A Low-Frequency Compensation Method for Elastic Full Waveform Inversion Based on Blind Sparse-Spike Deconvolution

The elastic full waveform inversion takes the residual norm of multi-component simulation data and multi-component observed data as the objective function, comprehensively utilizes information such as amplitude and phase in multi-component seismic data to invert the P-wave and S-wave velocities in the depth domain. The accuracy of low-frequency components and wavelet parameters in three-component seismic data are the main factors affecting the precision of full waveform inversion of elastic waves. This paper proposes a low-frequency compensation algorithm for seismic data based on blind sparse pulse deconvolution to compensate for the low-frequency components missing in multi-component seismic data, providing input data rich in low-frequency components for the elastic full waveform inversion. Using this data, the correct construction of the initial P-wave and S-wave velocity model is achieved. Firstly, based on the convolution theory, the objective function constrained by L1 norm is constructed using the sparsity of underground reflection coefficients. Compressed sensing theory and sparse inversion method are utilized to solve the sparse inversion problem, achieving full bandwidth expansion of the low-frequency missing seismic data, and adopting the fast iterative shrinkage-thresholding algorithm to compress the observation record into a sharp pulse. Then, it is reconstructed with the wavelet rich in low-frequency components through convolution to obtain multi-component seismic records rich in low-frequency information, which are then used for full waveform inversion of elastic waves in the time domain. Finally, taking the inversion result as the initial model, the final inversion result is obtained by using the full waveform inversion algorithm of elastic waves in the time domain that does not rely on the wavelet. The model test results show that this inversion method can effectively improve the inversion accuracy under the condition of low-frequency missing and inaccurate wavelet.