An algorithm for solving a 1D seismic data inversion problem on quantum or digital annealers in the presence of a priori information on layer parameters specified by arbitrary functions

This work demonstrates the fundamental possibility of solving quite large-scale problems of seismic data inversion on modern hybrid (quantum-classical) and quantum-inspired annealers using the example of a one-dimensional problem for a horizontally layered model of the medium in the acoustic approximation. The optimization problem for the residual function of observed and model data is decomposed into three problems: the optimization problem for a simpler function of the same dimension, the problem of finding the minimum of a one-dimensional function, and the problem of calculating the terms of a simple recurrent series. Then, the optimization problem for a simpler function is transformed into a quadratic unconstrained binary optimization problem of such a dimension that its solution can be calculated on modern annealers.