Providing for uncertainty in non-linear inversions of geophysical data

摘要

A method of obtaining a 3D model of the sub-surface comprises providing a first approximation of said model, and performing simulations using the model to generate (i) a reference upgoing energy wave data set do, where the acquisition parameters used in the simulation are a set of known acquisition parameters, and (ii) a plurality of perturbed data sets d„ where the acquisition parameters are obtained by randomly perturbing known acquisition parameters. A matrix D is formed, the columns of which are the differences d, — do between the ith perturbed data set and the reference data set. The matrix D is described using a set of vectors, the most important vectors being taken as a subset of vectors describing matrix D to an approximation. An iterative procedure improves said first approximation of said model, or a further approximation model. At each step of the procedure, a model update Dm is determined, the model update minimising a measure of the data misfit between said upgoing energy wave data set and a data set simulated using the updated model, said measure using said subset of vectors to account for uncertainty in the upgoing energy wave data set.