Traveltime-based reflection full-waveform inversion for elastic medium

The main difficulty of full waveform inversion (FWI) based on local optimization methods is that it tends to trap in local minima or cycle-skipping associated with inaccurate initial models and waveform misfit functions, especially for elastic media. To address this issue, we first discuss the relationship between reverse time migration (RTM) and traditional reflection FWI (RFWI). Then, we present an elastic RFWI (ERFWI) methodology. However, for ERFWI, high nonlinearity still exists in data residuals related misfit function, when true amplitude migration is not adopted. To further mitigate the cycle skipping and avoid the requirements of true amplitude migration, we develop a traveltime-based ERFWI method to update the low-wavenumber components of P- and S-velocity models. The traveltime-based ERFWI only eliminates traveltime residuals along the wave-path of sensitivity kernels to extract the long-wavelength background of the middle and deep parts. Once the traveltime of reflected waves is described correctly, the inversion result using the traveltime-based ERFWI method could be used as a velocity model for prestack depth migration (PSDM) or as an initial model for the conventional FWI to obtain high-resolution velocity model. The final results by combining traveltime-based ERFWI and conventional FWI illustrate that the combined method can obtain an improved result, compared with regular FWI methods.