Source-Independent Full-Waveform Inversion Based on Convolutional Wasserstein Distance Objective Function

Full-waveform inversion (FWI), as a high-precision model building method, plays an invaluable role in seismic exploration. The accuracy of conventional FWI is universally reduced by the cycle skipping, which can be improved by the optimal transport distance (OTD) objective function; however, the OTD-based FWI cannot converge to meaningful results with an inaccurately estimated source wavelet. To solve this dilemma, we construct a novel convolutional Wasserstein (CW) distance objective function by applying the OTD objective function to convolved seismograms. Before the standard nonnegative and normalization preprocessing of OTD, we first convolve the observed data with a reference trace selected from simulated seismograms and convolve the simulated data with a trace selected from the observed data. Both convolved data sets are naturally regarded as with an identical source, so the data difference caused by the inaccurately estimated source wavelet is eliminated. The adjoint source corresponding to the new objective function is derived. The velocity model can be updated by using a quasi-Newton method according to the gradient of the objective function generated by the adjoint-state method. We investigate the effectiveness of our objective function by 1-D signals and several FWI examples. Furthermore, this new objective function still delivers an excellent performance in releasing the local minimum problem and resisting noise when the wavelet used in FWI is inaccurate.