Extended Reflection Waveform Inversion via Differential Semblance Optimization

Reflection-based waveform inversion introduces migration and demigration process to retrieve low-wavenumber component from reflection data, but both differenceand correlationbased methods suffer from the cycle-skipping problem when the time shifts change rapidly. In this abstract, we introduce model extension and differential semblance optimization into reflection-based waveform inversion. With another degree of freedom in the model space, we can eliminate the time difference between synthetic and observed data so that cycle skipping problem is solved. Differential semblance operator is used to detect the coherence of the extended model. The hybrid objective function, consisting of data misfitting and differential semblance term, shows better convexity than only data misfitting term. We propose a two-stage scheme to minimize the hybrid objective function, that is, the inner loop to update extended the reflectivity and the outer loop to update the background velocity. In order to accelerate the convergent rate of the two-stage scheme, we propose two different approximations of diagonal Hessian and use them as preconditioners in the inner and outer loop respectively. With numerical tests, we show the importance of linearized inversion in the inner loop and also demonstrate that our proposed method can successfully recover both highand low-wavenumber components of the subsurface model. Even though we specify the model extension in the subsurface offset domain and ignore non-linear effects, other extensions and non-linear inversion are also possible under the same framework.