Fast Iterative Solution of the Time-Harmonic Elastic Wave Equation at Multiple Frequencies

Fast Iterative Solution of the Time-Harmonic Elastic Wave Equation at Multiple Frequencies

Baumann, M.M. (TU Delft Numerical Analysis)

Vuik, Cornelis (promotor)
van Gijzen, M.B. (copromotor)

Delft University of Technology

2018-01-10

Seismic Full-Waveform Inversion is an imaging technique to better understand the earth's subsurface. Therefore, the reflection intensity of sound waves is measured in a field experiment and is matched with the results from a computer simulation in a least-squares sense. From a computational point-of-view, but also from an economic view point, the efficient numerical solution of the elastic wave equation on current hardware is the main bottleneck of the computations, especially when a large three-dimensional computational domain is considered. In our research, we focused on an alternative problem formulation in frequency-domain. The mathematical challenge then becomes to efficiently solve the time-harmonic elastic wave equation at multiple frequencies. The resulting sequence of shifted linear systems is solved with a new framework of Krylov subspace methods derived for this specific problem formulation. Our numerical analysis gives insight in the theoretical convergence behavior of the new algorithm.

Krylov subspace methods
Preconditioning
Shifted linear systems
Time-harmonic elastic wave equation
MSSS matrix computations
Spectral analysis

https://doi.org/10.4233/uuid:b1024bc5-46ad-450e-a3d3-090a166a67a7

978-94-6295-827-2

Institutional Repository

doctoral thesis

© 2018 M.M. Baumann