Time domain full waveform inversion with low frequency wavefield decompression

Full waveform inversion (FWI) aims to recover the most accurate velocity components with full wave information. FWI produces nearly perfect results when the input seismic data contains enough low-frequency information. We first analyze the relationship between the gradient and the velocity perturbation based on the Born approximation. Compared with the frequency domain, the wavefield in the time domain contains a second-order time-derivative operator. For this reason, time-domain schemes are not very effective at recovering the very low wavenumbers, which are suppressed by the derivative operators. Accordingly, we propose a new method introducing a low-frequency decompression operator into the objective function to compensate for the high-passed filter effects in the time domain FWI. The objective function after low-frequency decompression has better convexity, thus converges to the global minimum more easily. We then compare the new approach with the classical FWI through an application on the 2D Marmousi model. This example shows that the new approach can be useful for the determination of low wavenumbers of the velocity model.