Direct waveform inversion via iterative inverse propagation

Abstract

SUMMARYSeismic waves are the most sensitive probe of the Earth's interior we have. With the dense data sets available in exploration, images of subsurface structures can be obtained through processes such as migration. Unfortunately, relating these surface recordings to actual Earth properties is non-trivial. Tomographic techniques use only a small amount of the information contained in the full seismogram and result in relatively low resolution images. Other methods use a larger amount of the seismogram but are based on either linearization of the problem, an expensive statistical search over a limited range of models, or both. We present the development of a new approach to full waveform inversion, i.e., inversion which uses the complete seismogram. This new method, which falls under the general category of inverse scattering, is based on a highly non-linear Fredholm integral equation relating the Earth structure to itself and to the recorded seismograms. An iterative solution to this equation is proposed. The resulting algorithm is numerically intensive but is deterministic, i.e., random searches of model space are not required and no misfit function is needed. Impressive numerical results in 1D are shown for several test cases.

Extended Diffraction Tomography

“…More recently, advances in the area of inverse scattering theory (Weglein et al, 2003;Schlottmann, 2006) have arisen that may have the potential of solving the nonlinear full-waveform inversion problem more quickly and efficiently. However, these methods rely on having an efficient and reliable method of solving the linear waveform inversion problem, i.e., the problem that results from assuming that the wave propagation can be approximated by first-order scattering, yielding a linear relationship between the data and the unknown subsurface structure.…”