The implementation of the concept of empirical risk minimization in the VES inverse problems

Abstract

The authors has suggested a new mathematical approach to the inversion of vertical electric sounding (VES) data, which allows suppressing alternating interferences with an arbitrary distribution law, as well as conducting an approximate assessment of the quality of the results of quantitative interpretation. A necessary condition for its application is a close number of positive and negative interferences in the source data, the amplitude of the interference may exceed the value of the useful signal. The method is based on the concept of minimization of empirical risk (MER), which is implemented when choosing the optimal interpretation option from a previously constructed set of feasible solutions to the inverse VES problem. The expediency of use of the random search procedure in calculations is experimentally substantiated. The paper presents the model and practical examples of use of the MER method for the interpretation of individual VES and the simultaneous selection of geoelectric section parameters for several VES curves obtained on the same observation profile (quasi-one-dimensional inversion).

Keywords

• vertical electrical sounding
• interference
• interpretation
• minimization of empirical risk