Nonlinear inversion of seismic reflection data in a laterally invariant medium

Pica, A.; Diet, J.P.; Tarantola, Albert

doi:10.1190/1.1442836

Cited by 234 publications

(98 citation statements)

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“…On the other hand, the waveform inversion method for reflected waves is developed by Tarantola (1984), Mora (1987), Bourgeois et al (1989), Pica et al (1990), among others. According to them, the model parameters are iteratively updated using the gradient method for the non-linear inverse problem.…”

Section: Discussionmentioning

confidence: 99%

Estimation of the Subsurface Reflection Coefficient Using the Prestack Reverse-Time Depth Migration.

Kawasaki¹

1995

J,Phys,Earth

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The prestack reverse-time depth migration is developed to estimate the reflection coefficient of the subsurface. To examine the capability of this method, a numerical experiment is implemented and it is shown that this method gives proper reflection coefficients even for a structure with 45-degree dips. It is also applied to real data of land survey. A distribution map of the reflection coefficient can be obtained after compensating the amplitude from the 3D to 2D wavefield including consideration for the Q value. However, extracting the velocity perturbation from the estimated reflection coefficient is hard due to inaccuracy of the estimated source strength, oscillatory behavior of the image, and lack of information about the density. The waveform inversion method is compared with the present method and it is found that the first iteration of the former method is nearly identical to the present method. Problems which are inherent in these methods are discussed.

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Section: Discussionmentioning

confidence: 99%

Estimation of the Subsurface Reflection Coefficient Using the Prestack Reverse-Time Depth Migration.

Kawasaki¹

1995

J,Phys,Earth

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“…This so-called low frequency lacuna problem is rather well known in other seismic imaging approaches as well. Later literature on full wave inversion also met similar convergence problems [8][9][10][11][12]. The use of global minimizing processes [13][14][15][16] has shown much better convergence characteristics, but at the expense of computational efficiency.…”

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confidence: 92%

Full Waveform Inversion with Optimal Basis Functions

Sun

Chang²,

Sheng³

2003

Phys. Rev. Lett.

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Based on the approach suggested by Tarantola, and Gauthier et al., we show that the alternate use of the step (linear) function basis and the block function (quasi-function) basis can give accurate full waveform inversion results for the layered acoustic systems, starting from a uniform background. Our method is robust against additive white noise (up to 20% of the signal) and can resolve layers that are comparable to or smaller than a wavelength in thickness. The physical reason for the success of our approach is illustrated through a simple example. DOI: 10.1103/PhysRevLett.90.104301 PACS numbers: 43.90.+v, 91.30.-f Wave inversion means the recovery of the coefficients/ parameters of the wave equation from its solution(s). It is one of the most important problems in physical sciences. However, except for some cases of linear inversions (e.g., in 1D inversion) [1][2][3][4], most nonlinear inversions still present considerable difficulties. In seismic inversions, involving the imaging of Earth's deep subsurface structures, the traveltime inversion is the most tractable [5]. A more ambitious inversion approach is that of full waveform inversion, in which a common strategy is to retrieve the model parameters by minimizing a misfit function. While simple in concept, the success of full waveform inversion has been rather limited because of the extensive computational requirement and difficulty in realizing target convergence. Some time ago, Tarantola [6] proposed a scheme of full waveform inversion for acoustic systems, which was subsequently implemented by Gauthier et al. [7]. If only reflection data were used, the method can map the high spatial frequency components of the model, e.g., the interfaces, but totally fails in recovering the low spatial frequency information, e.g., the layer velocities. This so-called low frequency lacuna problem is rather well known in other seismic imaging approaches as well. Later literature on full wave inversion also met similar convergence problems [8][9][10][11][12]. The use of global minimizing processes [13][14][15][16] has shown much better convergence characteristics, but at the expense of computational efficiency. Symes [17] proposed a smooth and convex misfit function by using model parameters which are linear in the inversion calculation. This method has some successful applications [18,19]. Another proposal is to improve the initial model by using the hybrid inversion method, which minimizes a weighted combination of first-arrival traveltime and seismogram misfit functions [20,21].In this Letter, we consider the full waveform inversion for a 2D layered acoustic system, with point sources and receivers, perhaps the simplest test case for nonlinear inversion and a first-order approximation to the structure of Earth's subsurface. By using the optimal basis functions alternately in the inversion process, we not only overcame the low frequency lacuna problem encountered before, but also obtained robust and accurate results. The physical reason for this success is elucidat...

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“…Moreover, we improve the descent direction by using the nonlinear conjugate gradient algorithm. Finally, global step lengths that scale each parameter gradient can be estimated using a line-search method in which the second-order approximation of the objective function is evaluated (Pica et al, 1990;Sambridge et al, 1991). This estimation step requires solving an additional forward modeling problem for each parameter, as well as solving a linear system of equations (Masmoudi and Alkhalifah, 2017).…”

Section: Methodsmentioning

confidence: 99%

Full-waveform inversion in acoustic orthorhombic media and application to a North Sea data set

Masmoudi

Alkhalifah

2018

GEOPHYSICS

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Full-waveform inversion (FWI) in anisotropic media is challenging, mainly because of the large computational cost, especially in 3D, and the potential trade-offs between the model parameters needed to describe such media. By analyzing the trade-offs and understanding the resolution limits of the inversion, we can constrain FWI to focus on the main parameters the data are sensitive to and push the inversion toward more reliable models of the subsurface. Orthorhombic anisotropy is one of the most practical approximations of the earth subsurface that takes into account the natural horizontal layering and the vertical fracture network. We investigate the feasibility of a multiparameter FWI for an acoustic orthorhombic model described by six parameters. We rely on a suitable parameterization based on the horizontal velocity and five dimensionless anisotropy parameters. This particular parameterization allows a multistage model inversion strategy in which the isotropic, then, the vertical transverse isotropic, and finally the orthorhombic model can be successively updated. We applied our acoustic orthorhombic inversion on the SEG-EAGE overthrust synthetic model. The observed data used in the inversion are obtained from an elastic variable density version of the model. The quality of the inverted model suggests that we may recover only four parameters, with different resolution scales depending on the scattering potential of these parameters. Therefore, these results give useful insights on the expected resolution of the inverted parameters and the potential constraints that could be applied to an orthorhombic model inversion. We determine the efficiency of the inversion approach on real data from the North Sea. The inverted model is in agreement with the geologic structures and well-log information.

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Nonlinear inversion of seismic reflection data in a laterally invariant medium

Cited by 234 publications

References 0 publications

Estimation of the Subsurface Reflection Coefficient Using the Prestack Reverse-Time Depth Migration.

Estimation of the Subsurface Reflection Coefficient Using the Prestack Reverse-Time Depth Migration.

Full Waveform Inversion with Optimal Basis Functions

Full-waveform inversion in acoustic orthorhombic media and application to a North Sea data set

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