Automatic Estimation of the Regularization Parameter in the Inversion of Magnetotelluric Data

Data inversion is one of the most important and challenging steps in geophysical data analysis. One of the vital issues in doing so is underdeterminacy, that is, the available data being less than the parameters of the model. Tikhonov Regularization, which is done by adding a stabilizing functional to the misfit and making a target function, is one of the most common methods for solving this problem. The important challenge in Tikhonov Regularization is determining the regularization parameter automatically in each iteration. Unbiased Predictive Risk Estimator (UPRE) is one of the usual methods proposed for tackling the mentioned challenge. Due to its high convergence rate and acceptable results in synthetic and real data, especially in geomagnetic and gravity explorations, it has received much attention. Therefore, here, the method above was used for the inversion of the 2D magnetotelluric data, and its results were compared with the methods of Activated Constraint Balancing (ACB) and Discrepancy Principle. To do so, the standard program “MT2DinvMatlab” was used as a basis, which uses the methods Lavenberg-Marquardt and ACB for inversion and automatic estimation of the regularization parameter, respectively. Next, this program was modified to estimate the regularization parameter with both ACB, UPRE, and Discrepancy Principle. In order to compare the results of these methods, a relatively complicated synthetic case and a real case of geothermal exploration in the Sabalan region were employed. Finally, the efficiency of UPRE was established in terms of yielding accurate models, low computation time, and high convergence rate.