On Stability of Inverse Problem Solution for Rock Mass Stress State Reconstruction Based on Natural Fractures Analysis

The paper is devoted to the issue of stability of the solution of the inverse problem of estimating stress state of the rock mass based on data on natural fractures. Within the framework of the used method of estimating stress state of the geologic medium, it is assumed that geophysical methods allow estimating the stress state of individual fractures in the medium. The task of using information on the stress state of a set of fractures in a rock mass to reconstruct the parameters determining the stress state of the entire rock mass is posed. Previously, a method for solving this kind of problems was developed, and it was demonstrated that the inverse problem is ill-posed. In this paper, a synthetic fracture model is used to analyze how sensitive the solution of the inverse problem is to the noise of initial data. It is demonstrated that artificial degradation of the quality of information on the state of natural fractures in a rock mass leads to nonlinear increase in the distance between the true stress state and its estimation obtained by solving the inverse problem. The results of the work are used to determine the requirements for the analysis of natural fractures for the possibility to use its results to assess the stress state of rock masses.