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Nonlinear multifrequency wave equation inversion

Harris Jerry, M.; Yin Feng

SEG Annual Meeting Expanded Technical Program Abstracts with Biographies 64: 988-991

1994

A method of nonlinear wave equation inversion using multiple frequencies is developed. The method sequentially inverts low to high signal frequencies of the wave field. First, the low frequencies are used to reconstruct the low spatial wavenumbers of the heterogeneities. Then, higher frequencies are used to reconstruct higher spatial wavenumbers. A subspace method is used to minimize the misfit between the observed total wave field and the corresponding theoretical synthetic wave field. The gradient of the misfit function, the rate of change of the gradient, and a regularization factor are used to find the optimum search direction to the solution of inverse problem. It is not necessary to assume weak scattering, e.g., Born or Rytov, nor is it necessary to remove the incident field before inversion as required in linear diffraction tomography. These advantages make this method more flexible than linear diffraction tomography. Tests on synthetic data show that the method is effective in reconstructing velocities with up to 15% variation and that the inversion is stable and more precise than single frequency wave equation methods. These advantages are available with not much penalty of computation effort or time.

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