Details

Autor(en) / Beteiligte

• Leonov, A S

Titel

Application of M.Riesz potentials for solving a 3D inverse problem of acoustic sounding

Ist Teil von

• Journal of physics. Conference series, 2019-04, Vol.1205 (1), p.12036

Ort / Verlag

Bristol: IOP Publishing

Erscheinungsjahr

2019

Link zum Volltext

Quelle

EZB Free E-Journals

Beschreibungen/Notizen

• An inverse coefficient problem for time-dependent 3D wave equation is under consideration. We recover a spatially varying coefficient of this equation knowing special time integrals of the wave eld in an observation domain. The inverse problem has applications to the acoustic sounding, medical imaging, etc. We reduce the inverse problem to a new linear 3D Fredholm integral equation of the first kind in which the integral operator has the form of well-known M.Riesz potentials. The equation has a unique solution for a considered class of coefficients. Assuming a special scheme for recording the data of the inverse problem, we present and substantiate a numerical algorithm of solving this integral equation. The algorithm does not require significant computational resources and a long solution time. It is based on the use of fast Fourier transform. Typical results of solving 3D inverse problem in question on a personal computer for simulated data demonstrate high capabilities of the proposed algorithm.