Wavefield Reconstruction in the Presence of a Dipping Layer

Abstract

The accuracy of a model obtained by full-waveform inversion can be estimated by analysing the sensitivity of the data to perturbations of the model parameters in selected subsurface points. Each perturbation requires the computation of the seismic response in the form of Born scattering data for a typically very large number of shots, making the method time consuming. The computational cost can be significantly reduced by considering the point where the subsurface parameters are perturbed as a Born scatterer. Instead of modelling each shot separately, reciprocity relations provide the Green functions from the sources to the scatterer in terms of Green’s functions from the scatterer to the sources. In this way, the Born scattering data from a single point in the isotropic elastic case for a marine acquisition with pressure sources and receivers can be expressed in terms of the Green functions for force and moment tensor sources located at the scatterer and only a small number of forward runs are required. A 2-D example illustrates how the result can be used to determine the hessian and local covariance matrix for the model parameters at the scatterer at the cost of 5 forward simulation.