A Helmholtz iterative solver with semianalytical preconditioner for the frequency‐domain full‐waveform inversion

Neklyudov, Dmitry; Silvestrov, Ilya; Tcheverda, Vladimir

doi:10.1190/1.3513031

Cited by 2 publications

(6 citation statements)

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“…Finally, we obtain the conditions the data should satisfy for reconstructing reliably the macrovelocity below the well bottom. The theoretical results are verified by non-linear fullwaveform inversion of synthetic data using the forward modelling algorithm in the time-frequency domain developed by Neklyudov, Silvestrov and Tcheverda (2010).…”

Section: Introductionmentioning

confidence: 80%

“…Since the background is inhomogeneous in this case, the Green functions in equation are computed using the iterative forward modelling algorithm in the frequency domain with a semi‐analytical preconditioner proposed in Neklyudov et al . () (see Appendix ). We consider a 10 × 10 m grid in the target area and obtain matrix approximations of operators

\tilde{L} (c_{0}, ω_{i})

using equation , for the frequencies 3Hz, 2 Hz and 1 Hz.…”

Section: Singular Value Decomposition Analysismentioning

confidence: 99%

“…In order to identify the frequency content of the data required to recover the low-frequency velocity model, as in the previous example, we analyse the SVD of the linearized modelling operator. Since the background is inhomogeneous in this case, the Green functions in equation (5) are computed using the iterative forward modelling algorithm in the frequency domain with a semi-analytical preconditioner proposed in Neklyudov et al (2010) (see Appendix B). We consider a 10 × 10 m grid in the target area and obtain matrix approximations of operatorsL(c 0 , ω i ) using equation (5), for the frequencies 3Hz, 2 Hz and 1 Hz.…”

Section: The Gullfaks Modelmentioning

confidence: 99%

“…In this appendix we briefly review the results obtained in Neklyudov et al (2010) where a new method for numerical solution of the Helmholtz equation was proposed. The method is based on a Krylov-type linear solver, similar to several other iterative approaches (see e.g., Plessix 2007).…”

Section: Appendix Bmentioning

confidence: 99%

“…Therefore, an efficient preconditioner that improves the convergence is essential for application of such methods. C 2013 European Association of Geoscientists & Engineers, Geophysical Prospecting, 61, [1099][1100][1101][1102][1103][1104][1105][1106][1107][1108][1109][1110][1111][1112][1113] Full-waveform inversion for macro velocity model reconstruction 1113 Neklyudov et al (2010) proposed a novel right preconditioner as an inverse to a complex damped Helmholtz operator with 1D background velocity. To introduce this preconditioner let us rewrite the Helmholtz equation (2) as…”

Section: Appendix Bmentioning

confidence: 99%

See 4 more Smart Citations

Full‐waveform inversion for macro velocity model reconstruction in look‐ahead offset vertical seismic profile: numerical singular value decomposition‐based analysis

Silvestrov

Neklyudov

Kostov

et al. 2013

Geophysical Prospecting

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Full‐waveform inversion is currently considered as a potential tool for improving depth‐velocity models for areas with complex geology. It is well‐known that success of the inversion is very sensitive to the available low‐frequency content of the data. In the paper we investigate this issue considering a look‐ahead offset vertical seismic profile survey and applying singular value decomposition analysis of a linearized forward map as the main tool. We demonstrate with this technique the difference between the sequential full‐waveform inversion strategy and the original time‐domain approach proposed in the early 1980s. We emphasize the role of the lowest frequency in the data, which is necessary for reliable velocity model inversion in particular cases. Finally we show the existence of a trade‐off between the lowest frequency and a regularization parameter of the inversion procedure. The presented approach may be adapted to answer general questions regarding the quality of data and acquisition system parameters required for feasible full‐waveform inversion.

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Section: Introductionmentioning

confidence: 80%