Numerical implementation of the full waveform inversion method using the asymptotic solution of the Helmholtz equation

In this paper, we consider the numerical implementation of the Full Waveform Inversion method based on the asymptotic solution of the Helmholtz equation. The standard method finds the minimum of the penalty function, which characterizes the mean-square deviation of the modeled data from the observed ones during conducting the field works. Local optimization methods, such as the conjugate gradient method, are usually used to minimize the objective functional. The calculation of the penalty function gradient is the most resource-intensive part of the task. An asymptotic approach to solving an inverse dynamic seismic problem is to replace the expensive finite-difference procedure for calculating the Green's function of a boundary value problem by the frequency-dependent ray tracing. The Green's functions are calculated from data on the travel time along the rays, the amplitude and the geometric divergence. A series of numerical experiments for the widespread Marmousi model demonstrates the efficiency of applying of this approach to the reconstruction of macrovelocity structure of complex media for low temporal frequencies. In comparison with the standard finite-difference approach, applied to solving the inverse problem, the speed of calculations of the asymptotic method is an order of magnitude higher upon comparable quality of the solution.