Uncertainties in seismic inverse calculations

Abstract

As in all such calculations, seismic inversion requires careful estimation of prior information and data uncertainties in order to be able to make quantitative inferences about the Earth. The prior information comes from diverse sources, some of which may best be incorporated as hard constraints on parameters or functions of parameters, and some which may best be described probabilistically. There are also sources of subjective prior information from experts. It is important that we assimilate such information consistently and quantitatively. In the event that all the uncertainties can be treated as being Gaussian random variables, this information conveniently takes the form of model and data covariance matrices. In that case, the computational formalism applied is superficially similar to Tikhonov regularization, or constrained least squares, although the goals and conclusions are potentially rather different. But in some cases such Gaussian assumptions may not be justified. In the general case, in which the probability distribution associated with the prior information can only be sampled point-wise, it may be necessary to use an importance sampling procedure based on Monte Carlo methods. But this begs the question of how one estimates such a general prior probability. I have given some suggestions as to how these probabilities may be estimated, but I suspect we are a long way from a definitive answer to this question.