TY - JOUR

T1 - A homotopy continuation inversion of geoelectrical sounding data

AU - Ghanati, Reza

AU - Müller-Petke, Mike

N1 - Funding information: The first author would like to thank Leibniz Institute for Applied Geophysics for funding the postdoctoral fellowship. The first author also acknowledge the financial support from University of Tehran for this research under grant number 30730/1/01 . We would like to thank Mahdi Fallahsafari for collecting the geo-electrical sounding data used in case 1.

PY - 2021/8

Y1 - 2021/8

N2 - 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.

AB - 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.

KW - Geoelectrical data

KW - Homotopy continuation inversion

KW - Non-linear inversion

KW - Uncertainty analysis

UR - http://www.scopus.com/inward/record.url?scp=85107680961&partnerID=8YFLogxK

U2 - 10.1016/j.jappgeo.2021.104356

DO - 10.1016/j.jappgeo.2021.104356

M3 - Article

AN - SCOPUS:85107680961

VL - 191

JO - Journal of applied geophysics

JF - Journal of applied geophysics

SN - 0926-9851

M1 - 104356

ER -