Time domain elastic-wave FWI based on first-order approximate instantaneous frequency

The weak signal of the artificial seismic record contains the information of the subsurface medium needed for the inversion. However, in full waveform inversion (FWI), weak signals contribute hardly to the objective function. Therefore, how to improve the contribution of weak signals in the objective function of FWI is an urgent issue to be addressed. The instantaneous frequency attribute is extremely sensitive to subsurface velocity changes and has the potential to extract weak signals from the seismic record. However, this frequency can only be estimated from complex seismic signals. Instantaneous frequency estimated by empirical mode decomposition (EMD) is difficult to apply to FWI due to the large amount of computation. To address this issue, the instantaneous frequency in FWI is replaced by a first-order approximation of the exponential frequency. In this paper, the objective function of first-order approximate exponential frequency FWI (FRE-EFWI) and the source term of its back propagation formula are derived. In addition, the FRE-EFWI method has been shown to improve the contribution of weak signals to the FWI objective function. Finally, FWI is used as an example to validate the correctness and effectiveness of the proposed method.