Enhancing Tomography Component of Full-Waveform Inversion Based on Gradient Decomposition

It is widely known that the full-waveform inversion (FWI) gradient contains both tomography and migration components. One of the key points for the successful implementation of FWI is to first build a background velocity model by utilizing the tomography component and then recover the model interfaces using the migration component. Therefore, it is necessary to separate the two types of components in the FWI gradient. We propose a gradient-decomposition FWI (GFWI) method that provides a good initial velocity model for FWI using the tomography component. We first derive the FWI gradient based on the first-order stress-velocity acoustic wave equation and then decompose it into the tomography and migration components with a weighted Poynting vector separation method. Since the Poynting vectors can be directly obtained in the forward and backward wavefield extrapolation, the separation algorithm adds little additional computational effort. To better recover the low-wavenumber part of the model, only the tomography component is used for background velocity updates in the early iterations. Finally, we perform conventional FWI to obtain the final inversion result. Analyses on a sensitivity kernel test indicate that the proposed gradient decomposition algorithm is effective in separating the tomography and migration components. Numerical examples on a layered model with a high-velocity anomaly and the Marmousi model demonstrate that the new FWI method is robust and effective even for low-frequency missing data.