Accurate and efficient velocity estimation using Transmission matrix formalism based on the domain decomposition method

Wang, Benfeng; Jakobsen, Morten; Wu, Ru‐Shan; Lu, Wenkai; Chen, Xiaohong

doi:10.1088/1361-6420/aa5998

Cited by 12 publications

(13 citation statements)

References 20 publications

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“…This special case deserves particular attention since exact results for the SPMs of two interacting domains can be used in a fast recursive manner for an arbitrary model, using either the so‐called thin‐slab propagator method (Jakobsen and Wu , ,b; Wang et al . ) or new formulas based on Strassen's () algorithm for fast matrix inversion. We start by discussing standard formulas for the SPM's of two interacting domains before we introduce new Strassen‐based formulas we have derived.…”

Section: Domain Decomposition Methodsmentioning

confidence: 99%

“…The above algorithm is somewhat faster Gauss elimination (Wang et al . ), but the asymptotic computational complexity still scales like N 3 .…”

Section: Domain Decomposition Methodsmentioning

confidence: 99%

“…However, Gauss elimination is not optimal (Strassen ), and thus, we may accelerate the calculation of the T‐matrix by using the domain decomposition method (Jakobsen and Wu ; Jakobsen and Wu ,b; Wang et al . ) further developed here.…”

Section: T‐matrix Approach To Seismic Full‐waveform Modellingmentioning

confidence: 96%

“…Jakobsen and Ursin () presented a T‐matrix approach to seismic FWI, which shares many of the same advantages as the CSI method but is fully consistent with the (quadratically convergent) Gauss–Newton method and compatible with multiple scattering and renormalisation theory that may potentially help us further reduce the computational cost and starting model sensitivity (e.g., Jakobsen and Wu ,b; Levinson and Markel ,b; Jakobsen and Wu ; Wang et al . ).…”

Section: Introductionmentioning

confidence: 97%

“…We have also derived analytical results for the special case of two interacting domains (Jakobsen and Wu , ,b; Wang et al . ) and established a link to Strassen's method for fast matrix inversion.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Domain Decomposition Methodsmentioning

confidence: 99%

“…The above algorithm is somewhat faster Gauss elimination (Wang et al . ), but the asymptotic computational complexity still scales like N 3 .…”

Section: Domain Decomposition Methodsmentioning

confidence: 99%