Wences' Inverse Theory Home Page

Take a look at this to get a feel for the research ideas you will find here.

Check the following items:

A comprehensive software library for Bayesian inverse calculations. The library provides the capability of inverting seismic waveform reflection data under the assumption of a stratified medium. Petrophysical information in the form of well-log data can be included in the inversion process aiming at reducing the uncertainty on the final estimates (P-wave and S-wave impedances and bulk density). Given the high computational cost of this particular calculation this library resorts to parallel computer architectures to a large extent.

The Bayesian library was used to generate all the results you will find in my PhD thesis "Bayesian Seismic Waveform Data Inversion: Parameter Estimation and Uncertainty Analysis." Here are chapters 1, 2, 3 and 4 and here are chapters 5 and 6 and the appendixes of the thesis.

A couple of inversion papers you may find useful:

A predecessor of the paper "Resolution of seismic waveform inversion: Bayes versus Occam." This was published in Inverse Problems, 13, 1997, pp.323-349.
A predecessor of the paper "Bayesian seismic waveform inversion: Parameter estimation and uncertainty analysis." This was published in the Journal of Geophysical Research, 103, B2, 1998, pp. 2759-2779. Essentially this paper describes the methodology proposed in my thesis to a field seismic data set.
A tutorial on entropy and its potential application to Bayesian inversion.