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New regularized algorithms based on the spectral method for solving deformable layer tomography. (English) Zbl 1311.65099

Summary: 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.

MSC:

65L09 Numerical solution of inverse problems involving ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34A55 Inverse problems involving ordinary differential equations
86A15 Seismology (including tsunami modeling), earthquakes
86A22 Inverse problems in geophysics
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