Application of Envelope in Salt Structure Velocity Building: From Objective Function Construction to the Full-Band Seismic Data Reconstruction

For full-waveform inversion (FWI), building the salt structure velocity model is a challenging problem. In the absence of a high-fidelity initial model, low-frequency seismic data are indispensable for accurate reconstruction of the long-wavelength components of salt domes, which are often missing in field data. The envelope isolates the amplitude information from the seismic data and has a stronger linear relationship with the velocity than the seismic data. It is used to enhance the convexity of the objective function in an envelope inversion (EI). However, the properties of the envelope are not effectively utilized in EI due to the lack of their proper understanding. In order to solve the problems that EI has in building the salt structure velocity, such as the cycle-skipping problem, the gradient calculation problem caused by the waveform Fréchet derivative, and the multisolution problem caused by the missing polarity information of the envelope, we propose a multiscale direct signed EI (MSDSEI) based on the direct envelope Fréchet derivative and multiscale signed envelope. The development process from EI to MSDSEI also inspired us to understand the physical mechanism involved in the low-frequency components of the envelope: the signed envelope can be regarded as a low-pass filter of the reflection sequences in the subsurface. Thus, we use the smoothness and phase-independent properties of the envelope to propose an envelope-based full-band seismic data reconstruction method for multiscale FWI. Finally, the performance of various EI methods is verified on the Sigsbee2A model.