Estratégia híbrida de otimização sem derivadas para a inversão completa da forma da onda

Abstract

In the seismic exploration, the subsurface characteristics have been investigated 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, a Derivative-Free Optimization (DFO) methodology was adopted to find the global minimum. In this type of approach, the Random Jump (RJT), Controlled Random Search (CRS) and Adaptive Nelder-Mead Simplex (ANMS) techniques were used. A FWI-DFO algorithm which 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 was developed. The strategy is to automatically balance global and local searches iteratively by CRS and ANMS, respectively. The methodology to five synthetic subsurface models was applied. The results showed a significative agreement with the synthetic 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 to be very promising in the seismic inversion.