Maximum-Likelihood Seismic Deconvolution

The purpose of this paper is to describe a broad spectrum of seismic deconvolution problems and solutions which we refer to collectively as maximum-likelihood (seismic) deconvolution (MLD). Our objective is to perform deconvolution and wavelet estimation for the case of nonminimum phase wavelets. Our approach is to exploit state-variable technology, maximum-likelihood estimation, and a sparse spike train (Bernoulli-Gaussian) model for the reflection signal. Our solution requires detection of significant reflectors, wavelet and variance identification (nonlinear optimization), and estimation of the spike density parameter.     

Identifiability of nonminimum phase linear stochastic systems

This paper considers the identifiability of time-invariant non-minimum phase systems for the ease of unobserved white Gaussian driving noise and no control input. It is shown that a sufficient condition for identifiability is that the driving noise should have a known time-varying perpetually exciting variance. Simulation results are given which support the theory.