ALBERT

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: 〈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: 〈span〉〈div〉SUMMARY〈/div〉A study is presented using a meshfree approach and a radial basis function generated finite difference (RBF-FD) method for numerically modelling three-dimensional (3-D) gravity data. The gravity responses, i.e., vertical gravity and gravity gradients, are obtained by solving the partial differential equation (PDE), that is, the Poisson’s equation for gravitational potential. The meshfree approach discretises PDEs using exclusively a cloud of unconnected nodes, instead of traditional tessellated meshes as used by mesh-based numerical methods such as finite difference, finite element and finite volume. Thus, the potentially computationally expensive and unstable creation and manipulation of 3-D meshes can be entirely avoided. A new type of finite-smoothness radial basis functions (RBFs), namely, the quintic-order polyharmonic spline (PHS) RBF, is proposed here in the RBF-FD frame for solving the gravity problem. Previous geophysical data modelling studies using RBF-FD have employed the infinitely smooth RBFs, such as the popular Gaussian (GA) RBFs. Here, both GA and PHS RBFs were tested with different numbers of nodes per meshfree subdomain and with various shape parameter values (only GA RBFs have a shape parameter). The test results show that the PHS RBF-FD method is more computationally efficient than the GA RBF-FD counterpart. To achieve more efficiency, unstructured node distributions are proposed in discretising the density models. For both quasi-uniform and unstructured node distributions, numerical results from the proposed PHS RBF-FD demonstrate that the computed vertical gravity and gravitational potential values agree well with analytical solutions with a reasonable number of degrees of freedom. A comparison study of modelling a complex density model with the PHS RBF-FD scheme and nodal finite-element method shows that the RBF-FD scheme generates sparse, asymmetric, linear systems of equations, supports unstructured nodal discretisation and local refinement, and can have non-linear 〈span〉h〈/span〉-convergence under refinement. Finally, the proposed RBF-FD method was applied to obtain the vertical gravity and gravity gradients over a real-world density model, where the benefits of meshfree discretisation are clearly illustrated.〈/span〉

Description: Understanding the patterns of genetic diversity and adaptation across species’ range is crucial to assess its long-term persistence and determine appropriate conservation measures. The impacts of human activities on the genetic diversity and genetic adaptation to heterogeneous environments remain poorly understood in the marine realm. The roughskin sculpin (Trachidermus fasciatus) is a small catadromous fish, and has been listed as a second-class state protected aquatic animal since 1988 in China. To elucidate the underlying mechanism of population genetic structuring and genetic adaptations to local environments, RAD tags were sequenced for 202 individuals in nine populations across the range of T. fasciatus in China. The pairwise FST values over 9,271 filtered SNPs were significant except that between Dongying and Weifang. All the genetic clustering analysis revealed significant population structure with high support for eight distinct genetic clusters. Both the minor allele frequency spectra and Ne estimations suggested extremely small Ne in some populations (e.g., Qinhuangdao, Rongcheng, Wendeng, and Qingdao), which might result from recent population bottleneck. The strong genetic structure can be partly attributed to genetic drift and habitat fragmentation, likely due to the anthropogenic activities. Annotations of candidate adaptive loci suggested that genes involved in metabolism, development, and osmoregulation were critical for adaptation to spatially heterogenous environment of local populations. In the context of anthropogenic activities and environmental change, results of the present population genomic work provided important contributions to the understanding of genetic differentiation and adaptation to changing environments.