Nonlinear seismic waveform inversion using a Born iterative T-matrix method

Jakobsen, Morten; Ursin, Bjørn

doi:10.1190/segam2012-0532.1

Cited by 8 publications

(3 citation statements)

References 9 publications

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“…An alternative way, which is more convenient and computational efficient, is to formulate the inverse scattering in the image space (model space). This is the approach of contrast-source approach and T-matrix approach (e.g., Prosser, 1969;Weglein et al, 2003;Jakobsen, 2012;Jakobsen and Ursin, 2012). Here, we will apply the T-matrix approach to the NLSO (nonlinear sensitivity operator).…”

Section: Forward and Inverse Scattering Series In T-matrix Approachmentioning

confidence: 99%

Nonlinear sensitivity operator and inverse thin-slab propagator for tomographic waveform inversion

Wu¹,

Hu²,

Wang³

2014

SEG Technical Program Expanded Abstracts 2014

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We derived the nonlinear sensitivity operator and the related inverse thin-slab propagator (ITSP) for nonlinear tomographic waveform inversion based on the theory of nonlinear partial derivative operator. The inverse propagator is based on a renormalization procedure to the forward and inverse T-matrix series. The inverse thin-slab propagator solves the divergence problem of the inverse series for strong perturbations by stepwise partial summation (renormalization). Numerical tests showed that the inverse Born T-series starts to diverge at 20% perturbation (for the given model), while the inverse thinslab propagator has no convergence problem for up to 50% perturbation. This convergence improvement has potential applications to the iterative procedure of waveform inversion.

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Section: Forward and Inverse Scattering Series In T-matrix Approachmentioning

confidence: 99%

Nonlinear sensitivity operator and inverse thin-slab propagator for tomographic waveform inversion

Wu¹,

Hu²,

Wang³

2014

SEG Technical Program Expanded Abstracts 2014

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“…; Jakobsen and Wu , ; Liu and Zheng ). FWI can be implemented using the adjoint‐state method or an equivalent scattering‐integral formulation (Remis and van den Berg ; Chen, Jordan and Zhao ) either in the time domain (Tarantola , ; Mora ; Vigh and Starr ) or in the frequency domain (Pratt and Worthington ; Jakobsen and Ursin ; Tao and Sen ; Jakobsen and Ursin ; Malovichko et al . ).…”

Section: Introductionmentioning

confidence: 99%

“…FWI is normally formulated as an optimisation problem in which one minimises the difference between observed and predicted waveform data (Tarantola 1984;Metivier et al 2014), although promising direct nonlinear inversion methods also exist (Weglein et al 2003;Jakobsen andWu 2016c, 2017;Liu and Zheng 2017). FWI can be implemented using the adjoint-state method or an equivalent scattering-integral formulation (Remis and van den Berg 2000;Chen, Jordan and Zhao 2007) either in the time domain (Tarantola 1984(Tarantola , 1986Mora 1987;Vigh and Starr 2008) or in the frequency domain (Pratt and Worthington 1990;Jakobsen and Ursin 2012;Tao and Sen 2013;Jakobsen and Ursin 2015;Malovichko et al 2017). Here, we address only iterative nonlinear inversion methods in the frequency domain.…”

Section: Introductionmentioning

confidence: 99%

Accelerating the T‐matrix approach to seismic full‐waveform inversion by domain decomposition

Jakobsen

2018

Geophysical Prospecting

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A seismic variant of the distorted Born iterative inversion method, which is commonly used in electromagnetic and acoustic (medical) imaging, has been recently developed on the basis of the T‐matrix approach of multiple scattering theory. The distorted Born iterative method is consistent with the Gauss–Newton method, but its implementation is different, and there are potentially significant computational advantages of using the T‐matrix approach in this context. It has been shown that the computational cost associated with the updating of the background medium Green functions after each iteration can be reduced via the use of various linearisation or quasi‐linearisation techniques. However, these techniques for reducing the computational cost may not work well in the presence of strong contrasts. To deal with this, we have now developed a domain decomposition method, which allows one to decompose the seismic velocity model into an arbitrary number of heterogeneous domains that can be treated separately and in parallel. The new domain decomposition method is based on the concept of a scattering‐path matrix, which is well known in solid‐state physics. If the seismic model consists of different domains that are well separated (e.g., different reservoirs within a sedimentary basin), then the scattering‐path matrix formulation can be used to derive approximations that are sufficiently accurate but far more speedy and much less memory demanding because they ignore the interaction between different domains. However, we show here that one can also use the scattering‐path matrix formulation to calculate the overall T‐matrix for a large model exactly without any approximations at a computational cost that is significantly smaller than the cost associated with an exact formal matrix inversion solution. This is because we have derived exact analytical results for the special case of two interacting domains and combined them with Strassen's formulas for fast recursive matrix inversion. To illustrate the fact that we have accelerated the T‐matrix approach to full‐waveform inversion by domain decomposition, we perform a series of numerical experiments based on synthetic data associated with a complex salt model and a simpler two‐dimensional model that can be naturally decomposed into separate upper and lower domains. If the domain decomposition method is combined with an additional layer of multi‐scale regularisation (based on spatial smoothing of the sensitivity matrix and the data residual vector along the receiver line) beyond standard sequential frequency inversion, then one apparently can also obtain stable inversion results in the absence of ultra‐low frequencies and reduced computation times.

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Bayesian estimation of reservoir properties—effects of uncertainty quantification of 4D seismic data

et al. 2016

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Nonlinear seismic waveform inversion using a Born iterative T-matrix method

Cited by 8 publications

References 9 publications

Nonlinear sensitivity operator and inverse thin-slab propagator for tomographic waveform inversion

Nonlinear sensitivity operator and inverse thin-slab propagator for tomographic waveform inversion

Accelerating the T‐matrix approach to seismic full‐waveform inversion by domain decomposition

Bayesian estimation of reservoir properties—effects of uncertainty quantification of 4D seismic data

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