Speaker:  Guillermina Senn, PhD Candidate, Department of Mathematical Sciences, Norwegian University of Science and Technology

Title: Bayesian Seismic Wavelet and Subsurface Estimation via Gibbs Sampling on a Cyclic Domain

Abstract:

In geophysics, seismic data is often modeled as the convolution of an unknown true subsurface property with an unknown seismic wavelet. In this work, we introduce a Bayesian model and an associated Gibbs sampler to jointly estimate both the wavelet and the subsurface property over a 2D regular lattice. Sampling from the resulting posterior distribution with Gibbs sampling is computationally demanding due to matrix operations whose dimensions scale non-linearly with the number of observations. To address this challenge, we embed the seismic data lattice within an extended cyclic lattice. This gives circulant properties to all large matrices involved in the Gibbs updates, which in turn allows computationally intensive matrix operations to be efficiently performed using Fourier techniques. Application of our method to real data from an offshore gas reservoir in Egypt demonstrates convergence within reasonable computational time.