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Geophys. J. Int. (1996) 127,415-426 Teleseismic imaging of subaxial flow at mid-ocean ridges: traveltime effects of anisotropic mineral texture in the mantle Donna K. Blackman,' J.-Michael Kendall,2y* Paul R. D a ~ s o n , ~ H.-Rudolgh Wenk,4 Donald Boyce3 and Jason Phipps Morgan' IGPP, Scripps Institution of Oceanography, La Jolla, CA 92093-0225, USA Department of Physics, Unioersity of Toronto, Toronto, Ontario, Canada Sibley School of Mechanical & Aerospace Engineering, Cornell University, Ithaca, NY 14853-7501, USA Department of Geology & Geophysics, Unioersity of California, Berkeley, CA 94720, USA Accepted 1996 July 5. Received 1996 June 24; in original form 1995 October 5 SUMMARY Deformation of peridotite caused by mantle flow beneath an oceanic spreading centre can result in the development of seismic anisotropy. Traveltime anomalies and shearwave splitting will develop as seismic energy propagates through such an anisotropic region, thus providing a signature of the deformation field at depth. In this study we investigate the nature of deformation associated with mantle upwelling for two models of flow in the upper 100 km of the mantle. The finite-strain fields of the passive upwelling model versus the buoyancy-enhanced upwelling model are quite different. This suggests that mineral aggregates deform differently in the two models, thus developing seismic signatures that are distinguishable. Numerical estimates of the corresponding mineral textures are made using polycrystal theory for olivine with four operative slip systems. The activation of a slip system is determined for each grain on the basis of the local critical resolved shear stress. The computed grain deformation reflects a balance between stress equilibrium, for the aggregate as a whole, and strain continuity between neighbouring grains within the aggregate. This approach enables a direct link to be made between the model flow fields and the resulting texture development. Given these mineral orientation distributions, elastic parameters are calculated and wavefronts are propagated through the anisotropic structure. Traveltimes for teleseismic body waves are computed using ray theory, and amplitudes are estimated for an across-axis profile extending 100 km from the ridge axis. Relative P-wave residuals of up to 1 s are predicted for the buoyant model with on-axis arrivals being earliest, since near-vertical velocities are fastest beneath the axis. On-axis P-wave arrivals for the passive model are half a second earlier than arrivals 60 km off-axis, and relative delays continue to increase slowly as distance from the ridge increases. S-wave splitting of almost a second is predicted for the buoyant model, whereas less than a half-second of splitting is determined for the passive model. Key words: anisotropy, body waves, mid-ocean ridge, ray tracing, upper mantle. 1 INTRODUCTION The evidence available for determining the nature of mantle flow beneath oceanic spreading centres is indirect: surface volcanism occurs only in a narrow axial zone; the deep median valley at slow-spreading ridges is dynamically maintained, whereas at fast-spreading ridges an axial volcanic high occurs; *Now at: Department of Earth Sciences, University of Leeds, Leeds, LS2 9JT, UK. 01996 RAS ophiolite sequences commonly show significant alignment of minerals along the palaeo shear direction in their mantle sections; and seismic anisotropy in the upper mantle beneath old ocean crust exhibits a fast propagation direction aligned with palaeo plate motion. The narrow axial zone of surface volcanism (Macdonald 1982) indicates that although mantle upwelling probably occurs over a broad region at depths of 1W200 km beneath a spreading centre (e.g. Sleep 1975), the magma, and perhaps the residual matrix flow as well, must become more focused at shallow depths. The dynamic support 415 416 D.K . Blackman et al. of a deep median valley indicates rapid across-axis changes in mantle structure, either in the form of an axial asthenospheric suction due to the separation of thick plates (Lachenbruch 1973) or necking of a rigid lithosphere that thickens rapidly off-axis (Tapponnier & Francheteau 1978). The lack of a deep valley at fast-spreading ridges suggests that mantle structure varies less rapidly across the axis than at slow-spreading ridges. The alignment of mantle minerals in ophiolite sections (e.g. Nicolas & Christensen 1987) provides a means for mapping the deformation field that may exist beneath oceanic crust. The fact that these minerals have highly anisotropic seismic properties allows us to relate measurements of seismic anisotropy in the oceans (Raitt et al. 1969; Shimamura 1984; Nishimura & Forsyth 1989) to current and past mantle-flow geometries. Only now is the geophysical community beginning to undertake long-term teleseismic experiments at mid-ocean ridges that image the in situ deep structure at a resolution that can improve our understanding of processes on the scale of ten to a few hundred kilometres (e.g. Forsyth & Chave 1994). To assess the sensitivity of teleseismic body-wave observations to changes in the physical parameters that may control mantle upwelling at mid-ocean ridges, we present an integrated numerical study: first we perform geodynamical modelling of subaxial flow fields; this is followed by calculation of the mineral texture development in the corresponding mantle rock; elastic coefficients of the mantle are then determined from this polycrystal orientation distribution using single-crystal properties and appropriate averaging; finally wavefront propagation through the resulting anisotropic structure is analysed. There are two components of mantle flow beneath an oceanic spreading centre, passive and buoyancy driven, and the different relative strengths of the two can lead to a significantly different subaxial structure (Turcotte & Phipps Morgan 1992; Scott 1992). The passive component is induced by the spreading of the lithospheric plates with a simple pattern of upwelling beneath the axis and overturn to follow the spreading direction off-axis (Sleep & Rosendahl 1979; Reid & Jackson 1981). As the subaxial asthenosphere rises during passive upwelling, melting occurs due to decompression. This basaltic melt separates from the peridotite matrix and eventually rises to form oceanic crust at the ridge axis. Localized buoyancy forces develop in the upwelling mantle due to the presence of the interstitial melt (Rabinowicz, Nicolas & Vigneresse 1984; Scott & Stevenson 1989). In addition, compositional buoyancy of mantle that has experienced melt extraction (Oxburgh & Parmentier 1977) and thermal buoyancy will also enhance vertical flow rates beneath a spreading centre. The strength of the buoyancy-driven flow relative to ongoing passive upwelling is not well known, so we investigate two end-member flow models to estimate the possible differences in seismic structure that could occur, and to assess our ability to recognize them in teleseismic body-wave arrivals at the seafloor. The upper mantle beneath a spreading ridge is composed of peridotite and the main mineral component is olivine. Olivine single crystals are highly anisotropic for elastic-wave propagation, with P-waves travelling along the a-axis 25 per cent faster than along the b-axis (Verma 1960). Based on observations of peridotite xenoliths in basalts, it is likely that olivine deforms at upper-mantle conditions largely by intracrystalline slip accompanied by dynamic recrystallization. With such mechanisms, preferred orientation (texture) develops, as has been observed experimentally (Raleigh 1968; Carter & Ave’Lallemant 1970) and is predicted by polycrystal plasticity models (e.g. Wenk et al. 1991). Elastic-wave anisotropy has been observed in experimental and natural peridotite samples (Christensen 1984). Recently Boudier & Nicolas (1995) described high fabric anisotropies in Oman peridotites. Using petrofabric analysis and modelling elastic properties, Mainprice (1995) reported effective P-wave anisotropies, T)/ V r , up to 20 per cent from these sub-Moho peridotites. Crystalline alignment in a polycrystal during deformation is a complicated non-linear process. In the case of deformation by slip, polycrystal plasticity theories, developed to predict the deformation of metals, have been successfully applied to many minerals. If dynamic recrystallization occurs by subgrain rotation, similar mechanisms apply. In fact, in the case of olivine, recrystallization and deformation produce similar textures in experiments (Raleigh 1968; Carter & Ave’Lallemant 1970). For simple monotonic strain histories the strength of preferred orientation increases (though non-linearly) with overall strain. Such deformation regimes have been recently incorporated in heterogeneous, large-scale models to predict texture and anisotropy development during mantle convection (Chaste1 et al. 1993). This model was able to plausibly predict the general azimuthal variation in P-wave velocities associated with horizontal flow due to plate motion as observed by Raitt et al. (1969). It also showed that preferred orientation along a streamline is highly variable, increasing or decreasing, depending on the local incremental strain. Clearly preferred orientation cannot be predicted if only the finite-strain ellipsoid is known. In this paper we apply a similar approach to a more local feature and demonstrate that the elastic structure can vary significantly on the scale of 10 km in regions of high flow or thermal gradients, both of which occur in the vicinity of a spreading centre. Surface-wave studies of anisotropy in the oceanic mantle have necessarily assumed that large layers of constant elastic properties (e.g. hexagonal anisotropy or transverse isotropy) can approximate the actual seismic structure (Forsyth 1975; Tanimoto & Anderson 1984; Nishimura & Forsyth 1989). Our detailed investigation of mantle deformation via polycrystal plasticity, which is linked directly to velocity structure, allows us to construct a continuous, spatially varying anisotropic seismic model. Since we can accommodate all symmetries, no assumption about the symmetry class of the effective sample anisotropy is required and we are not restricted to a layered geometry, which would be a poor representation of the subaxial structure. (v- 2 L I N K E D MODELS O F FLOW, TEXTURE DEVELOPMENT A N D SEISMIC VELOCITY STRUCTURE 2.1 Flow models A finite-element flow model developed by Phipps Morgan and co-workers (Cordery & Phipps Morgan 1992; Jha, Parmentier & Phipps Morgan 1994) is used to predict deformation in the vicinity of a spreading ridge. Boundary conditions imposed at the surface require that the temperature is 0 “C and the velocity equals the spreading rate. The centre of spreading, the ridge axis at the surface, defines a symmetry plane for both temperature and velocity. Far off-axis (250 km in these runs), velocities 0 1996 RAS, GJI 127, 415-426 Subaxial $ow at mid-ocean ridges are set to match the predictions of a corner-flow model (e.g. Reid & Jackson 1981), except that the monotonic decrease from the spreading velocity begins at the base of the lithosphere rather than at the seafloor. Horizontal temperature gradients vanish at the right boundary. At the base (250 km depth), velocities are constrained to match the predictions of a simple corner-flow model and the temperature is held at 1325"C. The melting curve is defined to be T, = 1100"C + 3.25 ("C k m - ' ) ~ , so melting begins at about 70 km depth. The degree of melting affects the density of the residual, which is tracked, and the amount of melt retained in the interstices of the residual is controlled by the specified porosity (4). The viscosity of the mantle has a simple temperature dependence such that the asthenosphere has constant viscosity and there is an increase of two orders of magnitude for the viscosity of the lithosphere, whose base is marked by an isotherm (either 700 "C or 1000"C). Physical parameters that affect the pattern of mantle flow beneath a spreading centre include asthenosphere viscosity, the amount of melt retained in the mantle matrix, the degree of depletion of the residual mantle (how much melt has been removed), the temperature at which mantle becomes more rigid in the lithosphere, and the plate-spreading rate. A series of simulations in which these parameters were varied individually shows that viscosity plays the major role in controlling whether buoyancy effects dominate the flow structure. Fig. 1 shows that for an asthenosphere viscosity (p) of 10'' Pa s the flow is essentially a passive response to plate spreading. In 417 contrast, for p = 5 x 10" Pa s vertical flow rates are enhanced by a factor of three and the flow is focused beneath the axis in response to buoyant forces. About 20km off axis, the competing effects of depletion buoyancy, melt buoyancy and lithospheric thickening combine to force material to sink. Thus, a rather tight circulation pocket forms at depths of 40-70 km and distances of 20-50 km off-axis (Sotin 8~Parmentier 1989; Scott 1992). The finite strain that develops is quite different for these two models (Fig. 1, lower panels). There is notable vertical stretching beneath the axis for the buoyant case and high strains develop in the tight circulation region. The highly strained material is then rafted off-axis to create a layer of subhorizontally oriented strain ellipses at depths of 4-80 km. The orientations of the strain ellipses in the lithosphere are inclined counterclockwise to the horizontal in the passive-flow case, indicating that deformation continues to some extent within the plate. In the passive upwelling zone and below the base of the plate, the finite strain basically matches that predicted by McKenzie (1979) for a constant-viscosity cornerflow model. In the buoyant case the ellipses rotate clockwise towards the vertical near the base of the plate due to the relative motion between the lithosphere and the asthenosphere. The basic nature of the buoyant-flow regimes remains the same for a range of parameter choices, but the details vary with assumed melt retention factor (4, porosity), rigidus temperature of the lithosphere ( T )and spreading rate (SR). The flows depicted in Fig. 1 have 4=O.ll, ?;=700°C and SR= Figure 1. Models of flow and deformation fields for the buoyant case (right) and the passive case (left). Viscosity j1=5 x 10" Pa s for the buoyant case and p = 10'' Pa s for the passive case; melt retention Q =0.11; spreading rate = 18 mm yr-'; rigidus temperature T = 700 "C.Top: flow vectors overlying greyshade of the temperature field; solid lines show melt content increasing from 1 per cent (outermost contour) at intervals of 1 per cent; dashed lines show the fraction of mantle depletion increasing upwards from 0.04 at that interval. Bottom: finite strain ellipses for the flow models above. Strain begins to accumulate along flow lines (dotted lines) at 100 km depth in these cases. 0 1996 RAS, G J I 127,415-426 D.K . Blackman et al. 418 SR = 75 mm/yr 60 km 80 # *s-" I00 1 0 40 80 - 1 0 120 Tlith = 1000°C d e P t h km 1 0 40 ao 120 distance from axis (km) Figure 2. The dependence of finite strain on the physical parameters assumed in flow modelling. Values are as is Fig. 1 except where otherwise specified (viscosity p = 5 x 10" Pas; melt retention d=O.ll; spreading rate= 18 mm yr-'; rigidus temperature T = 700 "C). Top: SR=75 mm yr-l. A similar pattern of strain ellipses results for p = 10'' Pa s or $=0.06. Bottom: 7;=1000°C. 18 mm yr-' half-rate (the rate with respect to the ridge axis; relative motion between the two plates would be twice the half-rate). Relative to this reference, the strength of focusing and subaxial flow enhancement decreases similarly for either p = 10'' Pa s, 4=0.06 or S R = 7 5 mm yr-'. Fig. 2 (top) illustrates how the tight circulation region is muted for these parameter values and the lobe extending toward the ridge axis on the right in Fig. 1 is absent. The vertical stretching beneath the axis is reduced and the high-strain region at depth occurs only beyond 40 km off-axis. A value of 1000°C for 'I; results in a reduction in the magnitude of finite strain 10-30 km deep in the asthenosphere (Fig. 2, bottom), but the predicted orientations remain essentially the same as for 'I;= 700 "C (compare Fig. 2 and Fig. 1, left). Within the shallow lithosphere, the finite strain is greater for T = 1000 "C due to the higher velocity gradients within the wedge formed by the steeper isotherms directly beneath the ridge axis. 2.2 Development of mineral texture Texture simulations assumed a 'lower-bound' approach, which was described in some detail by Chaste1 et at. (1993). Initially aggregates having a random orientation distribution of 1000 grains are assumed to reside at each nodal point at the base of the texture model (100 km). The responses of these aggregates to the flow gradient are evaluated numerically using local incremental velocity gradients. Deformation is assumed to occur by slip on the four different slip systems documented for olivine (Bai, Mackwell & Kohlstedt 1991). Their activity is specified with the critical resolved shear stress (Table 1). A viscoplastic lower-bound model that favours stress equilibrium over strain compatibility has been chosen on the basis of the limited number of independent slip systems in olivine crystals. Earlier work found that the self-consistent theory (Wenk et al. 1991) and even a relaxed Taylor model (Takeshita et al. 1990) yield similar results in the case of olivine. Using the lowerbound approach, the stresses in all crystals of an aggregate are identical, trivially satisfying equilibrium. The deformation may vary from crystal to crystal, but the stress is constrained to ensure that the average of the crystal deformations equals the macroscopic deformation. By allowing the crystals within an aggregate to deform independently, it is possible to accommodate an arbitrary deformation while having only four slip systems in each crystal, provided that all crystals do not have equivalent orientations. Straining in general is non-uniform and variations in the deformation rate as great as a factor of two arise. This numerical approach does not incorporate possible effects of recrystallization (see Section 4), and, as is the case for nearly all polycrystal models, the lower-bound approach tends to overemphasize the role of texturing in polycrystal deformation. The predicted orientation distributions are qualitatively similar, although the strength of the determined fabrics may differ somewhat in intensity from those that would occur in actual peridotite. The calculated textures for the buoyant and passive flow models are quite different, as shown by pole figures of the [ 1001 and [OlO] axes of the olivine aggregates throughout the models (Fig. 3). Particularly important is the [ 1001 pole figure, which displays the distribution of fast seismic axes. Textures in the passive case develop below the base of the lithosphere so the thickness and depth extent of the layer with strong preferred orientation increases steadily off-axis. The buoyantcase textures can be broken into three regions, each with rather different characteristics: ( 1 ) a subaxial zone within 15-20 km of the ridge axis; (2) an intermediate zone about 15-40 km from the ridge axis; (3) an off-axis zone at distances greater than 40-50 km. During buoyant flow, the initially random distribution of aaxes quickly evolves to a distribution restricted to the x2-x3 plane directly below the ridge axis (x, is the horizontal, acrossaxis direction, x2 points into the page and x3 is vertical). At depths of 20-60 km and within 15 km of the axis, a high percentage of a-axes are oriented vertically. This high degree of alignment is reduced near the surface as the stagnation point in the flow is reached and material is incorporated into the lithosphere. This weakening of the fabric is expected as the Table 1. Active slip systems of olivine used in texture calculations. Slip-plane normal Slip direction Critical shear stress at 1400°C (0 10) (001) (0 1 0) (100) ClOOl ClOOl 15 MPa 16 MPa 40 MPa 35 MPa coo11 coo 11 0 1996 RAS, GJI 127, 415-426 Figure 3. Pole figures showing the calculated orientation distributions of 1000 olivine grains within the aggregate at each node point in the buoyant (right) and passive (left) models. The aggregates are undeformed at 100 km depth. Deformation of the grains within the aggregate is tracked as it moves along a streamline and is subjected to the gradients in flow velocity corresponding to the models shown in Fig. 1. The pole figures are equal-area projections in the x1-x3 plane. Top panels show [lo01 (a-axis) orientations (fast P direction); bottom panels show [OlO] (b-axis) orientations (slow P direction). The missing pole figures in the centre of the tight circulation region of the buoyant model indicate that the texture calculation was not used here (see text). The thick grey line shows the 700°C isotherm. Subaxial $ow at mid-ocean ridges 0 1996 RAS, GJI 127, 415-426 419 420 D.K . Blackman et al. orientation of the shear changes with respect to the axis of the texture orientation when the aggregate transits the near-axis region at shallow depths (Chaste1 et al. 1993). 15-30 km offaxis the a-axis girdle is inclined about 45" from the vertical at depths of 60-80 km. As the aggregates enter the tight circulation region, most a-axes migrate to the edge of the girdle, but some remain in the very centre (pointing out of the page). Flow gradients below the base of the lithosphere act to diffuse the olivine alignment. Thus, the a-axis concentrations are not as high in any single plane or direction at depths of 20-30 km in this intermediate region as they are directly beneath the axis. Further off-axis, the lithosphere is characterized by a shallow section with a diffuse a-axis girdle inclined 15-20" clockwise from horizontal. With depth in and below the lithosphere, this girdle is replaced by a better-defined one that is about 30" counterclockwise from horizontal, although many poles stay at the apex of a slightly rotated vestige of the shallow girdle. The b- and c-axis distributions are more diffuse in this region, although there is a tendency for the b-axes to congregate perpendicular to the a-axis girdles. A layer of strong preferred orientation occurs at depths of 65-85 km with [lo01 horizontal. At the top of this off-axis layer there is a strong maximum with [ 1001 pointing to the right but most of the layer shows varying a-axis directions throughout an x1-x2 plane. The b-axes tend to be vertical in the lower part of the layer. The tight circulation region presented difficulties in tracking several streamlines of the flow. The interpolation of flow rates between nodes implies the existence of a point of zero velocity within this region and a small zone of recirculation about that point. The textures for particles that experienced recirculation were not used in the computation of node-point stiffnesses since their relevance is questionable. The seismic model requires a continuous distribution of elastic parameters, so the values from the horizontally adjacent node points (3 km to the side rather than the 6 km spacing used in Fig. 3 for illustrative purposes) were assigned to the nodes at the centre of the recirculation zone. During passive flow, the most significant crystal alignment develops in the high-shear region below the base of the rigid lithosphere. A girdle of [loo] poles essentially parallels the base of the plate with subhorizontal orientations off-axis. Close to the axis, the girdles incline about 45", corresponding to the steep dip of the axial wedge formed by the plate; although it is difficult to discern in Fig. 3, there is a concentration in the plate-spreading direction within the horizontal projection of the girdle of a-axis directions. The definition of the preferredorientation plane is clearest about 20 km below the rigidus and slowly becomes more diffuse with depth. Above the base of the lithosphere, textures are diffuse, reflecting the competing effects of basal shear and the stress-free surface. [OlO] tends to align perpendicular to the [ 1001 girdle so that off-axis poles align 15-20' clockwise from vertical within the layer of preferred orientations. Below this layer, textures remain random for this model. The a-axes are only roughly aligned parallel to the flow directions: there are asymmetric deviations and large scatter. These deviations are due to simple shear, which has been discussed in detail by Wenk & Christie (1991) and for olivine by Wenk et a!. (1991). In summary, polycrystal plasticity simulations predict neither that slip directions align with flow lines (Francis 1969) nor that they align with the long strain- ellipsoid axes. This lack of clearly discernible behaviour was also observed experimentally in the field of dislocation slip (Zhang & Karato 1995), where deformed crystal alignment generally plotted between curves defined by the finite-strain orientation and the flow-parallel direction. 2.3 Velocity structure The texture predictions for each 1000-grain aggregate are expressed by the orientations of the constituent olivine crystals. The effective elasticity for each aggregate is calculated using a simple Voigt average of the stiffnesses (expressed as the fourthorder tensor cijkl) over all crystal orientations. Therefore, Cijkl for each olivine crystal must be rotated into a global coordinate system. In general, this results in 21 independent elastic constants from which the P- and S-wave velocities for a given nodal point and wavefront normal (or slowness) can then be calculated (Fig. 4; see Appendix of Kendall & Thomson 1989). Although monoclinic symmetry is expected due to the 2-D nature of the flow field, averaging the elastic constants for each crystal aggregate yields non-monoclinic terms that arise from the initially random crystal orientations. In practice these terms have little effect on the wave velocities as they are generally two orders of magnitude, or more, smaller than the 13 monoclinic elastic constants. To isolate the effects of the flow-induced anisotropy we have used very simple velocity models. The effects of heterogeneity due to the presence of melt and lithospheric thickening are not included here (we return to the subject of possible melt effects in the Discussion). The elastic models are 3-D, symmetric about the ridge axis and uniform along this axis. Although the flow and texture predictions of the previous section are for 2-D flow, the elastic model must be 3-D as wave propagation in anisotropic media is not necessarily confined to the sourcereceiver plane. Variations in the direction of maximum S-wave splitting generally do not coincide with the direction of maximum Pwave velocity, as is shown by the vectors in Fig.4. For the buoyant case, the only region where the two directions coincide is at the base of the off-axis layer 60-80 km deep. Throughout the rest of this model, maximum S-wave splitting tends to occur 35-45' from the direction of maximum P-wave velocity. In the passive case, the two directions do coincide more frequently, particularly in the layer beneath the lithosphere where the greatest preferred orientation develops. The degree of S-wave anisotropy is a few per cent lower than the degree of P-wave anisotropy at most of these locations. Differences in the direction of maximum P-wave velocity versus maximum S-wave splitting are typically 30-50" in the region below the wedge formed by the steep lithosphere within 30 km of the axis. The degree of anisotropy in the horizontal plane is generally somewhat lower than the maximum at a given location within the models due to the fact that preferred crystal orientation tends to be at an angle to the horizontal. In the passive case, there are somewhat greater a-axis concentrations in the spreading direction than in the other horizontal directions. This results in horizontal P-wave anisotropies of 2-8 per cent in the region near and below the base of the plate, fastest in the plate-spreading direction and at the higher values in the older part of the plate. In the buoyant model, horizontal P-wave anisotropies are low (1-4 per cent) in the upper 50 km, but 0 1996 RAS, GJI 127, 415-426 Subaxial $ow at mid-ocean ridges Passive Model 421 Buoyant Model O T T 0 100 km distance from axis 100 km 0 distance from axis Figure 4. Wave surfaces for the effective elastic parameters, cijkl,computed at each node point from the polycrystal distributions shown in Fig. 3. The outermost surface (heavy line) is the P wave and the inner surfaces (thin lines) are the S waves. The thick vector shows the direction of fastest P-wave propagation, and its length is proportional to the degree of anisotropy. The largest vectors correspond to 18 per cent anisotropy. The thin vector shows the direction/degree of maximum S-wave splitting, (Sfaat -Sslow)/Saverage, in the wavefront-normal direction. The scale for the degree of splitting is the same as for the P-wave anisotropy. - the high-strain layer at 60-80km depth has higher values (6-12 per cent). 3 BODY-WAVE PROPAGATION BENEATH A SPREADING CENTRE Wave propagation is simulated using a program designed to trace seismic rays through multilayered 3-D inhomogeneous anisotropic media with curved interfaces (Guest & Kendall 1993). The program is based on asymptotic ray theory for anisotropic media (cervenf 1972; Kendall & Thomson 1989). Density and 21 independent elastic constants are specified on a rectangular grid of knot points. A four-point 3-D cubic spline is used to interpolate between knot points, returning the required parameter and its first and second derivatives. These derivatives are required to solve the ray and geometricalspreading equations that track the ray and its amplitude through a given seismic velocity model (cerveni 1972). The ray angle of incidence on the bottom of the model is varied to simulate lower-mantle and core phases. Fig. 5 shows nearly vertically travelling P rays (PKP, corresponding to a compressional wave that travels through the Earth's core as well as the mantle) and the resulting traveltimes through the buoyant and passive models. In the buoyant model, traveltimes at the ridge axis are about a second earlier than arrivals further than 50km off-axis. This is due to the high-velocity subaxial region for vertically travelling P waves. The transition in this model from the axial region, which has high velocities compared to the surrounding lower-verticalvelocity regions, is sharp enough to cause wavefront folding and caustics. This produces traveltime triplications and increased amplitudes at about 40 km distance from the axis. In the passive-flow case, P-wave traveltimes are again predicted 0 1996 RAS, GJI 127, 415-426 to be earlier at the axis than off-axis but the magnitude of the relative delay at 100 km distance is about 0.5 s. Unlike the buoyant case, for which off-axis traveltimes are essentially constant beyond 50 km distance, the passive case is characterized by slowly but steadily increasing P-wave traveltimes off-axis. For both models, ray paths and traveltimes for P waves with an incident-ray angle of 25" (i.e. lower-mantle turning phase) are similar to the P K P results, but, relative to the axis, they are asymmetrical and the traveltime anomaly is somewhat larger. Because the model is anisotropic, at least two shear waves will arrive at the surface. Fig. 6 shows the predicted traveltimes for these quasi-orthogonally polarized shear waves. In the buoyant case, the shear wave polarized in the (quasi-) radial direction (particle motion in the x1-x3 plane) arrives at the ridge axis 0.8 s ahead of the shear wave that is polarized in the (quasi-) transverse direction (particle motion parallel to xz). Conversely, the off-axis region beyond 25 km in the buoyant model shows the opposite effect, with the transversely polarized shear wave leading the radially polarized shear wave. At the axis in the passive model, the radially polarized shear wave leads the transversely polarized wave by only a couple of tenths of a second. Off-axis the sense of polarization of the first- versus the second-arriving shear wave switches, similar to the buoyant case, but the time separation is about half that of the former model. For the buoyant model it is difficult to trace S waves of a single polarization vertically through the region 15-20km off-axis, since the two S wavesheets have similar velocities and energy is coupled between the polarization directions. Ray theory for anisotropic media is not strictly valid in regions where the S wavesheets cross, but these cases are easily monitored and the handful of S rays along which this occurred do not have traveltimes plotted in Fig. 6. 422 D.K . Blackman et al. Passive Model B u o y a n t Model ''.Or 10.51 i , , , f ........." a I t * *-. ....... ... * 8.0 8.5 1 -80 -40 0 40 80 d i s t a n c e from a x i s (km) -40 0 40 80 distance from a x i s ( k m ) Figure 5. Ray paths and traveltimes for near-vertical P waves that propagate through the anisotropic velocity models shown in Fig. 4. Buoyant model at right, passive at left. The complex shallow (10-40 km depth) velocity structure within 15-40 km of the axis acts to defocus energy in the buoyant model and to slightly focus it in the passive model. Traveltime triplication occurs 35-45 km off-axis in the buoyant case as the defocused rays cross other straighter rays. All rays arrive at the surface within 400 m of the cross-axis profile along which they started at 100 km depth, the base of the seismic model, and most are within 200m of the surface trace of the starting profile. Deviations from the starting profile are greater for the S waves near the axis than off-axis, or for the P waves in general. The amplitudes of body-wave arrivals contain diagnostic information about the underlying velocity structure. For example, comparison of P-wave amplitudes with S-wave amplitudes across the axis can suggest different types of structural complexity. In our models, high amplitudes for P waves are predicted at off-axis distances of 35-40 km in the buoyant case, as opposed to predictions of high S-wave amplitudes at distances of 10 km (radially polarized shear wave), or 0 and 42 km (transversely polarized). Amplitudes in the passive case display less variation across the profile, with only a small Pwave increase at the axis and small S-wave amplitude peaks at about 40 km off-axis. 4 DISCUSSION 4.1 Recognizing subaxial structure in teleseismic data The difference in teleseismic P-wave traveltimes predicted for the two models of mantle anisotropy at a spreading centre is substantial, suggesting that it should be possible to distinguish between passive and buoyancy-enhanced upwelling. The Pwave anomaly increases slowly with off-axis distance to a fraction of a second for the passive case. In contrast, for the buoyant case the U-shaped traveltime delay is predicted to increase away from the axis to about 40 km where it levels off at about 1 s relative to arrivals at the axis. This pattern could be resolved for teleseismic P waves whose angle of incidence is up to 30" from the vertical. Observing an axis-centred traveltime P-wave anomaly such as we predict would require an array of receivers deployed on the seafloor. The resolution of Global Seismic Network teleseismic data with surface bounce-points near the ridge will not, in general, be sufficient to image structures on the scale of a few tens of kilometres. P-wave traveltime anomalies across an array of ocean-bottom seismometers can be determined to within about 0.3 s accuracy in typical conditions (Blackman, Orcutt & Forsyth 1995), so a 1 s anomaly would be well above the uncertainty level. The nature of the traveltime anomaly predicted for anisotropy developed during mantle upwelling is similar to the pattern observed on the east flank of the southern mid-Atlantic ridge. A relative P-wave delay of about 0.5 s was observed between an ocean-bottom seismometer 25 km east of the axis and those 55-75 km off-axis on the same ridge flank (Blackman et al. 1993a; Blackman et al. 1995). This traveltime anomaly includes corrections for topographic effects, and contributions due to crustal structure are probably less than about 0.2 s (Tolstoy, Harding & Orcutt 1993). Although they do not conclusively show an axis-centred fast anomaly pattern, the sparse high-quality data from this experiment suggest that anisotropy may be a major contributor to the observed traveltimes. Seafloor experiments conducted to date have not been designed to image this type of structure so we must look to future data sets for constraints on whether the buoyant or passive models best explain the observations. Because of the 10s-100km lateral scale of the subaxial structure, it is unlikely that surface waves of 15-100 s periods can be used to examine the near-ridge anisotropy. Beyond 0 1996 RAS, GJI 127,415-426 Subaxial $ow at mid-ocean ridges Buoyant Model 18.0 17.5 (r, 17.0 -8 5 ********,** 16.5 ** *** - I I *** ********** f * * a, (r, 16.0 15.5 15.0 I I I I I I I I I I I I Passive Model 75.51 15.0‘ I -80 I I I I I -40 0 40 80 distance f r o m axis ( k m ) Figure 6 . Traveltimes for near-vertical, quasi-orthogonal S waves traced through the anisotropic velocity models illustrated in Fig. 4. The traveltime of the quasi-radially polarized shear wave is indicated by dots; that of the quasi-transversely polarized shear wave is shown by asterisks. For both models, the polarization of the first-arriving shear wave at the axis is opposite to that of the first-arriving shear wave more than 40km off axis. The off-axis splitting should be resolvable in both cases, although the prediction for the buoyant model is twice that for the passive model. In practice, resolving the predicted axial splitting may be possible in the buoyant case but is unlikely for the passive case. about 70 km off-axis, on the other hand, surface waves could provide constraints on whether a layer of subhorizontal fastaxis alignment occurs, as is predicted for all models of buoyancy-enhanced flow. Given a sufficiently small resolution kernel [30-40 km depth extent, such as could be expected at the upper end of observable frequencies (15-25 s periods) in oceanic data (Blackman et aE. 1995)] in the appropriate depth range (at the base of the lithosphere in the passive case or 60-80 km depth in the buoyant case), one might discern a layer whose properties differ significantly from those of the surrounding media. We find that fairly thin ‘layers’ with high degrees of anisotropy are expected to result from mantle deformation at a spreading centre rather than thicker layers with low degrees of anisotropy. In the buoyant case, the layer that is rafted offaxis after material transits the tight circulation region has Pand S-wave anisotropies up to 18 per cent and 14 per cent respectively. Values directly beneath the axis in this model also reach 12-18 per cent for P waves travelling at depths of 30-60 km. The highest degree of P-wave anisotropy in the 0 1996 RAS, GJI 127, 415-426 423 passive case is about 12 per cent and occurs in a layer about 30 km thick beneath the base of the lithosphere. This is important since many studies determine fairly low degrees of anisotropy but the region in which the interpreted anisotropy occurs is limited or not well constrained. Raitt et al. (1969) and Shearer & Orcutt (1985) determined P-wave anisotropies of 6-8 per cent in the uppermost several kilometres of the oceanic mantle. Nishimura & Forsyth (1989) determined Swave anisotropies of about 2 per cent for upper-mantle regions 10s to 100 km thick. On land, S K S studies (e.g. Silver & Chan 1991) assumed a value of 4 per cent anisotropy to interpret SKS data in terms of subcontinental mantle anisotropy. Our results suggest that the actual degree of anisotropy may be substantial but that it occurs over a smaller region. Interpreting P-wave traveltimes alone to determine anisotropic velocity structure does not provide a unique answer; only through a combined analysis of P- and S-wave traveltimes, and of the variations in their amplitude, do we stand a chance of narrowing the field of candidate models. The predicted offaxis shear-wave splitting is twice as large for the buoyant model as it is for the passive model. The deep U-shaped traveltime anomaly pattern and its levelling off beyond 40-50 km is characteristic of the P waves in the buoyant case. This type of signal would be expected for a range of flow models where buoyant flow rates are of the order of, or larger than, passive flow rates. 4.2 Limitations of modelling approach Our numerically linked calculations of flow, mineral texture and its seismic velocity signature, and anisotropic ray tracing produce a consistent picture of the structure of the upper mantle beneath a spreading centre. We can have confidence in our predictions of the velocity structure to the extent that we believe we have captured the essential physics of the systems abstracted in our computer codes. One important aspect that we cannot directly quantify is that of the recrystallization of deforming minerals and the influence it may have on mantle textures. The effect of recrystallization on olivine preferred orientation has been the subject of study for some time (Ave’Lallement & Carter 1970; Karato 1994). A definitive explanation of olivine behaviour during shear flow is not yet available but recent work by Zhang & Karato (1995) indicates that subgrain rotation may be the dominant mechanism for dynamic recrystallization at the temperatures and pressures expected in the upper mantle beneath spreading centres. If this is indeed the case, our texture estimates should be reasonable representations since the deformation mechanism we have employed will remain the operative mechanism during subgrain rotation. If olivine grains recrystallize with a texture that reflects the local stress field (Karato 1988), the regions of our model that would be most affected are the very high-strain areas just below the lithosphere and the tight circulation region for buoyant flow. In the case of the latter, material that transits the circulation lobe will experience a continuously changing stress field so it is unlikely that any strong preferred orientation of recrystallized grains would result. Note that even under the assumption of shear-induced deformation, the rather high degree of alignment that forms on the upgoing limb of the lobe is diffused as the aggregates follow the streamlines around and back down off-axis (Fig. 3). 424 D. K . Blackman et al. Our assumption of a simple stepwise temperature dependence of mantle viscosity influences the details of the strain field within which texture develops, but the nature of our predictions would not change drastically if a more realistic viscosity field was used. The 3-D spreading-centre flow field calculated using a stepwise temperature-dependent viscosity (Blackman & Forsyth 1992) is quite similar to the flow predicted for fully temperature- and depth-dependent viscosity (Shen & Forsyth 1992). Schubert, Froidevaux & Yuen (1976) showed that with a self-consistent thermo-mechanical flow model, the region of high strain near the base of the lithosphere is fairly narrow for plate ages of 10 Myr (120 km off-axis in our models), but that the transition in mantle strength broadens significantly with age. This suggests that the basic pattern of texture that we predict for the region within 100 km of the axis is robust; a more complete model would likely predict further textural evolution off-axis. Incorporation of the effects of melt in the mantle could significantly modify our seismic predictions in the axial region, particularly for the S waves. We chose to examine the effects of anisotropy alone for two reasons: (1) the possible contribution of this aspect of the seismic structure is more easily understood in isolation; (2) the effect that melt may have on wave propagation depends very strongly on the nature of melt distribution, which is not well known (e.g. Schmeling 1985; Forsyth 1992). In the passive-flow model, the melt fractions are low, exceeding 0.02, melt/(melt+matrix), only in a small region just below the axis (Fig. 1). Kendall (1994) estimated that such small melt contents, uniformly distributed in pennyshaped pores within the melt zone, would produce a P-wave traveltime delay with an axial maximum of less than 0.2 s and a monotonic decrease in delay away from the axis as the thickness of the melt region decreases. The corresponding passive-case S-wave delays reached 0.4 s at the axis (Kendall 1994). In our buoyant model, melt fractions reach 0.06 in the shallowest part of the melt zone, increasing steadily from 0.01 at 70 km depth where melting begins. For this model, melt is restricted to a region within about 20 km of the axis, much narrower than in the passive case. If the melt is uniformly distributed in grain intersections, a narrow axial P-wave delay of about half a second could result. Kendall (1994) showed that if melt is distributed in thin, vertically aligned cracks, the introduced anisotropy can result in S-wave splitting of up to 2 s near the axis. A more complete series of ray-tracing experiments, with a range of assumed melt geometries and distributions (Blackman & Kendall 1996), suggests that even in the higher-melt-fraction buoyant case the textural anisotropy signal dominates the P-wave traveltime anomaly pattern. The presence of melt complicates the shear-wave signal but the effect is to accentuate the shape of the traveltime anomaly predicted for the texture-only models. We have assumed that the peridotite arrives at the 100 km deep base of the texture model with a random orientation, a simplification that allows us to investigate the structure associated only with the upwelling and melting beneath the spreading centre. If material encounters significant flow gradients elsewhere in its journey through the mantle, our predicted texturing would act to modify pre-existing fabrics. As discussed by Chaste1 et al. (1993), mantle textures are likely to be reset at the olivine-to-spinel phase transition. These authors show that broad convective cells develop preferred orientation planes about 30" off-vertical in the upwelling zone. Imposing the texturing that we calculate for the local region around the spreading centre on such pre-existing structure should not produce major differences in the end result since the sense of texturing is the same as we determine. If, on the other hand, there is significant lateral flow in the upper mantle as it is fed to a spreading centre (e.g. Phipps Morgan & Smith 1992). the pre-existing textures may be quite different. The orientation of pre-existing texture does affect the evolution of subsequent alignments since the activation of a usually easy slip system may not be possible if most grains are not favourably aligned (note the way textures evolve near the axial stagnation point in our models-the nature of the textures that develop off-axis reflect, to some extent, the fact that a fairly strong texture already exists due to deformation in the upwelling zone). The flow gradients in the buoyant model beneath the axis and in the tight circulation regions are most likely much higher than gradients that would occur due to larger-scale mantle flow. Thus, we would expect that deformation associated with the very localized buoyancy forces would dominate the texture development near the axis as soon as material enters the melting region (about 70 km depth). There is clearly no direct relationship between the olivine orientation distributions that we determine from the texture calculations and the distribution that would be inferred from the finite strain (compare the lower panels in Fig. 1 and the Pwave anisotropy vectors in Fig. 4). It has previously been suggested that the preferred orientation of olivine a-axes will follow the finite-strain ellipse (e.g. McKenzie 1979; Ribe 1989; Ribe & Yu 1989), and computing the finite strain associated with a given flow field is much less computationally demanding than the texture calculation. Using such models may be applicable for a certain material in a limited range of conditions but this cannot be generalized. By choosing an ad hoc linear relationship between finite-strain magnitude and degree of anisotropy, we can produce P-wave traveltime anomalies that are similar in shape to those determined from the full analysis (Blackman et al. 1993b) but we are unable to match simultaneously the magnitude of the predicted delays for buoyant and passive models. 5 CONCLUSIONS Deformation by intracrystalline slip in olivine during viscous mantle flow beneath an oceanic spreading centre results in a strong preferred orientation in peridotites and significant seismic anisotropy in the upper 100 km of the mantle. Our linked numerical models of flow, texture development and anisotropic wave propagation provide quantitative insight into how thin layers of high anisotropy can characterize regions of rapid variation in the flow field of the upper mantle. Very different distributions of shear-induced olivine alignment are determined for passive upwelling versus buoyancyenhanced upwelling. In the passive case, the strongest preferred orientation develops at and below the base of the lithosphere, the fast P-wave axis of olivine grains tending to parallel the plate base. In the buoyant case, strong vertical alignment occurs directly beneath the ridge axis due to focusing of the flow and a tight circulation lobe forms in response to the focusing. The associated texture development produces a 60-80 km deep layer of subhorizontally aligned fast seismic axes that is rafted away off-axis. Ray tracing through these generally anisotropic structures 0 1996 RAS, GJI 127, 415-426 Subaxial flow at mid-ocean ridges indicates that sufficient across-axis variation would exist to produce observable signals on an array of seafloor instruments with apertures of about 100 km. 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