Applications of seismic travel-time tomography

Bording, Ralph Phillip; Gersztenkorn, Adam; Lines, Larry; Scales, John A.; Treitel, Sven

doi:10.1111/j.1365-246x.1987.tb00728.x

Cited by 121 publications

(47 citation statements)

References 24 publications

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“…the reconstruction of maps of properties through a domain from sets of measurements, has applications in a number of areas, including medicine [1,2] and geophysics [3]. One important application of quantitative imaging methods is guided wave tomography.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of inversion approaches for guided wave thickness mapping

Huthwaite

2014

Proc. R. Soc. A.

111

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Accurate inversion is vital for quantitative imaging, including ultrasonic guided wave tomography, where thickness maps of plate-like structures are reconstructed to quantify corrosion damage. The dispersive properties of guided waves are often exploited to enable thickness maps to be produced from wave speed reconstructions. Ray tomography, diffraction tomography and a hybrid algorithm combining their features were investigated to reconstruct wave speed. Test data produced from simple defects of different sizes using a realistic full elastic guided wave model and the equivalent idealized acoustic model were passed to the imaging algorithms, generating wave speed maps, and, from these, thickness maps. For both datasets, ray tomography exhibited poor resolution. Diffraction tomography performed better, but was limited to shallow, small defects. The hybrid algorithm achieved the best results, giving a resolution around 1.5-2 wavelengths from the realistic test data compared to half wavelength from the idealized case. These results were validated with experimental data, and also extended to a realistic corrosion patch confirming the trends demonstrated with simple defects. The resolution loss with realistic data compared with idealized data indicates the acoustic model cannot accurately capture guided wave scattering and an alternative approach is necessary for better resolution reconstructions.

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Section: Introductionmentioning

confidence: 99%

Evaluation of inversion approaches for guided wave thickness mapping

Huthwaite

2014

Proc. R. Soc. A.

111

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“…where x and y are spatial Cartesian coordinates in the horizontal direction, dl is the differential distance along the ray, and s x; y ð Þ ¼ 1=v x; y ð Þ is the slowness (inverse of velocity) at point (x, y) [Bording et al, 1987]. With the simple straight ray path assumption, this formulation leads to travel times (measurements) that are linearly related to the slowness of the medium (parameters).…”

Section: Computational Complexitymentioning

confidence: 99%

Learning sparse geologic dictionaries from low-rank representations of facies connectivity for flow model calibration

Liu

Jafarpour

2013

Water Resour. Res.

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[1] Sparse geologic dictionaries provide a novel approach for subsurface flow model representation and calibration. Learning sparse dictionaries from prior training data sets is an effective approach to describe complex geologic connectivity patterns in subsurface imaging applications. However, the computational cost of sparse learning algorithms becomes prohibitive for large models. Performing the sparse dictionary learning process on smaller image patches (segments) provides a simple approach to address this problem in image processing applications. However, in underdetermined subsurface flow model calibration inverse problems, reconstruction of a segmented image can introduce significant structural distortion and discontinuity at the boundaries of the segments. This paper proposes an alternative sparse learning approach where the sparse dictionaries are learned from low-rank representations of the large-scale training data set in spectral domains (e.g., frequency domain). The objective is to develop a computationally efficient dictionary learning approach that emphasizes large-scale spatial connectivity patterns. This is achieved by removing the strong spatial correlations in the training data, thereby eliminating a large number of insignificant components from the sparse learning computation. In addition to improving the computational complexity, sparse learning from low-rank training data sets suppresses the small-scale details from entering the reconstruction of large-scale connectivity patterns, thereby providing a regularization effect in solving the resulting illposed inverse problems. We apply the proposed approach to travel-time tomography inversion and nonlinear subsurface flow model calibration inverse problems to demonstrate its effectiveness and practicality.Citation: Liu, E., and B. Jafarpour (2013), Learning sparse geologic dictionaries from low-rank representations of facies connectivity for flow model calibration, Water Resour. Res., 49,[7088][7089][7090][7091][7092][7093][7094][7095][7096][7097][7098][7099][7100][7101]

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“…The misfit function is highly nonlinear in nature, particularly when anisotropy is taken into account. Smoothing aims to prevent the algorithm from getting trapped in one of the many local minima (Bording et al, 1987;Bunks et al, 1995;Woodward et al, 2008). In this regard, we begin with a large filter length and gradually reduce it.…”

Section: Smoothing the Gradientmentioning

confidence: 99%

First-arrival traveltime tomography for anisotropic media using the adjoint-state method

Waheed

Flagg

Yarman

2016

SEG Technical Program Expanded Abstracts 2016

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Traveltime tomography using transmission data has been widely used for static corrections and for obtaining near-surface models for seismic depth imaging. More recently, it is also being used to build initial models for full-waveform inversion. The classic traveltime tomography approach based on ray tracing has difficulties in handling large data sets arising from current seismic acquisition surveys. Some of these difficulties can be addressed using the adjoint-state method, due to its low memory requirement and numerical efficiency. By coupling the gradient computation to nonlinear optimization, it avoids the need for explicit computation of the Fréchet derivative matrix. Furthermore, its cost is equivalent to twice the solution of the forwardmodeling problem, irrespective of the size of the input data. The presence of anisotropy in the subsurface has been well established during the past few decades. The improved seismic images obtained by incorporating anisotropy into the seismic processing workflow justify the effort. However, previous literature on the adjoint-state method has only addressed the isotropic approximation of the subsurface. We have extended the adjointstate technique for first-arrival traveltime tomography to vertical transversely isotropic (VTI) media. Because δ is weakly resolvable from surface seismic alone, we have developed the mathematical framework and procedure to invert for v NMO and η. Our numerical tests on the VTI SEAM model demonstrate the ability of the algorithm to invert for near-surface model parameters and reveal the accuracy achievable by the algorithm.

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Applications of seismic travel-time tomography

Cited by 121 publications

References 24 publications

Evaluation of inversion approaches for guided wave thickness mapping

Evaluation of inversion approaches for guided wave thickness mapping

Learning sparse geologic dictionaries from low-rank representations of facies connectivity for flow model calibration

First-arrival traveltime tomography for anisotropic media using the adjoint-state method

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