Elastic frequency controllable envelope inversion

Abstract Although elastic full waveform inversion is considered a high-resolution seismic inversion method, it is sensitive to the initial model. When the initial model lacks long-wavelength components, the inversion results may be inaccurate. This limitation frequently results in cycle-skipping during the inversion process. Elastic envelope inversion (EEI) is an effective way to build initial models as input for EFWI. However, EEI ignores the difference in sensitivity of different frequency data to the cycle-skipping problem, which limits its performance. This paper introduces the elastic frequency controllable envelope (EFCE), a novel type of envelope with frequency-selection characteristics tailored for elastic data. Moreover, to enhance the utilization of weak reflected information, a modified version of EFCE named residual-modification-aided EFCE (RMAEFCE) is proposed. Building on RMAEFCE, we define a novel objective function and subsequently propose an innovative EFWI approach called RMAEFCE inversion (RMAEFCEI), with the aim of building accurate long-wavelength velocity models that include both P-wave and S-wave. Numerical experiments carried out using the Marmousi model show that our approach markedly outperforms EEI, effectively mitigating the cycle-skipping issue. When employing the initial models established by RMAEFCEI, EFWI can output satisfactory final models. In addition, RMAEFCEI can build acceptable long-wavelength velocity models even with an inaccurate wavelet, indicating that it is more robust to wavelet error.