Résumé:
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.
