We investigated the characteristics of the subsurface seismic exploration using Full Waveform Inversion (FWI) formulated as a nonlinear optimization problem in one dimension (1D). The FWI technique originally used mathematical methods based on the calculation of derivatives to optimize the objective function that quantifies the misfit between the data observed in seismic exploration and calculated by inversion. This entails a high computational cost and limited accuracy to local minima. In this work we adopt a Derivative-Free Optimization (DFO) methodology to find the desired global minimum. The technique used was the Controlled Random Search (CRS). We developed a FWI-CRS algorithm that numerically solves the 1D acoustic wave equation with the Finite Difference Method (FDM) and that minimizes the misfit by the CRS method, allowing to find the global minimum in the seismic inverse problem. The results using the FWI-CRS technique showed a good match with the actual model. The computational time was also reasonable. The objective function was shown to be very sensitive to small changes in the model parameters for the cases analyzed here.

Full Waveform Inversion (FWI), Derivative Free Optimization (DFO), Controlled Random Search (CRS), Seismic Inverse Problem(SIP), Finite Difference Method (FDM).