Scalable Bayesian seismic wavelet estimation

In seismic amplitude-versus-angle data, the forward model connecting the elastic properties with the data involves the convolution of seismic reflection coefficients with a wavelet. If the wavelet is erroneously specified, the modelled seismic will be biased and associated seismic inversion results will be difficult to trust. Therefore, it is of interest to estimate the wavelet from the observations, prior to the seismic inversion. An existing Bayesian estimation procedure proposes a Bayesian model for the problem and explores the posterior distribution with a Gibbs sampler algorithm. However, the algorithmic complexity scales non-linearly with the number of observations, thus limiting input data to elastic well-log data and seismic data at the well. We adopt a similar hierarchical Bayesian model but introduce a computationally efficient Gibbs sampler to allow estimation from large two-dimensional seismic images. The efficiency is obtained by embedding the seismic image in an extended cyclic lattice so that large matrices acquire circulant properties and expensive matrix operations can be done with the fast Fourier transform. We include results for simulated datasets and a real dataset from an offshore gas reservoir in Egypt.