Open AccessOn reconstruction of the coefficient in complex Helmholtz’s equation
Author(s) -
Mikhail Malovichko,
A Orazbayev,
Yu. Yu. Kloss,
Н. И. Хохлов
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2056/1/012015
Subject(s) - helmholtz equation , jacobian matrix and determinant , mathematics , gauss , helmholtz free energy , inverse problem , mathematical analysis , computation , algorithm , physics , quantum mechanics , boundary value problem
This note summarizes some preliminary results on the fast solution of the coefficient inverse problem for the Helmholtz equation, given measured pressure in a set of observation points. The Helmholtz equation is the model PDE for the harmonic problem of the linear theory of elasticity, and this work is a move in that direction. The problem has been the primary focus for several research areas, most notably seismic exploration. Still, practical problems are very challenging because they are non-linear and large. In this paper, we develop a novel numerical method for seismic full-waveform inversion based on Newton iterations. Its distinctive future is that it does not require the Jacobian of the target functional. Thus, in certain scenarios, it will perform only a fraction of computations comparing to the conventional Gauss-Newton algorithm. We present some early results on the Helmholtz equation in two dimensions.