A widely convergent generalized pulse-spectrum technique for the inversion of two-dimensional acoustic wave equation

Han, Bo; Feng, G.F.; Liu, J.Q.

doi:10.1016/j.amc.2005.02.011

Cited by 7 publications

(3 citation statements)

References 19 publications

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“…The real problem is usually defined in the whole domain, but for simplicity, this paper uses the bounded domain to approximate to the infinite domain (see also [5,6,8,9,21]). In reality, the energy decays to zero at infinity.…”

Section: Inversion Model and Discretizationmentioning

confidence: 99%

“…With the progress of science and technology, studies on wave equation inversion attract more and more attention, prompting people to investigate the inversion of wave equation from different angles and put forward various methods, see for example [1,8,9,20,21]. At present, there are still some difficulties in the practical application of these methods.…”

Section: Introductionmentioning

confidence: 98%

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A nonlinear multigrid method for inversion of two-dimensional acoustic wave equation

Zhao¹,

Liu²,

Feng³

2014

Journal of Inverse and Ill-Posed Problems

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We investigate the problem of estimating the velocity in a two-dimensional acoustic wave equation, which plays an important role in geological survey. The forward problem is discretized using finite-difference methods and the estimation is formulated as a least-square minimization problem with a regularization term. To reduce the computational burden, a nonlinear multigrid method is applied to solve this inverse problem. In the multigrid inversion process, in order to make the objective functionals at different scales compatible, they are dynamically adjusted. In this way, the necessary condition of "the optimal solution should be the fixed point of multigrid inversion" can be met. The stable and fast regularized Gauss-Newton method is applied to each grid. The results of numerical simulations indicate that the proposed method can effectively reduce the required computation, improve the inversion results, and have the anti-noise ability.

show abstract

Section: Inversion Model and Discretizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

A nonlinear multigrid method for inversion of two-dimensional acoustic wave equation

Zhao¹,

Liu²,

Feng³

2014

Journal of Inverse and Ill-Posed Problems

View full text Add to dashboard Cite

show abstract

“…Recently, a large amount of literature is devoted to the homotopy method for parameter estimation. The homotopy method is applied to the parameter identification of an elliptical equation [26], the parameter identification of twodimensional acoustic wave equation [27,28], the parameter identification of two-phase viscoelastic media [29], the PEM identification of ARMAX models [30] the reconstruction of mountain surface [31] and the well-log constraint waveform inversion [32][33][34]. The homotopy method for nonlinear inverse problems is given in [35] and the homotopyprojection method for the parameter estimation problems is given in [36].…”

Section: Introductionmentioning

confidence: 99%

An adaptive homotopy method for permeability estimation of a nonlinear diffusion equation

Zhao

Liu

2012

Inverse Problems in Science and Engineering

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We investigate the problem of estimating the permeability function in a nonlinear diffusion equation, which plays an important role in promoting the permeability estimation within multiphase porous media flow. The forward problem is discretized using finite-difference methods and the parameter estimation is formulated as a least-square minimization problem with a regularization term. To overcome the weakness of the local convergence of traditional methods, a homotopy method is applied to solve this inverse problem. By introducing the Tikhonov regularization and adaptively choosing the homotopy parameters, a new and globally convergent algorithm is constructed. Finally, many numerical simulations are presented to show the global convergence, computational efficiency and anti-noise ability of the proposed algorithm.

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Reconstruction of a permeability field with the wavelet multiscale–homotopy method for a nonlinear convection–diffusion equation

Liu¹

2016

Applied Mathematics and Computation

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A widely convergent generalized pulse-spectrum technique for the inversion of two-dimensional acoustic wave equation

Cited by 7 publications

References 19 publications

A nonlinear multigrid method for inversion of two-dimensional acoustic wave equation

A nonlinear multigrid method for inversion of two-dimensional acoustic wave equation

An adaptive homotopy method for permeability estimation of a nonlinear diffusion equation

Reconstruction of a permeability field with the wavelet multiscale–homotopy method for a nonlinear convection–diffusion equation

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