A. G. Guzhva, S. A. Dolenko, E. A. Obornev, I. G. Persiantsev, M. I. Shimelevich, Yu. S. Shugai

This study is devoted to development of an algorithm for selection of significant features in neural network based solution of the inverse problem (IP) of magnetotellurics (MT) in geophysics. Solution of such problem is the process of creation of an operator mapping a data vector of the values of electromagnetic field observed on earth surface to the vector of the sought-for geophysical parameters of the section. These parameters include distribution of electrical conductivity in different points of the studied region, geometrical dimensions of separate sub-regions (geological structures) etc. Actual sections are extremely complex and require a very large number of parameters to describe them, thus leading to the known instability (incorrectness) of MT IP. In this study, MT IP was solved with the help of neural networks (NN), namely multilayer perceptions. The dimensionality of 2D MT IP considered in this study is about DI=6.5-103 at the input (the dimension of the vector of the observed values) and about DO=3-102 at the output (dimensionality of the vector describing the distribution of electrical conductivity). To reduce the output dimensionality of a problem, it was divided into DO problems with one output each. To reduce the input dimensionality, the following methods of significant feature selection (SSF) were used: NN weight analysis (NNWA) and correlation analysis (CA). In this study, a three-step algorithm for IP solution using SSF has been suggested and considered. Two modifications of the algorithm have been considered: the one using NNWA only and the one using CA at one of the steps of the algorithm. Several geo-electrical models have been considered, differing by distribution of electrical conductivity, in particular, by presence or absence of conductive or isolating screening layer in the upper part of the section, and in different number of layers with alternating conductivity type (conductor-dielectric-conductor or dielectric-conductor-dielectric). Comparative analysis of the results led to the following conclusions: 1) The proposed algorithm showed its efficiency. Results obtained at the third step demonstrate significant increase of the solution precision when compared to the "base" NN, with significant (about two orders of magnitude) reduction of the number of the input features. 2) The key issue in the efficiency of IP solution is presumably the number of input features. The optimal number of input features lies in the range from 20 to about 100, depending on the complexity of the specific problem being solved. 3) It has been found that the quality of NN IP solution highly depends on the depth where the block being studied resides (a block corresponds to an output feature), specifically it decreases with increasing depth. This effect can be explained from the physical point of view (upper layers screen bottom layers); the results of IP solution by NN allow obtaining quantitative estimation of this effect. 4) The SSF method used has a serious impact on the results. In a number of cases, using the less computationally expensive CA as a method for preliminary selection at the second step of the algorithm, allows obtaining better results than using NNWA at all the three steps of the algorithm. 5) Analysis of the list of input features adaptively selected with SSF methods shows that this list agrees well with a priori physical considerations on relative importance of the features. Usually, the version of the algorithm using CA gives a picture with much less contrast, with the number of features selected at the second step about an order of magnitude higher. This effect is in part compensated by NNWA at the third step. 6) When the screening layer is present, the blocks situated just below this layer have very little influence on the measured values of the field; therefore, the IP on determination of the conductivity of such blocks is solved poorly. SSF for such blocks brings practically no improvement to the result, or even makes it worse. For blocks corresponding to a large conducting or non-conducting element in the structure of geo-electrical models, the IP is solved much better, and a very small number of input features are sufficient for such solution. Thus, adaptive data analysis discovers effects that can be easily explained form geophysical point of view.