Monte Carlo full waveform inversion of tomographic crosshole data using complex geostatistical a priori information

Abstract

This paper presents a Monte Carlo full waveform inversion strategy based on a Bayesian formulation of the inverse problem. Existing full waveform inversion strategies often relies on a migration based approach, which suffers from lack of uncertainty estimates. Using a Bayesian approach, the solution to the inverse problem is formulated as an a posteriori probability density. We demonstrate that samples from the solution to the full waveform inverse problem can be obtained using the extended Metropolis algorithm in conjunction with complex a priori information. The a priori information is described by a training image using a geostatistical algorithm. A posteriori samples from the solution to the inverse problem provide a means of obtaining resolution analysis of the solution. The suggested strategy is tested on synthetic crosshole full waveform ground penetrating radar (GPR) data, but is equally well applicable to seismic waveform data. The forward problem is solved using finite‐difference time‐domain calculations of Maxwell's equations. To our knowledge this is the first example of performing full waveform inversion using the extend Metropolis Algorithm and, in this way, provide an uncertainty estimate of a tomographic full waveform inverse problem.