Nonlinear Inversion by Stochastic Relaxation With Applications to Residual Statics Estimation
, by Daniel Rothman
Several data processing problems in reflection seismology are cast as
general inverse problems, and are solved by maximizing the posterior
probability of a model, given the observed data and prior probability
function for the model. Both the Beyesian solution and the
computational techniques employed may be generally applicable: no
assumptions of local probabilities of the model parameters exhibit
local dependencies, or, specifically, that the model be expressible as
a stochastic process called a Markov random field. Maximizing posterior
probabilities for this relatively unrestricted class of problems is
usually considered to be computationally intractable due to the
existence of many local extrema. By making an analogy to statistical
physics, however, it is shown that many large-scale nonlinear inverse
problems that exhibit these local characteristics may be solved by a
method that can yield solutions superior to previous efforts. This
inversion procedure I successfully applied to the problem of residual
statics estimation. The well-known problem of "cycle-skipping" is
effectively attacked because no assumptions of local linearity are
made. Further applications and extensions of the method are proposed.
STANFORD