Optimal selection of regularization parameter in inversion of magnetotelluric data

Magnetotellurics is widely used for exploration of geothermal resources because of its potential in the conductivity contrast of deep geological structures in geothermal regions. Hence, 2D inversion of the MT data is a major step in determination of physical properties of exploration targets and their geometric quantitative dimensions. In recent years, many attempts have been made on the development of 2D MT inversion algorithms and interpretation of the results. The solutions for inverse problems of MT data are nonunique and unstable since the measured data are accompanied by noise. The Tikhonov regularization theory is a common method for resolving unstable and ill posed inverse problems. In solving this regularized inverse problem, selection of an optimal regulation parameter value is important for achieving an ideal inverse modeling result. This parameter controls the balancing between the minimization process of the stabilizing and the misfit function. Therefore, it must be chosen carefully. In this paper, a novel method has been
presented in which the optimal value of the regularization parameter for 2D inversion of the MT data is selected based on the LB method to increase the speed and accuracy of the results of the inversion.

Numerical modeling of geophysical response for a given geophysical model is known as forward problem. The directly inverting of the forward sensitivity matrix is very difficult especially in large scale problems, instead, one needs to use iterative methods to calculate it quickly. To achieve this, a fast iterative solver like LB algorithm is used for smooth inversion of MT field data. In this method, the large forward sensitivity matrix is substituted by a smaller dimension bidiagonal matrix, which avoids large matrix multiplication and basis vectors storing. Therefore, the inversion process speed in solving the large inversion problems and obtaining accurate results will increase, and the required memory and inversion calculation time will also be decreased. In order to find an appropriate value for the regularization parameter, a novel method has been presented in which adaptive regularization, has been used and compared with two conventional methods, namely MGCV and ACB. All these methods have been used in MATLAB codes and combined with the LB method, and then has been has been added to software package MT2DInvMatlab developed by Lee (2009). To demonstrate the efficiency of the proposed technique comprising of the above-mentioned methods, it has been applied on synthetic MT data having 3 percent Gaussian noise, and also, real MT data of the Bushli (Nir) geothermal field in Ardabil Province, Iran.

The models produced from the inversion of the synthetic MT data and the Bushli MT field data set using the adaptive regularization, MGCV, and ACB methods are almost similar. The constructed model from using adaptive regularization is slightly better than the model obtained from MGCV and ACB methods. therefore, with respect to the results obtained from 2D inversion of the synthetic MT data and the Bushli (Nir) MT field data, the adaptive regularization

provides a more accurate solution especially in estimating the conductive layer and reservoir boundaries. In addition, this method, compared to the MGCV and ACB methods, is faster and requires less memory in the inversion process. Hence, this method can be considered as the most reliable method for selection of the optimal regularization parameter in the inversion of large 2D and 3D magnetotelluric data sets.