Time-domain waveform modeling and inversion from millimeters to the Globe

Time-domain waveform modeling and inversion from millimeters to the Globe

By Christian Böhm of ETH

Abstract: Waveform inversion has become a powerful tool for parameter estimation in many exciting domains such as seismic tomography, medical imaging, and non-destructive testing. Despite the vastly different scales, all these applications have in common that they can be stated as a PDE-constrained optimization problem governed by some variant of the time-dependent wave equation that invert for unknown material properties or external forces.
In this talk we present Salvus, an HPC software package designed to solve large-scale full-waveform inverse problems, with a focus on both flexibility and performance. Salvus is a collection of packages covering the complete toolchain of waveform inversion, ranging from creating unstructured meshes in two and three dimensions to an automated, interactive and graph-based workflow management framework capable of orchestrating all necessary components. The wave equation solver is based on a high-order spectral-element discretization and supports a diverse collection of wave propagation physics, such as viscoelasticity or solid-fluid coupling. Adjoint-based computations of gradients and Hessian-vector products as well as custom-tailored compression methods are built-in, which allows a tight integration with optimization methods to solve the inverse problem.
Salvus bridges the gap between research and production codes with a design based on C++ template mixins and Python wrappers that separate the physical equations from the numerical core. It was constructed by following modern software design practices, testing protocols, and by establishing its foundations upon existing high-level scientific libraries, such as PETSc and Eigen.
The goal of this presentation is to introduce the code and its underlying mathematical framework. Furthermore, we show several numerical examples across the scales.

Organizer:
Martin Hammerschmidt, Zuse-Institut Berlin (ZIB)
Bereich Numerische Mathematik
Abteilung Numerische Analysis und Modellierung
Takustr. 7, D-14195 Berlin-Dahlem