Adding Prior Information in FWI Formalism Through Relative Entropy
Seismic Processing, Prior Information, Entropy, FWI, Regularized
Full waveform inversion is an advantageous technique to obtain high-resolution subsurface information. In the petroleum industry (mainly in reservoir characterisation) it is common to use information from wells as previous information to decrease the ambiguity of the obtained results. Consequently, we propose to add a relative entropy term to the formalism of the full waveform inversion. In this context, entropy will be just a nomenclature for regularisation and it will have the role of helping the converge to the global minimum. The application of entropy in inverse problems usually formulates the problem to allow statistical concepts to be used. To avoid this step, we propose a deterministic application to the full waveform inversion. We will discuss some aspects of relative entropy and we show three different ways of using them to add prior information through entropy in the inverse problem. We use a dynamic weighting scheme to add prior information through entropy. The idea is that the prior information can help to find the path of the global minimum at the beginning of the inversion process. In all cases, the prior information can be incorporated very quickly into the full waveform inversion and this leads the inversion to the desired solution. When we include the logarithmic weighting that constitutes entropy to the inverse problem, we suppress the low-intensity ripples and sharpen the point events. Thus, the addition of entropy relative to full waveform inversion can provide a result with a better resolution.
In regions where salt is present in the BP 2004 model, we obtained a significant improvement by adding prior information through the relative entropy for synthetic data. We show that the prior information added through entropy in full-waveform inversion formalism can help to avoid local minimums.