Reliable initial velocity model for seismic waveform inversion based on adaptive envelope inversion

Seismic full-waveform inversion (FWI) is a strongly nonlinear and ill-posed geophysical inverse problem, which may converge to a local minimum without a reliable initial model. Seismic envelope inversion (EI) can mitigate the local minimum by reconstructing a reliable initial model for FWI. Conventional EI method attempts to match the envelopes of simulated and observed data in a point-to-point comparison. However, EI based on point-to-point comparison has limited convexity and is sensitive to differences in source wavelets. To enhance the convexity and the stability of EI, we developed an adaptive envelope inversion (AEI) method. In AEI, we introduced a deconvolution filter into the objective function. The deconvolution filter changes the point-to-point comparison of the envelope data to a trace-to-trace similarity comparison, that significantly improves the convexity of EI. Meanwhile, the objective function of AEI contains the normalization of the deconvolution filter, for reducing the interference caused by the differences in source wavelets. Due to the complexity of the objective function of AEI, we employed automatic differentiation to compute the gradient of AEI. Numerical experiments show that the AEI method can reconstruct a reliable velocity model, even when the initial model and the source wavelets deviate significantly from the true situations. The reconstructed velocity model by AEI effectively preserves the background information of the true model. Therefore, the velocity model constructed by AEI can be used as a reliable initial model to mitigate the local minima of FWI, thereby improving the accuracy of inversion results.