Summary. We present forward and adjoint spectral-element simulations of coupled acoustic and (an)elastic seismic wave propagation on fully unstructured hexahed

We present a methodology to compute 3-D global seismic wavefields for realistic earthquake sources in visco-elastic anisotropic media, covering applications across the observable seismic frequency band with moderate computational resources. This is accommodated by mandating axisymmetric background models that allow for a multipole expansion such that only a 2-D computational domain is needed, whereas the azimuthal third dimension is computed analytically on the fly. This dimensional collapse opens doors for storing space–time wavefields on disk that can be used to compute Fréchet sensitivity kernels for waveform tomography. We use the corresponding publicly available AxiSEM (www.axisem.info) open-source spectral-element code, demonstrate its excellent scalability on supercomputers, a diverse range of applications ranging from normal modes to small-scale lowermost mantle structures, tomographic models, and comparison with observed data, and discuss further avenues to pursue with this methodology.

We present a tomographic model of radially anisotropic shear velocity variations in the Earth's mantle based on a new compilation of previously published data sets and a variable block parameterization, adapted to local raypath density. We employ ray‐theoretical sensitivity functions to relate surface wave and body wave data with radially anisotropic velocity perturbations. Our database includes surface wave phase delays from fundamental modes up to the sixth overtone, measured at periods between 25 and 350 s, as well as cross‐correlation traveltimes of major body wave phases. Before inversion, we apply crustal corrections using the crustal model CRUST2.0, and we account for azimuthal anisotropy in the upper mantle using ray‐theoretical corrections based on a global model of azimuthal anisotropy. While being well correlated with earlier models at long spatial wavelength, our preferred solution, savani, additionally delineates a number of previously unidentified structures due to its improved resolution in areas of dense coverage. This is because the density of the inverse grid ranges between 1.25° in well‐sampled and 5° in poorly sampled regions, allowing us to resolve regional structure better than it is typically the case in global S wave tomography. Our model highlights (i) a distinct ocean‐continent anisotropic signature in the uppermost mantle, (ii) an oceanic peak in above average ξ<1 which is shallower than in previous models and thus in better agreement with estimates of lithosphere thickness, and (iii) a long‐wavelength pattern of ξ<1 associated with the large low‐shear velocity provinces in the lowermost mantle.

We present a new method and implementation (Instaseis) to store global Green's functions in a database which allows for near-instantaneous (on the order of milliseconds) extraction of arbitrary seismograms. Using the axisymmetric spectral element method (AxiSEM), the generation of these databases, based on reciprocity of the Green's functions, is very efficient and is approximately half as expensive as a single AxiSEM forward run. Thus, this enables the computation of full databases at half the cost of the computation of seismograms for a single source in the previous scheme and allows to compute databases at the highest frequencies globally observed. By storing the basis coefficients of the numerical scheme (Lagrange polynomials), the Green's functions are 4th order accurate in space and the spatial discretization respects discontinuities in the velocity model exactly. High-order temporal interpolation using Lanczos resampling allows to retrieve seismograms at any sampling rate. AxiSEM is easily adaptable to arbitrary spherically symmetric models of Earth as well as other planets. In this paper, we present the basic rationale and details of the method as well as benchmarks and illustrate a variety of applications. The code is open source and available with extensive documentation at www.instaseis.net .

An important goal of computational seismology is to simulate dynamic earthquake rupture and strong ground motion in realistic models that include crustal heterogeneities and complex fault geometries. To accomplish this, we incorporate dynamic rupture modelling capabilities in a spectral element solver on unstructured meshes, the 3-D open source code SPECFEM3D, and employ state-of-the-art software for the generation of unstructured meshes of hexahedral elements. These tools provide high flexibility in representing fault systems with complex geometries, including faults with branches and non-planar faults. The domain size is extended with progressive mesh coarsening to maintain an accurate resolution of the static field. Our implementation of dynamic rupture does not affect the parallel scalability of the code. We verify our implementation by comparing our results to those of two finite element codes on benchmark problems including branched faults. Finally, we present a preliminary dynamic rupture model of the 2011 M_w 9.0 Tohoku earthquake including a non-planar plate interface with heterogeneous frictional properties and initial stresses. Our simulation reproduces qualitatively the depth-dependent frequency content of the source and the large slip close to the trench observed for this earthquake.