On the Application of the Method of Linear Integral Representations to the Local Reconstruction of the Wave Potential

A new version of the linear integral representation method is developed for solving inverse problems in geophysics. This approach is applied to the interpretation of anomalous time-dependent field data. The reconstruction of field elements is reduced to solving a system of linear algebraic equations (SLAE) with an approximately given right-hand side. Since the matrix elements of this system are derived analytically, the modeling process is significantly simplified. The article also analyzes how the approximation quality of a non-stationary field element depends on the observation network geometry, enabling its optimization for more accurate detection of geological properties. The proposed method for solving inverse problems for hyperbolic partial differential equations with constant coefficients can also be applied to data described by systems of nonlinear PDEs, provided the target field is represented as a composition of components differing in magnitude. Finally, the results of non-stationary gravity field modeling are presented.