Probabilistic Approach to Seismic Waveform Inversion

Abstract

Elastic waves carry substantial information about the characteristics of the medium they propagate in. However, most of the current methods which use elastic waves for engineering evaluations, only utilize a limited portion of this information, such as peak return frequency or dispersion curve. Seismic waveform inversion is a relatively new technique for engineering applications, which seeks to use full information content of the seismic waveform. The objective of the waveform inversion is to find a reasonable subsurface model which its theoretically predicted waveforms match reasonably well the observed waveforms. The inversion of seismic data in general and waveform inversion in particular can be carried out using either a deterministic or a probabilistic approach. In the deterministic approach, a single model is identified as the problem solution, which implicitly assumed there are no uncertainties in the problem. However, in the probabilistic approach uncertainties in the data and forward model are included in the analysis and their effects on the obtained results are evaluated as a part of the solution. The probabilistic seismic waveform inversion is introduced in this paper as a robust technique for subsurface evaluations in engineering applications. To provide the background, the probabilistic approach to inversion is presented in general terms and a technique for its numerical implementation using Monte Carlo Markov Chains (MCMC) with Neighborhood Algorithm (NA) approximation is outlined. Seismic waveform inversion for shallow subsurface evaluation is then described, and the results of a waveform inversion experiment using synthetic data are presented.