Convergence acceleration in scattering series and seismic waveform inversion using nonlinear Shanks transformation

Eftekhar, Roya; Hu, Hao; Zheng, Yingcai

doi:10.1093/gji/ggy228

Cited by 8 publications

(3 citation statements)

References 49 publications

(25 reference statements)

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“…Both the top and bottom boundaries of the model are set up as half-space boundary conditions. The synthetic data (pressure and particle velocity) in both examples are generated by a propagator matrix method (e.g., Eftekhar et al, 2018). The plane wave is injected at a depth of 0 m and propagated downward into the model.…”

Section: Numerical Examplesmentioning

confidence: 99%

Simultaneous Inversion of Layered Velocity and Density Profiles Using Direct Waveform Inversion (DWI): 1D Case

2022

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To better interpret the subsurface structures and characterize the reservoir, a depth model quantifying P-wave velocity together with additional rock’s physical parameters such as density, the S-wave velocity, and anisotropy is always preferred by geologists and engineers. Tradeoffs among different parameters can bring extra challenges to the seismic inversion process. In this study, we propose and test the Direct Waveform Inversion (DWI) scheme to simultaneously invert for 1D layered velocity and density profiles, using reflection seismic waveforms recorded on the surface. The recorded data includes primary reflections and interbed multiples. DWI is implemented in the time-space domain then followed by a wavefield extrapolation to downward continue the source and receiver. By explicitly enforcing the wavefield time-space causality, DWI can recursively determine the subsurface seismic structure in a local layer-by-layer fashion for both sharp interfaces and the properties of the layers, from shallow to deep depths. DWI is different from the layer stripping methods in the frequency domain. By not requiring a global initial model, DWI also avoids many nonlinear optimization problems, such as the local minima or the need for an accurate initial model in most waveform inversion schemes. Two numerical tests show the validity of this DWI scheme serving as a new strategy for multi-parameter seismic inversion.

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Section: Numerical Examplesmentioning

confidence: 99%

Simultaneous Inversion of Layered Velocity and Density Profiles Using Direct Waveform Inversion (DWI): 1D Case

2022

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“…Although they are frequently used in scalar sequences, series acceleration methods can also be applied to vector and matrix cases, giving rise to extrapolation methods [17], like the well known Richardson's method [18, p. 136]. Some acceleration methods have already been applied to fixed-point schemes in seismic [19] and electromagnetic [20] scattering. However, such implementations require, at each iteration, vector operations involving several terms of the original sequence.…”

Section: Introductionmentioning

confidence: 99%

Acceleration of Born Series by Change of Variables

Lopez-Menchon

Rius

Heldring

et al. 2021

IEEE Trans. Antennas Propagat.

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In this work, we propose a method to enhance the convergence of the Born series. The Born series is widely used in scattering theory, but its convergence is only guaranteed under certain restrictive conditions which limit the cases where this formulation can be applied. The proposed method, based on modifying the singularities of the resolvent operator by a change of variables, accelerates the convergence of the series or even achieves convergence in otherwise divergent cases. Due to its low computational cost and ease of implementation, the method preserves the advantages of the Born series while it extends its range of application. It can also be applied to a variety of methods relying on the same mathematical principles as the Born series. Numerical examples are provided to show that a significant improvement can be achieved with simple techniques and with a limited knowledge about the operator spectrum.

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“…Unlike other seismic forward modelling methods that include density and velocity, we have derived two coupled integral equations and combined them into a vectorial Lippmann–Schwinger (LS) equation. Because there are already many methods for solving the LS equation (Jakobsen and Ursin, 2015; Jakobsen and Wu, 2016; Eftekhar et al ., 2018; Huang et al ., 2020; Eikrem et al ., 2020), we may use those methods to solve the vectorial LS equation. This is our main motivation to extend the previous methods to the variable velocity and density case.…”

Section: Introductionmentioning

confidence: 99%

Homotopy scattering series for seismic forward modelling with variable density and velocity

Xiang

Eikrem

Jakobsen

et al. 2021

Geophysical Prospecting

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We have derived a convergent scattering series solution for the frequency-domain wave equation in acoustic media with variable density and velocity. The convergent scattering series solution is based on the homotopy analysis of a vectorial integral equation of the Lippmann-Schwinger type. By using the Green's function and partial integration, we have derived the vectorial integral equation of the Lippmann-Schwinger type that involves the pressure gradient field as well as the pressure field from the wave equation. The vectorial Lippmann-Schwinger equation can in principle be solved via matrix inversion, but the computational cost of matrix inversion scales like N 3 , where N is the number of grid blocks. The computational cost can be significantly reduced if one solves the vectorial Lippmann-Schwinger equation iteratively. A simple iterative solution is the Born series, but it is only convergent when the scattering potential is sufficiently small. In this study, we have used the so-called homotopy analysis method to derive an iterative solution for the vectorial Lippmann-Schwinger equation which can be made convergent even in strongly scattering media. The computational cost of our convergent scattering series scales as N 2 . Our algorithm, which is based on the homotopy analysis method, involves a convergence control operator that we select using hierarchical matrices. We use a three-layer model and a resampled version of the SEG/EAGE salt model to show the performance of the developed convergent scattering series.

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Convergence acceleration in scattering series and seismic waveform inversion using nonlinear Shanks transformation

Cited by 8 publications

References 49 publications

Simultaneous Inversion of Layered Velocity and Density Profiles Using Direct Waveform Inversion (DWI): 1D Case

Simultaneous Inversion of Layered Velocity and Density Profiles Using Direct Waveform Inversion (DWI): 1D Case

Acceleration of Born Series by Change of Variables

Homotopy scattering series for seismic forward modelling with variable density and velocity

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