Fast numerical method of solving 3D coefficient inverse problem for wave equation with integral data

摘要

An inverse coefficient problem for time-dependent waveequation in three dimensions is under consideration. We are lookingfor a spatially varying coefficient of this equation knowing specialtime integrals of the wave field in an observation domain.The inverse problem has applications to the reconstructionof the refractive index of an inhomogeneous medium, as well as to acousticsounding, medical imaging, etc. In the article, a new linear three-dimensional Fredholm integral equationof the first kind is introduced from which it is possible to find the unknowncoefficient. We present and substantiate a numerical algorithm for solving this integralequation. The algorithm does not require significant computationalresources and a long solution time. It is based on the useof fast Fourier transform under some a priori assumptions aboutunknown coefficient and observation region of the wavefield. Typical results of solving this three-dimensional inverse problem on apersonal computer for simulated data demonstrate highcapabilities of the proposed algorithm.