Multi-scale elastic full-waveform inversion in a hybrid domain based on deconvolution objective function

High-precision P-wave and S-wave velocity models are very important for seabed exploration. Elastic full-waveform inversion is an effective way to obtain the velocity models. Full-waveform inversion is strongly dependent on source wavelet, and inaccurate wavelet estimation will severely affect the inversion results. Furthermore, elastic full-waveform inversion is a highly non-linear problem and has larger calculation and memory cost. Based on the deconvolution method, we develop a multi-scale source-independent elastic full-waveform inversion method in a hybrid domain to alleviate the non-linearity, to improve computation efficiency and decrease memory cost and to reduce the influence of source wavelet. We reconstruct the deconvoluted objective function and further derive the adjoint source and gradient formulas for elastic full-waveform inversion with the adjoint-state method. We can obtain good inversion results by using this objective function, adjoint source and gradient even if the source wavelet is unknown. In order to illustrate the influence of different reference traces on the objective function, we provide the theoretical formula of the objective function changing with the variation of reference traces. Experiments show that the deconvolution objective function cannot completely eliminate the influence of inaccurate source wavelet on the inversion, and the inversion effect depends on the selection of reference trace. Different inversion results of the Marmousi2 model indicate that the minimum offset trace is the best reference trace. Comparison of the inverted Marmousi2 model by the proposed method and the conventional elastic full-waveform inversion method using correct wavelet shows that the two inversion results are very close, which proves the effectiveness of the proposed method and indicates a potential application of the method in seabed exploration.