[2] Lizardite, chrysotile and antigorite are the three dif- ferent polymorphs of serpentine, which is formed by the hydrothermal alteration of the oceanic lithosphere.
GEOPHYSICAL RESEARCH LETTERS, VOL. 38, L09315, doi:10.1029/2011GL047160, 2011
Trench parallel anisotropy and large delay times: Elasticity and anisotropy of antigorite at high pressures Mainak Mookherjee1 and Gian Carlo Capitani2 Received 16 February 2011; revised 27 March 2011; accepted 7 April 2011; published 13 May 2011.
[ 1 ] Using theoretical methods, we calculate the full elastic constant tensor and equation of state of antigorite up to 10 GPa, a pressure range that encompasses its experimentally observed stability field. At ambient conditions, the elastic constant tensor reveals significantly large acoustic anisotropy (38% in VP; 35% in VS) compared to the dominant mantle phase olivine. The shear anisotropy is enhanced upon compression. Upon compression, the full elastic constant tensor reveals anomaly at r ∼ 2.69 gm cm−3. At r < 2.69 gm cm−3, we find that the pressure‐volume results for antigorite are well represented by a third order Birch‐Murnaghan formulation, with K0 = 52 GPa, K0′ = 8.5 and V0 = 3037 Å3 (r0 ∼ 2.48 gm cm−3). Our results on elasticity and anisotropy at conditions relevant to the mantle wedge indicates that a 10–20 km layer of antigorite might account for the observed shear polarization anisotropy with fast polarization parallel to the trench and associated large delay times of 1–2 sec observed in some subduction zone settings. Citation: Mookherjee, M., and G. C. Capitani (2011), Trench parallel anisotropy and large delay times: Elasticity and anisotropy of antigorite at high pressures, Geophys. Res. Lett., 38, L09315, doi:10.1029/2011GL047160.
1. Introduction [2] Lizardite, chrysotile and antigorite are the three different polymorphs of serpentine, which is formed by the hydrothermal alteration of the oceanic lithosphere. Antigorite is the predominant structural form of serpentine in metasomatized mantle rocks [Hyndman and Peacock, 2003]. It has been shown experimentally to be the stable polymorph at high pressures [Ulmer and Trommsdorff, 1995]. Upon subduction, the hydrous phases are thermodynamically unstable and undergo dehydration. The released fluid migrates upwards, subsequently leading to hydration of the peridotitic mantle wedge. The dehydration of serpentine is believed to be one of the major causes of mantle wedge hydration and related partial melting processes [Ulmer and Trommsdorff, 1995], and possibly related to deep focus earthquakes [Dobson et al., 2002]. Serpentine along with other alteration products in the fore‐arc mantle exhibits stable sliding behaviour at plate velocities and could inhibit brittle behavior [Reinen, 2000]. The weaker rheology of the hydrous phase isolates the hydrated fore‐arc region from the mantle‐
1
Bayerisches Geoinstitut, University Bayreuth, Bayreuth, Germany. Dipartimento di Scienze Geologiche e Geotecnologie, Università di Milano Bicocca, Milan, Italy. 2
wedge corner flow system [Hilairet et al., 2007]. Despite the importance of antigorite for our understanding of upper mantle structure and dynamics, little is known of its atomic structure and elasticity at high pressure. What is the effect of pressure on the elastic anisotropy of antigorite? Could high‐pressure elasticity of antigorite explain the observed delay time of around 1–2 sec observed in certain subduction zones [Long and Silver, 2008]? To address these fundamental questions, we explore the full elastic constant tensor and anisotropy of antigorite at conditions relevant to mantle wedge.
2. Methods [3] Static, density functional theory calculations were performed with Vienna ab‐initio simulation package (VASP). The generalized gradient approximation (GGA) [Perdew et al., 1996] and Vanderbilt‐type ultrasoft pseudopotentials were used for all calculations as previously described by Mookherjee and Stixrude [2006, 2009] and Mookherjee and Steinle‐Neumann [2009a, 2009b]. Geophysically important physical properties such as elasticity and compressibility, depends on the specific volume, which are shifted in static calculations by a few percent relative to the experimental values at higher temperature; but the shift arises in a consistent manner. This makes the static (0K) elastic data extremely useful. We focus on the antigorite m = 17 polysome, monoclinic (Pm), with 194 atoms in the asymmetric unit i.e, 291 atoms in the one unit formula of Mg48Si34O85(OH)62 [Capitani et al., 2009], the stable phase at elevated pressure and temperature. We used an energy cutoff Ecut = 500 eV, and a Monkhorst‐Pack [Monkhorst and Pack, 1976] 1 × 2 × 2 k‐point mesh. A series of convergence test demonstrated that these computational parameters yield total energies that are converged within 0.5 meV/atom. Previous studies have shown that density functional theory captures the relevant physics of hydrous minerals with varying bond strengths from strong hydroxyl to weak interlayer forces [Mookherjee and Stixrude, 2006; Mainprice et al., 2008; Capitani et al., 2009]. We analyze bulk compression behavior using the third order‐Birch Murnaghan equation‐of‐state [Birch, 1978]. To compute the elastic constant tensor we strained the lattice and let the internal degrees of freedom of the crystal structure relax consistent with the symmetry: elastic constants are then obtained through changes in stress tensor () with respect to applied strain ("). We apply positive and negative strains of magnitude 1%, in order to accurately determine the stresses in the appropriate limit of zero strain. Finite strain fits to the elasticity data, computation of isotropic bulk (K) and shear (G) moduli were made using the formulations as previously described by Mookherjee et al. [2011].
Copyright 2011 by the American Geophysical Union. 0094‐8276/11/2011GL047160
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Figure 1. (a) Elastic constants vs. unit cell volume: the green filled symbols are from present study (GGA) and grey filled symbols are experimental data at 0 GPa [Bezacier et al., 2010], (a) compressional components, C11, C22 and C33; (b) off‐ diagonal components, C12, C13 and C23; (c) off‐diagonal components, C15, C25, C35 and C46; (d) shear components, C44, C55 and C66; (e) bulk KH and shear GH modulus; (f) VP, VS, VS1 and VS2 anisotropy vs. unit cell volume. Filled curve represents finite strain fit to the computational results. We computed the single crystal azimuthal anisotropy for P‐ and S‐waves in antigorite using the formulation for maximum polarization anisotropy [Mainprice, 1990].
3. Results [4] The calculated elastic constants are in good agreement with the experimental results [Bezacier et al., 2010], which also show substantially lower compressibility along the stacking direction (Figure 1 and Table S1 of the auxiliary material).1 The elastic constants also exhibit striking anisotropy at ambient pressures. At r ∼ 2.48 gm cm−3, C11 ∼ C22 is ∼2.8 times greater than C33, reflecting weaker bonding along [001] direction. Upon compression C33 increases more rapidly than C11 and at a r ∼ 2.90 gm cm−3 (V ∼ 2600 Å3) they are almost equal. Antigorite also has strong shear elastic anisotropy expressed by the ratio C66/C44, where C66 governs shear deformation of the tetrahedral‐octahedral (T‐O) sheets, and C44 shear sliding of sheets across each other. The C66/C44 ratio increases from 2.96 to 3.20 as r increases from 2.48 to 2.90 gm cm−3. The elastic constants of antigorite increase monotonically with pressure until r ∼ 2.69 gm cm−3 (V ∼ 2800 Å3). At r > 2.69 gm cm−3, few elastic constants 1 Auxiliary materials are available in the HTML. doi:10.1029/ 2011GL047160.
decrease (soften) (Figure 1). This is very similar to the discontinuity observed in lizardite [Mookherjee and Stixrude, 2009] and also in antigorite [Nestola et al., 2010]. The elastic softening is related to the adjustment of the relative misfit between the tetrahedral and octahedral layer as observed in lizardite. Isotropically averaged bulk and shear moduli, and the compressional and shear wave velocities are in good agreement with our computed equation of state, and with experimental measurements (Table S1 of the auxiliary material). We have described the pressure volume relation (for r < 2.69 gm cm−3) using Birch‐Murnaghan equation of state [Birch, 1978] (Figure S1 and Table S1 of the auxiliary material). The static zero pressure density within LDA is 3.7% larger, and that within GGA is 4.0% smaller than that of the room temperature experimental value [Nestola et al., 2010]. The static zero pressure value of the bulk modulus within LDA is 17% larger, and that within GGA is 13% smaller than that found in room temperature experiments [Bezacier et al., 2010]. The greater density of the experimental sample is partly due to the GGA, which tends to underbind the energy resulting in larger volume and lower density. However, GGA often describes hydrous phases [Mainprice et al., 2008; Mookherjee and Stixrude, 2006] better than the LDA. Hence, we focus on the volume dependent elastic constants from GGA. We infer the pressure from the volume based on experimental equation of state
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Figure 2. (a) Variation of seismic velocity and density of partially serpentinized peridotites [Christensen, 1966; Carlson and Miller, 2003]; the horizontal lines represent the observed seismic velocity 6.7 to 7.2 km sec−1 [Seno et al., 2001], the vertical red‐dashed lines represent the degree of mantle hydration estimated from chrysotile trend, the green dashed lines represent the degree of mantle hydration estimated from antigorite trend taking into account of the anisotropy (dotted green line); (b) Velocity density systematics of partially serpentinized peridotite, serpentine polymorphs such as antigorite (ant), lizardite (liz), hydrous phases such as talc (tlc) and brucite (bru), B10‐[Bezacier et al., 2010], C66‐[Christensen, 1966], C04‐[Christensen, 2004], CM03‐[Carlson and Miller, 2003], M08‐[Mainprice et al., 2008] and MS09‐[Mookherjee and Stixrude, 2009]. Anisotropy of serpentine: variation of (c) VP; (d) VS1 and VS2; (e) VP/VS1 and VP/VS2; (f) delay time/ layer thickness (dVS/(VS1 × VS2)) as a function of the angle of incidence between the seismic ray path and (001) plane of antigorite, at three distinct densities of 2.59 (blue), 2.63 (green) and 2.68 (red) gm cm−3. The r ∼ 2.63 gm cm−3 corresponds to the 30 km depth. Note that for a 10–20 km layer of antigorite, seismic ray path subparallel to the [001] direction could easily explain the observed delay time of 1–2 sec observed in the Ryukyu subduction zones. [Nestola et al., 2010]. As a function of volume the GGA results are in very good agreement with the experimental study (Figure S1 of the auxiliary material).
4. Geophysical Significance [5] At r ∼ 2.63 gm cm−3, similar to the density of antigorite at 30 km depth based on experimental equation of state [Nestola et al., 2010], we find that antigorite has VHill P ∼ ∼ 7.19 km sec−1 and VReuss ∼ 6.68 km 6.94 km sec−1 (VVoigt P P sec−1). This is faster than the chrysotile‐bearing serpentinites [Christensen, 1966; Carlson and Miller, 2003] and is in good agreement with the experiments [Bezacier et al., 2010] (Figure 2). Effect of temperature on the seismic velocities of antigorite is likely to be negligible with the temperature derivative (∂VP/∂T) being of the order of −0.6 × 10−3 km sec−1/°C [Carlson and Miller, 2003]. On the basis on the velocity density systematics of anhydrous mantle
minerals and hydrous minerals, it is evident that hydrous phases have lower density and slower velocity in comparison to anhydrous minerals [Mookherjee and Stixrude, 2009]. Hence it is expected that serpentinization of dry mantle rocks such as peridotites will lead to reduction of velocities. In the mantle wedge above subduction zones, slow velocity regions attributed to mantle hydration are widespread [Hyndman and Peacock, 2003]. Attempts have been made to infer the degree of mantle hydration based on the velocity density systematics of peridotite and chrysotile bearing serpentinite varieties [Carlson and Miller, 2003]. For instance, in the Kanto district of Japan, seismic tomographic model [Seno et al., 2001] indicates existence of significantly low compressional wave anomaly with velocity ranging between 6.7 to 7.2 km sec−1. This would imply 25 to 40% serpentinization of the mantle wedge. However, if one considers velocity of the antigorite polytype that is likely to be stable at the mantle wedge conditions, one
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Figure 3. 1) A “mantle wedge hydration” model to explain large magnitude shear polarization anisotropy with fast polarization parallel to the trench. Region 1‐ serpentine rich zone with some amount of talc formed at the base of the mantle wedge, due to excess silica rich fluids released from the subducting slab; Region 2‐ a mixture of serpentine, talc and olivine and Region 3‐ a zone rich in olivine mineral phase with B‐type fabric. In location (i) the (001) planes of antigorite are horizontal and parallel to the overriding plate, this is unlikely to contribute to the large delay time; in location (ii) and (iii) the (001) planes of antigorite are vertical and the teleseismic rays are sub parallel to these planes which is likely to generate large delay times, in addition the [010] axes is parallel to the trench axes that is likely to generate the trench parallel shear wave polarization anisotropy; in location (iv) (001) planes of antigorite and talc are parallel to the subducting plate, likely to be sub parallel to the rays from local events and are likely to account for observed large delay times. Note: diagram is not to scale.
would predict high degree of mantle hydration up to meaningless values of more than 100%. It is important to note that serpentinite is extremely anisotropic and if the anisotropy is considered then the likely degree of serpentinizaition is between ∼65 to ∼95% for 6.7 and 7.2 km sec−1 respectively (Figure 2). Mantle hydration or serpentinization has also been inferred from the high VP/VS ratio of 1.84 in comparison to 1.73 for anhydrous mantle mineral assemblages [Christensen, 2004]. However, at r ∼ 2.63 gm cm−3 (30 km), we find that the isotropically averaged VP/VS is
1.60, which is substantially lower than the observed higher value. Upon compression, the compressional wave anisotropy, (200 × (VX max − VX min)/(VX max + VX min)) [Mainprice, 1990] with VX referring to VP decreases from 38% at r ∼ 2.59 gm cm−3 (∼0 GPa) to 30% at r ∼ 2.68 gm cm−3 (∼2.5 GPa), in the same interval the shear wave anisotropy (where, VX refers to VS) increases from 35% to 37% (Figure 1). Non‐hydrostatic stresses of the order of 100 MPa (0.1 GPa) are likely in the subduction zone settings, we have not considered the effect of the non hydrostatic
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stresses on the elastic anisotropy. Mantle hydration is intricately linked with global sea level changes. For instance, 5% serpentinization would mean ∼500 m sea level change over the past 600 Ma [Rüpke et al., 2004] consistent with the geological record of sea level changes. In light of such global significance, in interpreting the seismic signature of mantle hydration through serpentinization, it is crucial to take into account the large elastic anisotropy of antigorite. In addition to anisotropy, hydrous phases such as brucite and fluids might further reduce the observed velocities. [6] Shear wave polarization anisotropy is ubiquitous in most subduction zone, however the nature of anisotropy is diverse including both trench parallel and trench normal splitting and delay time ranging from 0 to greater than 2 sec [Long and Silver, 2008]. The trench normal and trench parallel anisotropy is traditionally explained by the lattice preferred orientation (LPO) of olivine. In subduction zone settings dominated with the corner flow olivine is likely to develop A‐type fabric ([100](010)) that is associated with fast seismic anisotropy perpendicular to the trench and parallel to the plate motion. Various models have been proposed to explain the trench parallel mantle wedge anisotropy. These include, proton defects, stress and melt induced transition from A‐type to B‐type ([001](010)) olivine fabric [Jung and Karato, 2001; Holtzman et al., 2003], 3‐D flow parallel to the trench [Kneller and van Keken, 2007] and convection driven by crustal foundering [Behn et al., 2007]. The strength of the anisotropy is characterized by the delay time between the arrivals of the fast and slow shear‐waves. Many subduction zone with trench parallel anisotropy are also characterized by large delay times of the order of 1–2 sec [Long and Silver, 2008], such as in Ryukyu arc. In the Ryukyu arc setting, the slab rollback velocity is low (
