DERIVATIVE-FREE OPTIMIZATION HYBRID STRATEGY FOR FULL WAVEFORM INVERSION
Seismic inversion, Full waveform inversion, Derivative-free optimization
In the seismic exploration we have investigated the subsurface characteristics using Full Waveform Inversion (FWI) techniques which was approached as a nonlinear optimization problem. The FWI technique traditionally uses mathematical methods based on derivatives and therefore fails when an objective function is non differentiable. In addition, this entails a high computational cost and a precision limited to local minimum. Therefore, in this work we adopted a Derivative-Free Optimization (DFO) methodology to find the global minimum. In this type of approach we used the Random Jump (RJT), Controlled Random Search (CRS) and Adaptive Nelder-Mead Simplex (ANMS) techniques. We developed an FWI-DFO algorithm that numerically solves the 2D acoustic wave equation by the Finite Differences Method (FDM) and uses a hybrid method RJT-CRS-ANMS as the optimization technique for the seismic inversion. The strategy is to automatically balance global and local searches iteratively by CRS and ANMS, respectively. We applied the methodology to five real subsurface models. The results showed a good agreement with the real models. The computational time presented reasonable values and the objective function showed to be very sensitive to small changes in the model parameters for the cases analyzed here. In summary, the FWI-DFO methodology proved it was very promising about seismic inversion.