Adaptive traveltime inversion with information entropy regularization

A recently introduced Adaptive Traveltime Inversion (ATI) provided us with a robust misfit function for reducing cycle skipping in Full-Waveform Inversion (FWI). Unlike the conventional L2-norm approach, ATI computes a matching filter first by deconvolution of the predicted data with the measured ones. If the velocity model is relatively accurate, the resulting matching filter is close to a Dirac delta function. Its traveltime shift, which characterizes the defocusing of the matching filter, is computed by minimization of the cross-correlation between a penalty function like t2 and the matching filter. ATI is constructed by minimization of the least square errors of the calculated traveltime shifts. It has been shown that the resulting traveltime shift corresponds to a first-order moment, which corresponds to the mean value of the resulting matching filter distribution. In order to accelerate the convergence and improve the robustness of the ATI approach, in this abstract, we propose to constraint the variance of the resulting matching filter using an information entropy function. We further demonstrate that, in comparison to AWI which tries to minimize the sum of the mean and the vairance of the resulting matching filter, the misfit of ATI with entropy minimizes the sum of the mean and the logarithm of the variance instead. We use the Marmousi example and an offshore field dataset to demonstrate the effectiveness of the proposed method.