ALBERT

Description: Measurements of seismic anisotropy are commonly used to constrain deformation in the upper mantle. Observations of anisotropy at mid-mantle depths are, however, relatively sparse. In this study we probe the anisotropic structure of the mid-mantle (transition zone and uppermost lower mantle) beneath the Japan, Izu-Bonin, and South America subduction systems. We present source-side shear wave splitting measurements for direct teleseismic S phases from earthquakes deeper than 300 km that have been corrected for the effects of upper mantle anisotropy beneath the receiver. In each region, we observe consistent splitting with delay times as large as 1 s, indicating the presence of anisotropy at mid-mantle depths. Clear splitting of phases originating from depths as great as ~600 km argues for a contribution from anisotropy in the uppermost lower mantle as well as the transition zone. Beneath Japan, fast splitting directions are perpendicular or oblique to the slab strike and do not appear to depend on the propagation direction of the waves. Beneath South America and Izu-Bonin, splitting directions vary from trench-parallel to trench-perpendicular and have an azimuthal dependence, indicating lateral heterogeneity. Our results provide evidence for the presence of laterally variable anisotropy and are indicative of variable deformation and dynamics at mid-mantle depths in the vicinity of subducting slabs.

Description: 〈span〉〈div〉Summary〈/div〉The investigation of using a novel radial basis function-based meshfree method for forward modelling magnetotelluric data is presented. The meshfree method, which can be termed radial basis function-based finite difference (RBF-FD), uses only a cloud of unconnected points to obtain the numerical solution throughout the computational domain. Unlike mesh-based numerical methods (for example, grid-based finite difference, finite volume and finite element), the meshfree method has the unique feature that the discretization of the conductivity model can be decoupled from the discretization used for numerical computation, thus avoiding traditional expensive mesh generation and allowing complicated geometries of the model be easily represented. To accelerate the computation, unstructured point discretization with local refinements are employed. Maxwell’s equations in the frequency domain are re-formulated using $\mathbf {A}$-ψ potentials in conjuction with the Coulomb gauge condition, and are solved numerically with a direct solver to obtain magnetotelluric responses. A major obstacle in applying common meshfree methods in modelling geophysical electromagnetic data is that they are incapable of reproducing discontinuous fields such as the discontinuous electric field over conductivity jumps, causing spurious solutions. The occurrence of spurious, or non-physical, solutions when applying standard meshfree methods is removed here by proposing a novel mixed scheme of the RBF-FD and a Galerkin-type weak-form treatment in discretizing the equations. The RBF-FD is applied to the points in uniform conductivity regions, whereas the weak-form treatment is introduced to points located on the interfaces separating different homogeneous conductivity regions. The effectiveness of the proposed meshfree method is validated with two numerical examples of modelling the magnetotelluric responses over three-dimensional conductivity models.〈/span〉

Description: SUMMARY Measurements of the splitting or birefringence of seismic shear waves constitute a powerful and popular technique for characterizing azimuthal anisotropy in the upper mantle. The increasing availability of data sets from dense broad-band seismic arrays has driven interest in the development of techniques for the tomographic inversion of shear wave splitting data and in comparing splitting measurements with anisotropic upper-mantle models obtained from other constraints, such as surface wave analysis. Two different theoretical approaches have been developed for predicting apparent shear wave splitting parameters (fast direction and delay time) for models that include multiple layers of anisotropy at depth, which is useful for comparing azimuthally anisotropic surface wave models with shear wave splitting measurements. These approaches differ in one key aspect, which is whether or not the shear wave splitting operator can be treated as commutative. In this paper, we investigate the theoretical source of this discrepancy, and show that at frequencies relevant to most studies of upper-mantle anisotropy, the term that results in the non-commutivity of the shear wave splitting operator in the expressions for multiple-layer splitting must be retained. In contrast, the quantity known as the splitting intensity, which is closely related to the apparent fast direction and delay time, does commute at these frequencies. We illustrate these inferences with forward modelling examples and discuss their implications for the tomographic inversion of shear wave splitting measurements, the comparison of surface wave models with shear wave splitting observations and the joint inversion of surface wave and shear wave splitting observations for upper-mantle anisotropic models.

Description: 〈span〉〈div〉SUMMARY〈/div〉Different mechanisms have been proposed as explanations for seismic anisotropy at the base of the mantle, including crystallographic preferred orientation of various minerals (bridgmanite, post-perovskite and ferropericlase) and shape preferred orientation of elastically distinct materials such as partial melt. Investigations of the mechanism for D" anisotropy usually yield ambiguous results, as seismic observations rarely (if ever) uniquely constrain a mechanism or orientation and usually rely on significant assumptions to infer flow patterns in the deep mantle. Observations of shear wave splitting and polarities of SdS and PdP reflections off the D" discontinuity are among our best tools for probing D" anisotropy; however, currently available data sets cannot constrain one unique scenario among those suggested by the mineral physics literature. In this work, we determine via a forward modelling approach what combinations of body wave phases (e.g. SKS, SKKS and ScS) are required to uniquely constrain a mechanism for D" anisotropy. We test nine models based on single-crystal and polycrystalline elastic tensors provided by mineral physics studies. Our modelling predicts fast shear wave splitting directions for SKS, SKKS and ScS phases, as well as polarities of 〈span〉P-〈/span〉 and 〈span〉S-〈/span〉wave reflections off the D" interface, for a range of propagation directions, via solution of the Christoffel equation. We run tests using randomly selected synthetic data sets based on a given starting model, controlling the total number of measurements, the azimuthal distribution, and the type of seismic phases. For each synthetic data set, we search over all possible elastic tensors and orientations to determine which are consistent with the synthetic data. Overall, we find it difficult to uniquely constrain the mechanism for anisotropy with a typical number of seismic anisotropy measurements (based on currently available studies) with only one measurement technique (SKS, SKKS, ScS or reflection polarities). However, data sets that include SKS, SKKS and ScS measurements or a combination of shear wave splitting and reflection polarity measurements increase the probability of uniquely constraining the starting model and its orientation. Based on these findings, we identify specific regions (i.e. North America, northwestern Pacific and Australia) of the lowermost mantle with sufficient ray path coverage for a combination of measurement techniques.〈/span〉

Description: 〈span〉〈div〉SUMMARY〈/div〉The investigation of using a novel radial-basis-function-based mesh-free method for forward modelling magnetotelluric data is presented. The mesh-free method, which can be termed as radial-basis-function-based finite difference (RBF-FD), uses only a cloud of unconnected points to obtain the numerical solution throughout the computational domain. Unlike mesh-based numerical methods (e.g. grid-based finite difference, finite volume and finite element), the mesh-free method has the unique feature that the discretization of the conductivity model can be decoupled from the discretization used for numerical computation, thus avoiding traditional expensive mesh generation and allowing complicated geometries of the model be easily represented. To accelerate the computation, unstructured point discretization with local refinements is employed. Maxwell’s equations in the frequency domain are re-formulated using $\mathbf {A}$-ψ potentials in conjunction with the Coulomb gauge condition, and are solved numerically with a direct solver to obtain magnetotelluric responses. A major obstacle in applying common mesh-free methods in modelling geophysical electromagnetic data is that they are incapable of reproducing discontinuous fields such as the discontinuous electric field over conductivity jumps, causing spurious solutions. The occurrence of spurious, or non-physical, solutions when applying standard mesh-free methods is removed here by proposing a novel mixed scheme of the RBF-FD and a Galerkin-type weak-form treatment in discretizing the equations. The RBF-FD is applied to the points in uniform conductivity regions, whereas the weak-form treatment is introduced to points located on the interfaces separating different homogeneous conductivity regions. The effectiveness of the proposed mesh-free method is validated with two numerical examples of modelling the magnetotelluric responses over 3-D conductivity models.〈/span〉

Description: 〈span〉〈div〉Summary〈/div〉Different mechanisms have been proposed as explanations for seismic anisotropy at the base of the mantle, including crystallographic preferred orientation of various minerals (bridgmanite, post-perovskite, and ferropericlase) and shape preferred orientation of elastically distinct materials such as partial melt. Investigations of the mechanism for D" anisotropy usually yield ambiguous results, as seismic observations rarely (if ever) uniquely constrain a mechanism or orientation and usually rely on significant assumptions to infer flow patterns in the deep mantle. Observations of shear wave splitting and polarities of SdS and PdP reflections off the D" discontinuity are among our best tools for probing D" anisotropy; however, currently available datasets cannot constrain one unique scenario among those suggested by the mineral physics literature. In this work, we determine via a forward modeling approach what combinations of body wave phases (e.g. SKS, SKKS, and ScS) are required to uniquely constrain a mechanism for D" anisotropy. We test nine models based on single-crystal and polycrystalline elastic tensors provided by mineral physics studies. Our modeling predicts fast shear wave splitting directions for SKS, SKKS, and ScS phases, as well as polarities of P and S wave reflections off the D" interface, for a range of propagation directions, via solution of the Christoffel equation. We run tests using randomly selected synthetic datasets based on a given starting model, controlling the total number of measurements, the azimuthal distribution, and the type of seismic phases. For each synthetic dataset, we search over all possible elastic tensors and orientations to determine which are consistent with the synthetic data. Overall, we find it difficult to uniquely constrain the mechanism for anisotropy with a typical number of seismic anisotropy measurements (based on currently available studies) with only one measurement technique (SKS, SKKS, ScS, or reflection polarities). However, datasets that include SKS, SKKS, and ScS measurements or a combination of shear wave splitting and reflection polarity measurements increase the probability of uniquely constraining the starting model and its orientation. Based on these findings, we identify specific regions (i.e. North America, northwestern Pacific, and Australia) of the lowermost mantle with sufficient raypath coverage for a combination of measurement techniques.〈/span〉

Description: 〈span〉〈div〉SUMMARY〈/div〉Here we develop a theoretical and practical framework for the tomographic inversion of shear wave splitting intensity measurements for anisotropic structure in the upper mantle using a model space search approach. Treating the anisotropic scatterers as a first order perturbation to the background isotropic state, we implement the Born approximation to compute the integral sensitivity kernels in a finite frequency framework. We implement a parametrization of the anisotropy based on insights from olivine elasticity and fabric development that involves three parameters (corresponding to the azimuth and dip of the anisotropic symmetry axis, plus a strength parameter). Previous work on finite-frequency shear wave splitting tomography has implemented a linearization technique to invert splitting intensity data for the spatial distribution of anisotropic scatterers. The inverse problem, however, is strongly non-linear in terms of several of the involved parameters (those that describe the orientation of the symmetry axis), and their variation is not of first order. Therefore, in the case of a realistic upper mantle where anisotropic structure varies in a complicated manner, a linearization technique may not be adequate. To ameliorate these problems, we implement a model space search approach (specifically, a Markov chain Monte Carlo with Gibbs sampling algorithm) to the tomographic inversion of splitting intensity data. This approach allows for the visualization of posterior probability distributions for anisotropic parameters in the inversion. We perform a suite of synthetic resolution tests to demonstrate the reliability of our method, using a station distribution from an actual deployment of a dense seismic network. These resolution tests show that anisotropic structure may be resolved up to a length scale of roughly 50 km with teleseismic SKS waves for station spacing of 10–15 km.〈/span〉

Description: 〈span〉〈div〉Summary〈/div〉Here we develop a theoretical and practical framework for the tomographic inversion of shear wave splitting intensity measurements for anisotropic structure in the upper mantle using a model space search approach. Treating the anisotropic scatterers as a first order perturbation to the background isotropic state, we implement the Born approximation to compute the integral sensitivity kernels in a finite frequency framework. We implement a parameterization of the anisotropy based on insights from olivine elasticity and fabric development that involves three parameters (corresponding to the azimuth and dip of the anisotropic symmetry axis, plus a strength parameter). Previous work on finite-frequency shear wave splitting tomography has implemented a linearization technique to invert splitting intensity data for the spatial distribution of anisotropic scatterers. The inverse problem, however, is strongly non-linear in terms of several of the involved parameters (those that describe the orientation of the symmetry axis), and their variation is not of first order. Therefore, in the case of a realistic upper mantle where anisotropic structure varies in a complicated manner, a linearization technique may not be adequate. To ameliorate these problems, we implement a model space search approach (specifically, a Markov chain Monte Carlo with Gibbs sampling algorithm) to the tomographic inversion of splitting intensity data. This approach allows for the visualization of posterior probability distributions for anisotropic parameters in the inversion. We perform a suite of synthetic resolution tests to demonstrate the reliability of our method, using a station distribution from an actual deployment of a dense seismic network. These resolution tests show that anisotropic structure may be resolved up to a length scale of roughly 50 km with teleseismic SKS waves for station spacing of  10-15 km.〈/span〉

Description: Two arrays of broad-band seismic stations were deployed in the north central Andes between 8° and 21°S, the CAUGHT array over the normally subducting slab in northwestern Bolivia and southern Peru, and the PULSE array over the southern part of the Peruvian flat slab where the Nazca Ridge is subducting under South America. We apply finite frequency teleseismic P - and S -wave tomography to data from these arrays to investigate the subducting Nazca plate and the surrounding mantle in this region where the subduction angle changes from flat north of 14°S to normally dipping in the south. We present new constraints on the location and geometry of the Nazca slab under southern Peru and northwestern Bolivia from 95 to 660 km depth. Our tomographic images show that the Peruvian flat slab extends further inland than previously proposed along the projection of the Nazca Ridge. Once the slab re-steepens inboard of the flat slab region, the Nazca slab dips very steeply (~70°) from about 150 km depth to 410 km depth. Below this the slab thickens and deforms in the mantle transition zone. We tentatively propose a ridge-parallel slab tear along the north edge of the Nazca Ridge between 130 and 350 km depth based on the offset between the slab anomaly north of the ridge and the location of the re-steepened Nazca slab inboard of the flat slab region, although additional work is needed to confirm the existence of this feature. The subslab mantle directly below the inboard projection of the Nazca Ridge is characterized by a prominent low-velocity anomaly. South of the Peruvian flat slab, fast anomalies are imaged in an area confined to the Eastern Cordillera and bounded to the east by well-resolved low-velocity anomalies. These low-velocity anomalies at depths greater than 100 km suggest that thick mantle lithosphere associated with underthrusting of cratonic crust from the east is not present. In northwestern Bolivia a vertically elongated fast anomaly under the Subandean Zone is interpreted as a block of delaminating lithosphere.