A Time-shift Method For Time Domain Multiscale Full Waveform Inversion

Full waveform inversion (FWI) requires a multiscale method to avoid circle skip-ping and jump out of local minima. In traditional time domain multiscale inversion, both receiver data and source wavelet have to be low-pass filtered prior to inversion, and af-ter that the low-pass filtered data are used as the input data. In this paper, we develop a gradient-based multiscale method in time domain. Our time-shift method provides a natural and efficient way to realize multiscale inversion. Preprocessing on the data is no longer needed, and instead, time-shift imaging condition is performed multiple times in order to extract low-wavenumber gradients. Any low-pass filter applied to the gradient can be achieved by a summation of weighted time-shift crosscorrelations using the time-shift method. The extracted low wavenumber information helps reduce the dependence on the initial model in FWI. To test the validity of the time-shift method, we conduct the inversion of a 2D Overthrust example with a linear gradient initial model. The time-shift multiscale method guarantees a better and faster convergence to the global minimum while traditional single-scale inversion converges to a local minimum.