Uncertainty Analysis in Prestack Stratigraphic Inversion - A First Insight

Stratigraphic inversion of prestack seismic data allows the determination of subsurface elastic parameters (density, P and S-impedances). Based on a Bayesian approach, the problem is formulated as a non-linear least-squares local optimization problem. The objective function to be minimized is composed of two terms, the first one measures the mismatch between the synthetic seismic data (computed via a forward operator) and the observed seismic data, the second one models geological a priori information on the subsurface model. It is crucial to estimate the a posteriori uncertainties because the solution model of the inversion is only one solution among the range of admissible models that fit the data and the a priori information . The goal of this paper is to propose an optimized deterministic method to estimate a posteriori uncertainties in stratigraphic inversion. The proposed method is based on the hypothesis that the covariance matrices describing the uncertainties on the data and on the model are laterally uncorrelated (no cross correlation among parameters of different traces). Moreover, the covariance matrix on the data is also supposed laterally stationary. Application on 2D synthetic PP data illustrates the performances of the method. Extensions and limitations of the method are discussed.