A Homotopy Optimization Method for Non-Liner Inversion of Geoelectrical Sounding Data

In nonlinear inversion of geophysical data, bad initial approximation of the model parameters usually leads to local convergence of the normal Newton iteration methods, despite enforcing constraints on the physical properties. To mitigate this problem, we present a globally convergent Homotopy continuation algorithm to solve the nonlinear least squares problem through a path-tracking strategy in model space. The global convergence of the Homotopy algorithm is compared with a conventional iterative method through the synthetic and real 1-D resistivity data. Furthermore, a bootstrap-based uncertainty analysis is provided to quantify the error in the inverted models derived from the case study. The results of blocky inversion demonstrate that the proposed optimization method outperforms the Marquardt-type algorithm in the sense of the stability and the recovered models.