SVD analysis in application to full waveform inversion of multicomponent seismic data

An inverse problem of recovery the Earth's interior by multi-shot/multi-offset multicomponent seismic data is considered in this work. This problem may be considered as a nonlinear operational equation, and local derivative-based techniques are commonly used for its solution. Such method is known in seismic precessing as "full-waveform inversion". The major properties of the inversion process are governed by a Frechet derivative of the forward map. We show and study these properties by means of singular value decomposition(SVD) truncation. This decomposition depends strongly on the acquisition system and on the parameterization of the problem. We show, that it is very important to study the inverse problem in each particular case, otherwise unreliable results may be obtained. Surface and cross-well acquisition systems are considered in this work. Appropriate parameterizations for them are determined, and typical behavior of the inverse problem solution is studied.