SUMMARY Core-refracted phases such as SKS and SKKS are commonly used to probe seismic anisotropy in the upper and lowermost portions of the Earth’s mantle. Measurements of SK(K)S splitting are often interpreted in the context of ray theory, and their frequency dependent sensitivity to anisotropy remains imperfectly understood, particularly for anisotropy in the lowermost mantle. The goal of this work is to obtain constraints on the frequency dependent sensitivity of SK(K)S phases to mantle anisotropy, particularly at the base of the mantle, through global wavefield simulations. We present results from a new numerical approach to modelling the effects of seismic anisotropy of arbitrary geometry on seismic wave propagation in global 3-D earth models using the spectral element solver AxiSEM3D. While previous versions of AxiSEM3D were capable of handling radially anisotropic input models, here we take advantage of the ability of the solver to handle the full fourth-order elasticity tensor, with 21 independent coefficients. We take advantage of the computational efficiency of the method to compute wavefields at the relatively short periods (5 s) that are needed to simulate SK(K)S phases. We benchmark the code for simple, single-layer anisotropic models by measuring the splitting (via both the splitting intensity and the traditional splitting parameters ϕ and δt) of synthetic waveforms and comparing them to well-understood analytical solutions. We then carry out a series of numerical experiments for laterally homogeneous upper mantle anisotropic models with different symmetry classes, and compare the splitting of synthetic waveforms to predictions from ray theory. We next investigate the full wave sensitivity of SK(K)S phases to lowermost mantle anisotropy, using elasticity models based on crystallographic preferred orientation of bridgmanite and post-perovskite. We find that SK(K)S phases have significant sensitivity to anisotropy at the base of the mantle, and while ray theoretical approximations capture the first-order aspects of the splitting behaviour, full wavefield simulations will allow for more accurate modelling of SK(K)S splitting data, particularly in the presence of lateral heterogeneity. Lastly, we present a cross-verification test of AxiSEM3D against the SPECFEM3D_GLOBE spectral element solver for global seismic waves in an anisotropic earth model that includes both radial and azimuthal anisotropy. A nearly perfect agreement is achieved, with a significantly lower computational cost for AxiSEM3D. Our results highlight the capability of AxiSEM3D to handle arbitrary anisotropy geometries and its potential for future studies aimed at unraveling the details of anisotropy at the base of the mantle.
We present a novel numerical method to simulate global seismic wave propagation in realistic aspherical 3-D earth models across the observable frequency band of global seismic data. Our method, named AxiSEM3D, is a hybrid of spectral element method (SEM) and pseudospectral method. It describes the azimuthal dimension of global wavefields with a substantially reduced number of degrees of freedom via a global Fourier series parametrization, of which the number of terms can be locally adapted to the inherent azimuthal complexity of the wavefields. AxiSEM3D allows for material heterogeneities, such as velocity, density, anisotropy and attenuation, as well as for finite undulations on radial discontinuities, both solid–solid and solid–fluid, and thereby a variety of aspherical Earth features such as ellipticity, surface topography, variable crustal thickness, undulating transition zone and core–mantle boundary topography. Undulating discontinuities are honoured by means of the 'particle relabelling transformation', so that the spectral element mesh can be kept spherical. The implementation of the particle relabelling transformation is verified by benchmark solutions against a discretized 3-D SEM, considering ellipticity, topography and bathymetry (with the ocean approximated as a hydrodynamic load) and a tomographic mantle model with an undulating transition zone. For the state-of-the-art global tomographic models with aspherical geometry but without a 3-D crust, efficiency comparisons suggest that AxiSEM3D can be two to three orders of magnitude faster than a discretized 3-D method for a seismic period at 5 s or below, with the speed-up increasing with frequency and decreasing with model complexity. We also verify AxiSEM3D for localized small-scale heterogeneities with strong perturbation strength. With reasonable computing resources, we have achieved a corner frequency of up to 1 Hz for 3-D mantle models.
SUMMARY We present a new approach to simulate high-frequency seismic wave propagation in and under the oceans. Based upon AxiSEM3D, this method supports a fluid ocean layer, with associated water-depth phases and seafloor topography (bathymetry). The computational efficiency and flexibility of this formulation means that high-frequency calculations may be carried out with relatively light computational loads. A validation of the fluid ocean implementation is shown, as is an evaluation of the oft-used ocean loading formulation, which we find breaks down at longer periods than was previously believed. An initial consideration of the effects of seafloor bathymetry on seismic wave propagation is also given, wherein we find that the surface waveforms are significantly modified in both amplitude and duration. When compared to observed data from isolated island stations in the Pacific, synthetics which include a global ocean and seafloor topography appear to more closely match the observed waveform features than synthetics generated from a model with topography on the solid surface alone. We envisage that such a method will be of use in understanding the new and exciting ocean-bottom and floating seismometer data sets now being regularly collected.
Abstract The lowermost mantle right above the core-mantle boundary shows a complex and heterogeneous landscape containing multiple poorly understood seismic features visible across a wide range of length scales. The smallest, but most extreme, heterogeneities yet observed are 'Ultra-Low Velocity Zones' (ULVZ), several of which have recently been linked to the base of mantle plumes. We exploit seismic shear waves that diffract along the core-mantle boundary to provide new insight into these enigmatic structures. We demonstrate that these waves have a strong frequency-dependent sensitivity to structure at different length scales above the core-mantle boundary, similar to the dispersive characteristics of surface waves. We measure a rare core-diffracted signal refracted by a ULVZ at the base of the Hawaiian mantle plume at unprecedented high frequencies. This signal shows remarkably longer time delays compared to lower frequencies, indicating extreme internal variability within the Hawaiian ULVZ. Utilizing the latest computational advances in 3D synthetic waveform modeling, we are able to model this high frequency signal and constrain high-resolution structure on the scale of kilometers at the core-mantle boundary, for the first time. Results reveal that the lowermost part of the Hawaiian ULVZ is extremely reduced in shear wave velocity, by up to -40%. This new observation suggests a chemically distinct ULVZ with increasing iron content towards the core-mantle boundary, which has implications for Earth’s early evolutionary history and core-mantle interaction.
SUMMARY Small-scale heterogeneities in the Earth’s mantle, the origin of which is likely compositional anomalies, can provide critical clues on the evolution of mantle convection. Seismological investigation of such small-scale heterogeneities can be facilitated by forward modelling of elastic wave scattering at high frequencies, but doing so with conventional 3-D numerical methods has been computationally prohibitive. We develop an efficient approach for computing high-frequency synthetic wavefields originating from small-scale mantle heterogeneities. Our approach delivers the exact elastodynamic wavefield and does not restrict the geometry or physical properties of the local heterogeneity and the background medium. It combines the technique of wavefield injection and a numerical method called AxiSEM3D. Wavefield injection can decompose the total wavefield into an incident and a scattered part. Both these two parts naturally have low azimuthal complexity and can thus be solved efficiently using AxiSEM3D under two different coordinate systems. With modern high-performance computing (on an order of magnitude of 105 CPU-hr), we have achieved a 1 Hz dominant frequency for global-scale problems with strong deep Earth scattering. Compared with previous global injection approaches, ours allows for a 3-D background medium and yields the exact solution without ignoring any higher-order scattering by the background medium. Technically, we develop a traction-free scheme for realizing wavefield injection in a spectral element method, which brings in several flexibilities and simplifies the implementation by avoiding stress or traction computation on the injection boundary. For a spherical heterogeneity in the mid-lower mantle, we compare the 3-D full-wave solution with two approximate ones obtained, respectively, by the perturbation theory and in-plane (axisymmetric) modelling. As a comprehensive application, we study S-wave scattering by a 3-D ultra-low velocity zone, incorporating 3-D crustal structures on the receiver side as part of the background model.
Abstract The entry, descent, and landing (EDL) sequence of NASA's Mars 2020 Perseverance Rover will act as a seismic source of known temporal and spatial localization. We evaluate whether the signals produced by this event will be detectable by the InSight lander (3,452 km away), comparing expected signal amplitudes to noise levels at the instrument. Modeling is undertaken to predict the propagation of the acoustic signal (purely in the atmosphere), the seismoacoustic signal (atmosphere‐to‐ground coupled), and the elastodynamic seismic signal (in the ground only). Our results suggest that the acoustic and seismoacoustic signals, produced by the atmospheric shock wave from the EDL, are unlikely to be detectable due to the pattern of winds in the martian atmosphere and the weak air‐to‐ground coupling, respectively. However, the elastodynamic seismic signal produced by the impact of the spacecraft's cruise balance masses on the surface may be detected by InSight. The upper and lower bounds on predicted ground velocity at InSight are 2.0 × 10 −14 and 1.3 × 10 −10 m s −1 . The upper value is above the noise floor at the time of landing 40% of the time on average. The large range of possible values reflects uncertainties in the current understanding of impact‐generated seismic waves and their subsequent propagation and attenuation through Mars. Uncertainty in the detectability also stems from the indeterminate instrument noise level at the time of this future event. A positive detection would be of enormous value in constraining the seismic properties of Mars, and in improving our understanding of impact‐generated seismic waves.
SUMMARY Observations of seismic anisotropy at the base of the mantle are abundant. Given recent progress in understanding how deformation relates to anisotropy in lowermost mantle minerals at the relevant pressure and temperature conditions, these observations can be used to test specific geodynamic scenarios, and have the potential to reveal patterns of flow at the base of the mantle. For example, several recent studies have sought to reproduce measurements of shear wave splitting due to D″ anisotropy using models that invoke specific flow and texture development geometries. A major limitation in such studies, however, is that the forward modelling is nearly always carried out using a ray theoretical framework, and finite-frequency wave propagation effects are not considered. Here we present a series of numerical wave propagation simulation experiments that explore the finite-frequency sensitivity of SKS, SKKS and ScS phases to laterally varying anisotropy at the base of the mantle. We build on previous work that developed forward modelling capabilities for anisotropic lowermost mantle models using the AxiSEM3D spectral element solver, which can handle arbitrary anisotropic geometries. This approach enables us to compute seismograms for relatively short periods (∼4 s) for models that include fully 3-D anisotropy at moderate computational cost. We generate synthetic waveforms for a suite of anisotropic models with increasing complexity. We first test a variety of candidate elastic tensors in laterally homogeneous models to understand how different lowermost mantle elasticity scenarios express themselves in shear wave splitting measurements. We then consider a series of laterally heterogeneous models of increasing complexity, exploring how splitting behaviour varies across the edges of anisotropic blocks and investigating the minimum sizes of anisotropic heterogeneities that can be reliably detected using SKS, SKKS and ScS splitting. Finally, we apply our modelling strategy to a previously published observational study of anisotropy at the base of the mantle beneath Iceland. Our results show that while ray theory is often a suitable approximation for predicting splitting, particularly for SK(K)S phases, full-wave effects on splitting due to lowermost mantle anisotropy can be considerable in some circumstances. Our simulations illuminate some of the challenges inherent in reliably detecting deep mantle anisotropy using body wave phases, and point to new strategies for interpreting SKS, SKKS and ScS waveforms that take full advantage of newly available computational techniques in seismology.
