Time-Domain Elastic Full Waveform Inversion With Frequency Normalization

Time-domain elastic full waveform inversion (FWI) uses seismic data to recover the high-resolution subsurface medium properties for structural imaging and lithologic identification. The approximate pulse generated by the explosion source in seismic exploration evolves into a limited bandwidth seismic wavelet through the propagation of the seismic wave in the underground medium, exhibiting strong energy near the dominant frequency and weak energy far away. Therefore, time-domain FWI using the band-limited seismic wavelet can only match the energy of the dominant frequencies present in a dataset to a large extent, resulting in insufficient low-wavenumber updates of model parameters because of the weak energy of low frequencies. To remove the effect of finite-frequency-band wavelet spectra from the time-domain FWI, we propose a time-domain elastic FWI without wavelet spectral limitation. In our method, a newly refined seismic wavelet with a normalized amplitude and accurate phase is used to propagate seismic waves in the time domain. Data residual measurement is performed based on the summation of single-frequency residuals between the normalized synthetic and observed frequencies. The adjoint-state method is used to approximate the gradients of the model parameters, and the decoupled wavefields obtained by the phase-sensitive detection method were involved in the gradient calculation. Overall, the proposed method helps FWI to avoid falling into local minima by enhancing the low-wavenumber reconstruction of the velocity models. The elastic FWI numerical tests and field data FWI application demonstrate that our approach can reliably recover high-precision inversion results.