New regularized algorithms based on the spectral method for solving deformable layer tomography

Abstract

The deformable layer tomography (DLT) is now a popular way to characterize the unknown geometry of the velocity interface by using the traveling time observed in data, which is difficult to solve accurately, because of the strong ill-posedness. In this paper, new regularization approaches based on the spectral method are introduced, which can invert the velocity value and the geometry of the interface simultaneously. The unknown interfaces are parameterized by Legendre spectral expansion, and various regularization methods combined with traditional regularization parameters selections are utilized to solve the ill-conditioned algebraic equation system. Moreover, a regularized algorithm with prior choice of regularization parameters is proposed to solve the DLT.

Keywords:

• seismic tomography
• regularization methods
• spectral method
• deformable layer tomography

AMS Subject Classifications:

• 65F22
• 65J20
• 65N35

Notes

The work is supported in part by the Key Project National Science Foundation of China [grant number 91130004]; Natural Science Foundation of China [grant number 11331004].