A homotopy continuation inversion of geoelectrical sounding data - Ghanati, Reza; Müller-Petke, Mike (Journal of applied geophysics, 2021)
In nonlinear inversion of geophysical data, improper 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 proposed scheme is based on introducing a new functional to replace the quadratic Tikhonov-Phillips functional. The algorithm implementation includes a sequence of predictor-corrector steps to find the best direction of the solution. The predictor calculates an approximate solution of the corresponding new function in the Homotopy in consequence of using a new value of the continuation parameter at each step of the algorithm. The predicted approximate solution is then corrected by applying the corrector step (e.g., Gauss-Newton method). The global convergence of the Homotopy algorithm is compared with a conventional iterative method through the synthetic and real 1-D resistivity data sets. 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 and smooth inversion demonstrate that the presented optimization method outperforms the standard algorithm in the sense of stability, rate of convergence, and the recovered models. •Conventional non-linear inversion schemes are highly starting guess dependent.•A globally convergent Homotopy method is developed for 1D resistivity inversion.•The proposed method is less sensitive to the starting model.•A comparison of the proposed algorithm and the standard inversion is provided.•Our results revealed that the proposed method outperforms the standard inversion.