., II, and H. Houston, The mechanics of deep earthquakes, Annu. Rev. Earth Planet. Sci., 25, 169 – 213, 1995. Green, H. W., II, T. E. Young, D. Walker, and C. H. Scholtz, Anti-crack associated faulting at very high pressure in natural olivine, Nature, 348, 720 – 722, 1990. Hauck, S. A., II, R. J. Phillips, and A. M. Hofmeister, Variable conductivity: Effects on the thermal structure of subducting slabs, Geophys. Res. Lett., 26, 3257 – 3260, 1999. Hofmeister, A. M., Mantle values of thermal conductivity and the geotherm from phonon lifetimes, Science, 283, 1699 – 1706, 1999. Hogrefe, A., D. C. Rubie, T. G. Sharp, and F. Seifert, Metastability of enstatite in deep subducting lithosphere, Nature, 372, 351 – 353, 1994. Iidaka, T., and Y. Furukawa, Double seismic zone for deep earthquakes in the Izu-Bonin subduction zone, Science, 263, 1116 – 1118, 1994. Iidaka, T., and K. Obara, Seismological evidence for the existence of anisotropic zone in the metastable wedge inside the subducting Izu-Bonin slab, Geophys. Res. Lett., 24, 3305 – 3308, 1997. Iidaka, T., and D. Suetsugu, Seismological evidence for metastable olivine inside a subducting slab, Nature, 356, 593 – 595, 1992. Jarrard, R. D., Relations among subduction parameters, Rev. Geophys., 24, 217 – 284, 1986. Jordan, T. H., Lithospheric slab penetration into the lower mantle beneath the Sea of Okhotsk, J. Geophys., 43, 473 – 496, 1977. Kanamori, H., N. Fujii, and H. Mizutani, Thermal diffusivity measurement of rock-forming minerals from 300 to 1100K, J. Geophys. Res., 73, 595 – 605, 1968. Kendall, J.-M., and C. J. Thomson, Seismic modelling of subduction zones with inhomogeneity and anisotropy, I, Teleseismic P-wavefront tracking, Geophys. J. Int., 112, 39 – 66, 1993. Kirby, S. H., S. Stein, E. A. Okal, and D. C. Rubie, Metastable mantle phase transformations and deep earthquakes in subducting oceanic lithosphere, Rev. Geophys., 34, 261 – 306, 1996. Knittle, E., and R. Jeanloz, Synthesis and equation of state of (Mg, Fe)SiO3 perovskite to over 100 gigapascals, Science, 235, 668 – 670, 1987. Koper, K. D., and D. A. Wiens, The waveguide effect of metastable olivine in slabs, Geophys. Res. Lett., 27, 573 – 576, 2000. Koper, K. D., D. A. Wiens, L. M. Dorman, J. A. Hildebrand, and S. C. Webb, Modeling the Tonga slab: Can travel time data resolve a metastable olivine wedge?, J. Geophys. Res., 103, 30,079 – 30,100, 1998.

PANKOW ET AL.: DETECTING METASTABLE OLIVINE IN DEEP SLABS Lay, T., Structure and Fate of Subducting Slabs, 185 pp., Academic, San Diego, Calif., 1997. Liu, M., L. Kerschhofer, J. L. Mosenfelder, and D. C. Rubie, The effect of strain energy on growth rates during the olivine-spinel transformation and implications for olivine metastability in subducting slabs, J. Geophys. Res., 103, 23,897 – 23,909, 1998. Minear, J. W., and M. N. Tokso¨z, Thermal regime of a downgoing slab and new global tectonics, J. Geophys. Res., 75, 1397 – 1419, 1970. Mosenfelder, J. L., F. C. Marton, C. R. Ross II, L. Kerschhofer, and D. C. Rubie, Experimental constraints on the depth of olivine metastability in subducting lithosphere, Phys. Earth Planet. Inter., 127, 165 – 180, 2001. Pankow, K. L., and T. Lay, Constraints on the Kurile slab from shear wave residual sphere analysis, J. Geophys. Res., 104, 7255 – 7278, 1999. Pankow, K. L., and T. Lay, Modeling S wave amplitude patterns for events in the Kurile slab using three-dimensional Gaussian beams, J. Geophys. Res., 107, 10.1029/2001JB000594, in press, 2002. Ringwood, A. E., Phase transformations and differentiation in subducted lithosphere: implications for mantle dynamics, basalt petrogenesis and crustal evolution, J. Geol., 90, 611 – 643, 1982. Roecker, S. W., Velocity structure in the Izu-Bonin seismic zone and the depth of the olivine-spinel phase transition in the slab, J. Geophys. Res., 90, 7771 – 7794, 1985. Rubie, D. C., and C. R. Ross II, Kinetics of the olivine-spinel transformation in subducting lithsophere: Experimental constraints and implications for deep slab processes, Phys. Earth Planet. Inter., 86, 223 – 341, 1994. Schmeling, H., R. Monz, and D. C. Rubie, The influence of olivine metastability on the dynamics of subduction, Earth Planet. Sci. Lett., 165, 55 – 66, 1999. Schubert, G., D. A. Yuen, and D. L. Turcotte, Role of phase transformations in a dynamic mantle, Geophys. J. R. Astron. Soc., 42, 705 – 735, 1975. Schwartz, S. Y., T. Lay, and S. L. Beck, Shear wave travel time, amplitude, and waveform analysis for earthquakes in the Kurile slab: Constraints on deep slab structure and mantle heterogeneity, J. Geophys. Res., 96, 14,445 – 14,460, 1991a. Schwartz, S. Y., T. Lay, and S. P. Grand, Seismic imaging of subducted slabs: Trade-offs with deep path and near-receiver effects, Geophys. Res. Lett., 18, 1265 – 1268, 1991b. Sekiguchi, S., Amplitude distribution of seismic waves for laterally heterogeneous structures including a subducting slab, Geophys. J. Int., 111, 448 – 464, 1992. Solomon, S. C., and K. T. P. U, Elevation of the olivine-spinel transition in subducted lithosphere: Seismic evidence, Phys. Earth Planet. Inter., 11, 97 – 108, 1975. Stacey, F. D., Physics of the Earth, 3rd ed., 513 pp., Brookfield, Brisbane, Australia, 1992. Stein, C. A., and S. Stein, A model for the global variation in oceanic depth and heat flow with lithospheric age, Nature, 359, 123 – 129, 1992.

ESE 2 - 15

Sung, C. M., and R. G. Burns, Kinetics of high pressure phase transitions: Implications to the evolution of the olivine-spinel transition in the downgoing lithosphere and its consequences on the dynamics of the mantle, Tectonophysics, 31, 1 – 32, 1976a. Sung, C. M., and R. G. Burns, Kinetics of the olivine!spinel transition: Implications to deep-focus earthquake genesis, Earth Planet. Sci. Lett., 32, 165 – 170, 1976b. Tokso¨z, N., N. H. Sleep, and A. T. Smith, Evolution of the downgoing lithosphere and mechanisms of deep focus earthquakes, Geophys. J. R. Astron. Soc., 35, 285 – 310, 1973. Vacher, P., A. Mocquet, and C. Sotin, Computation of seismic profiles from mineral physics: The importance of the non-olivine components for explaining the 660 km depth discontinuity, Phys. Earth Planet. Inter., 106, 275 – 298, 1998. Vacher, P., W. Spakman, and M. J. R. Wortel, Numerical tests on the seismic visibility of metastable minerals in subduction zones, Earth Planet. Sci. Lett., 170, 335 – 349, 1999. Vidale, J. E., Waveform effects of a high-velocity, subducted slab, Geophys. Res. Lett., 14, 542 – 545, 1987. Vidale, J. E., Q. Williams, and H. Houston, Waveform effects of a metastable olivine tongue in subducting slabs, Geophys. Res. Lett., 19, 2201 – 2204, 1991. Wang, Y., D. J. Weidner, R. C. Liebermann, and Y. Zhao, P-V-T equation of state of (Mg,Fe)SiO3 perovskite: Constraints on composition of the lower mantle, Phys. Earth Planet. Inter., 83, 13 – 40, 1994. Watt, J. P., G. F. Davies, and R. J. O’Connell, The elastic properties of composite materials, Rev. Geophys., 14, 541 – 563, 1976. Weber, M., Computation of body-wave seismograms in absorbing 2-D media using the Gaussian beam method: Comparison with exact methods, Geophys. J., 92, 9 – 24, 1988. Weber, M., Subduction zones-their influence on travel times and amplitudes of P waves, Geophys. J. Int., 101, 529 – 544, 1990. Wiens, D. A., J. J. McGuire, and P. J. Shore, Evidence for transformational faulting from a deep double seismic zone in Tonga, Nature, 364, 790 – 793, 1993. Wu, T. C., W. A. Bassett, P. C. Burnley, and M. S. Weathers, Shearpromoted phase transitions in Fe2SiO4 and Mg2SiO4 and the mechanism of deep earthquakes, J. Geophys. Res., 98, 19,767 – 19,776, 1993.

T. Lay and Q. Williams, Earth Sciences Department, University of California, Applied Sciences Bldg., Santa Cruz, CA 95064-1077, USA. ([email protected]) K. L. Pankow, Seismograph Stations, 135 S 1460 E Rm 705, University of Utah, Salt Lake City, UT 84112-0111, USA. ([email protected])


Figure 2. Cross sections of the four models generated for this study. Perturbations in shear velocity are shown. (a and b) Tongues of metastable olivine. (c and d) Calculated for equilibrium transition. The numbered circles correspond to the locations of the 10 events for which synthetics were calculated.

ESE 2 - 3