Full waveform inversion using Gaussian process emulation

Developing efficient FWI using PSimPy and NEXD or SPECFEM

Thesis details
Full waveform inversion using Gaussian process emulation
  • 6 months
  • M.Sc.
  • 90% Programming
  • 80% Field work
  • 10% Lab work
  • 60% Theory
  • 70% Processing
  • 60% Interpretation
  • 50% Geology
Contact person
Marc S. Boxberg's profile picture's profile picture
Dr. rer. nat.
Marc S. Boxberg
 Postdoctoral researcher and deputy director
+49 241 / 80 99755

Emulation, also known as surrogate modeling or meta-modeling, is a type of method which is used to build cheap-to-evaluate emulators (surrogate models) to approximate expensive-to-evaluate simulators. It can greatly reduce computational costs of tasks in which a computationally intensive simulator needs to be run multiple times, such as a global sensitivity anlaysis, uncertainty quantification, or parameter calibration. Full waveform modeling can be such an expensive-to-evaluate simulator depending on the size of the computational model. This is especially important when it comes to the problem of full waveform inversion (FWI). FWI methods are among the most recent and most promising techniques for geophysical site characterization, and are still under continuous development. The method is fairly general, and is capable of imaging arbitrarily heterogeneous compressional and shear wave velocity distributions in the subsurface. FWI generally needs a forward code, that solves the wave equation (e.g., NEXD or SPECFEM) as well as code to solve the inverse problem (e.g., PSimPy). Typically the latter is done using methods like conjugate gradients with adjoint or sensitivity kernels. However, statistical methods may be used as well. The latter often give access to quantities related to uncertainty analysis and are, therefore, of great interest. This project aims at developing a FWI workflow leveraging on Gaussian process emulation based on open-source software packages.

Your tasks:

  • Implement an interface between PSimPy and the numerical solver (either NEXD or SPECFEM)
  • Run synthetic tests to show the capabilities of the Gaussian process emulation with respect to FWI
  • Application to real world data (e.g., ultrasound transmission experiments on rock samples)

Supplementary Documents

Zhao, H. (2021). Gaussian processes for sensitivity analysis, Bayesian inference, and uncertainty quantification in landslide research. Dissertation, RWTH Aachen University, doi: 10.18154/RWTH-2021-11693.

Lambrecht, L., Lamert, A., Friederich, W., Möller, T., and Boxberg, M. S. (2018). A nodal discontinuous Galerkin approach to 3-D viscoelastic wave propagation in complex geological media. Geophysical Journal International, 212(3):1570–1587, doi: 10.1093/gji/ggx494.

Komatitsch, D., Tromp, J. (2002). Spectral-element simulations of global seismic wave propagation — I. Validation, Geophysical Journal International, 149(2):390–412, doi: 10.1046/j.1365-246X.2002.01653.x.

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