SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Contributed Talk

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Wavefield simulation and velocity inversion based on the acoustic wave equation

W. Zhang and J. Luo

Abstract
In geophysical exploration the mathematical model based on the acoustic wave equation is usually adopted. Modelling the wave propagation underground and inversing the media velocity are very helpful in geophysical data processing. Here, we investigate numerical inversion methods for velocity based on the acoustic waveform. Waveform inversion is in fact an optimization problem which minimizes the residuals between the recorded data and the synthesized data. As the data are observed on the partial boundary this problem is the highly ill-posed problem. We use the least-square method to solve the problem. Various iterative methods such as the Gauss-Newton method and the Levenberg-Marquardt method may be used. The performance of the different iterative methods is compared. Considering the computational efficiency the second-order finite-difference method are used to simulate the wavefield. The absorbing boundary conditions in simulation are the Clayton-Engquist conditions.

Bibliography
[1] B. Engquist and A. Majda, Absorbing boundary conditions for the numerical simulation of waves, Math. Comput., 31 (1997), pp. 629-651.
[2] M. Hanke, A regularizing Levenberg-Marquardt scheme, with applications to inverse groundwater filtration problems, Inverse problems, 13 (1983), pp. 79-95.
[3] V. Isakov, Inverse Problems for Partial Differential Equations. 2010, Springer.
[4] D. Marquardt, An algorithm for least squares estimation on nonlinear parameters, SIAM J. Appl. Math., 11 (1963), pp. 431-441.

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