Blind marine seismic deconvolution using statistical MCMC methods

Abstract

In order to improve the resolution of seismic images, a blind deconvolution of seismic traces is necessary, since the source wavelet is not known and cannot be considered as a stationary signal. The reflectivity sequence is modeled as a Gaussian mixture, depending on three parameters (high and low reflector variances and reflector density), on the wavelet impulse response, and on the observation noise variance. These parameters are unknown and must be estimated from the recorded trace, which is the reflectivity convolved with the wavelet, plus noise. Two methods are compared in this paper for the parameter estimation. Since we are considering an incomplete data problem, we first consider maximum likelihood estimation by means of a stochastic expectation maximization (SEM) method. Alternatively, proper prior distributions can be specified for all unknown quantities. Then, a Bayesian strategy is applied, based on a Monte Carlo Markov Chain (MCMC) method. Having estimated the parameters, one can proceed to the deconvolution. A maximum posterior mode (MPM) criterion is optimized by means of an MCMC method. The deconvolution capability of these procedures is checked first on synthetic signals and then on the seismic data of the IFREMER ESSR4 campaign, where the wavelet duration blurs the reflectivity, and on the SMAVH high-resolution marine seismic data.

Blind Deconvolution of Sparse Pulse Sequences Under a Minimum Distance Constraint: A Partially Collapsed Gibbs Sampler Method

“…The problem of blind deconvolution (BD) arises in many applications where some desired signal is to be recovered from a distorted observation, e.g., in digital communications [1]- [5], seismology [6]- [9], biomedical signal processing [10]- [13], and astronomy [14], [15]. The BD problem is ill-posed since different input sequences and impulse responses can provide the same observation.…”

“…The Gibbs sampler is a simple and widely used MCMC method with interesting properties for BD [9], [24], [26], [31]; however, it is computationally inefficient when there are strong dependencies among the parameters [23], [32]. Such dependencies are caused by our minimum distance constraint, since a nonzero indicator b k determines all indicators within a certain neighborhood to be zero.…”

Multichannel Deconvolution of Seismic Signals Using Statistical MCMC Methods

“…[10]. The second algorithm which utilizes more information in the estimation process of each reflectivity column is shown to produce better results than the first algorithm.…”

“…The parameters θ can be estimated using the stochastic expectation maximization algorithm of Rosec et al [10]. Let y j denote the jth trace of the seismic data.…”

“…These parameters along with the reflectivity sequence are estimated using a Markov Chain Monte Carlo (MCMC) method called a Gibbs sampler [8], [9]. Rosec et al [10] use a moving average wavelet and model the reflectivity sequence as a mixture of Gaussian distributions [11]. They propose two parameter estimation methods.…”