Broadband Waveform Sensitivity Kernels for Large-Scale Seismic Tomography
Abstract:Seismic sensitivity kernels, i.e. the basis for mapping misfit functionals to structural parameters in seismic inversions, have received much attention in recent years. Their computation has been conducted via ray-theory based approaches (Dahlen et al., 2000) or fully numerical solutions based on the adjoint-state formulation (e.g. Tromp et al., 2005). The core problem is the exuberant computational cost due to the large number of source-receiver pairs, each of which require solutions to the forward problem. This is exacerbated in the high-frequency regime where numerical solutions become prohibitively expensive.
We present a methodology to compute accurate sensitivity kernels for global tomography across the observable seismic frequency band. These kernels rely on wavefield databases computed via AxiSEM (abstract ID# 77891, www.axisem.info), and thus on spherically symmetric models. As a consequence of this method's numerical efficiency even in high-frequency regimes, kernels can be computed in a time- and frequency-dependent manner, thus providing the full generic mapping from perturbed waveform to perturbed structure. Such waveform kernels can then be used for a variety of misfit functions, structural parameters and refiltered into bandpasses without recomputing any wavefields.
A core component of the kernel method presented here is the mapping from numerical wavefields to inversion meshes. This is achieved by a Monte-Carlo approach, allowing for convergent and controllable accuracy on arbitrarily shaped tetrahedral and hexahedral meshes. We test and validate this accuracy by comparing to reference traveltimes, show the projection onto various locally adaptive inversion meshes and discuss computational efficiency for ongoing tomographic applications in the range of millions of observed body-wave data between periods of 2-30s.