Waveform inversion by model reduction using spline interpolation

Barnier, Guillaume; Biondi, Ettore; Clapp, Robert G.

doi:10.1190/segam2019-3216866.1

Cited by 13 publications

(5 citation statements)

References 17 publications

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“…The success of FWIME requires the presence of two ingredients: (1) our new loss function formulation, and (2) our model-space multi-scale strategy. The multi-scale strategy by itself is not sufficient to mitigate the presence of local minima because the gradient relies on the useful tomographic component, as illustrated by the numerical examples in this section and thoroughly studied in [46]. We also show that minimizing our new loss formulation without being able to control the resolution of the model updates can initially introduce spurious high-wavenumber features, which are detrimental.…”

Section: Fwime Theory: Summarymentioning

confidence: 88%

“…In the FWIME scheme, we embedded prior information (lateral smoothness) by using an extremely coarse initial spline grid. For a fair comparison, we also attempted to improve the results obtained with conventional FWI by using the same spline parametrization sequence, as proposed by [46]. However (and as expected), this test did not manage to enhance the quality of the FWI inverted model.…”

Section: Inversion Of Diving Wavesmentioning

confidence: 99%

“…We devise a new optimization process which is a crucial ingredient of our method. We adapt the general model-space multi-scale method presented in [46] to our FWIME scheme. We parametrize our unknown velocity model on B-spline grids, and we simultaneously invert the full data-bandwidth while gradually refining the grid spacing with iterations [47, 48, ].…”

Section: Introductionmentioning

confidence: 99%

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Full-waveform inversion by model extension

Barnier

Biondi

2018

SEG Technical Program Expanded Abstracts 2018

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We describe a new method, full waveform inversion by model extension (FWIME) that recovers accurate acoustic subsurface velocity models from seismic data, when conventional methods fail. We leverage the advantageous convergence properties of wave-equation migration velocity analysis (WEMVA) with the accuracy and high-resolution nature of acoustic full waveform inversion (FWI) by combining them into a robust mathematically-consistent workflow with minimal need for user inputs. The novelty of FWIME resides in the design of a new cost function and a novel optimization strategy to combine the two techniques, making our approach more efficient and powerful than applying them sequentially. We observe that FWIME mitigates the need for accurate initial models and low-frequency long-offset data, which can be challenging to acquire. Our new objective function contains two components. First, we modify the forward mapping of the FWI problem by adding a data-correcting term computed with an extended demigration operator, whose goal is to ensure phase matching between predicted and observed data, even when the initial model is inaccurate. The second component, which is a modified WEMVA cost function, allows us to progressively remove the contributions of the data-correcting term throughout the inversion process. The coupling between the two components is handled by the variable projection method, which reduces the number of adjustable hyper-parameters, thereby making our solution simple to use. We devise a model-space multi-scale optimization scheme by re-parametrizing the velocity model on spline grids to control the resolution of the model updates. We generate three cycle-skipped 2D synthetic datasets, each containing only one type of wave (transmitted, reflected, refracted), and we analyze how FWIME successfully recovers accurate solutions with the same procedure for all three cases. In a second paper, we apply FWIME to challenging realistic examples where we simultaneously invert all wave modes.

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Section: Fwime Theory: Summarymentioning

confidence: 88%

Section: Inversion Of Diving Wavesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Full-waveform inversion by model extension

Barnier

Biondi

2018

SEG Technical Program Expanded Abstracts 2018

Self Cite

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“…Instead of smoothing the model according to the resolution, projection of the parameters from a modeling space to an inversion space could be considered to avoid over-parameterization issues. Projection on a spline basis (Dierckx, 1993) has been for instance used in FWI (Barnier et al, 2019), and is common in tomography (Nolet, 2008). Another example, at a more theoretical level, is a parameterization on a basis of eigenvectors of a TV-based regularization operator (Grote et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

On the use of nonlinear anisotropic diffusion filters for seismic imaging using the full waveform

Métivier¹,

Brossier²

2022

Inverse Problems

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Nonlinear anisotropic diffusion filters have been introduced in the field of image processing for image denoising and image restoration. They are based on the solution of partial differential equations involving a nonlinear anisotropic diffusion operator. From a mathematical point of view, these filters enjoy attractive properties, such as minimum-maximum principle, and an inherent decomposition of the images in different scales. We investigate in this study how these filters can be applied to help solving data-fitting inverse problems. We focus on seismic imaging using the full waveform, a well known nonlinear instance of such inverse problems. In this context, we show how the filters can be applied directly to the solution space, to enhance the structural coherence of the parameters representing the subsurface mechanical properties and accelerate the convergence. We \textcolor{red}{also} show how they can be applied to the seismic data itself. In the latter case, the method results in an original low-frequency data enhancement \textcolor{red}{technique} making it possible to stabilize the inversion process when started from an initial model away from the basin of attraction of the global minimizer. Numerical results on a 2D realistic synthetic full waveform inversion case study illustrate the interesting properties of both approaches.

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“…Many other solutions have been proposed and tested, such as, multiscale inversion (Bunks et al, 1995), wave-equation traveltime inversion (Luo & Schuster, 1991), tomographic full-waveform inversion (Biondi & Almomin, 2014), dictionary learning (L. Zhu et al, 2017;D. Li & Harris, 2018), model extension (Barnier et al, 2018a), and model reduction (Barnier et al, 2019). In addition to the strong non-linearity of FWI, uncertainty analysis of FWI results is challenging due both to the high dimensionality of the model space and to the demanding computational cost of solving the wave equation (Gebraad et al, 2020).…”

Section: Introductionmentioning

confidence: 99%

Integrating Deep Neural Networks with Full-waveform Inversion: Reparametrization, Regularization, and Uncertainty Quantification

Zhu,

Xu,

Darve

et al. 2020

Preprint

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Full-waveform inversion (FWI) is an imaging approach for modeling velocity structure by minimizing the misfit between recorded and predicted seismic waveforms. The strong nonlinearity of FWI resulting from fitting oscillatory waveforms can trap the optimization in local minima. We propose a neural-network-based full waveform inversion method (NNFWI) that integrates deep neural networks with FWI by representing the velocity model with a generative neural network. Neural networks can naturally introduce spatial correlations as regularization to the generated velocity model, which suppresses noise in the gradients and mitigates local minima. The velocity model generated by neural networks is input to the same partial differential equation (PDE) solvers used in conventional FWI. The gradients of both the neural networks and PDEs are calculated using automatic differentiation, which back-propagates gradients through the acoustic/elastic PDEs and neural network layers to update the weights and biases of the generative neural network. Experiments on 1D velocity models, the Marmousi model, and the 2004 BP model demonstrate that NNFWI can mitigate local minima, especially for imaging high contrast features like salt bodies, and significantly improves the inversion in the presence of noise. Adding dropout layers to the neural network model also allows analyzing the uncertainty of the inversion results through Monte Carlo dropout. NNFWI opens a new pathway to combine deep learning and FWI for exploiting both the characteristics of deep neural networks and the high accuracy of PDE solvers. Because NNFWI does not require extra training data and optimization loops, it provides an attractive and straightforward alternative to conventional FWI.

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Waveform inversion by model reduction using spline interpolation

Cited by 13 publications

References 17 publications

Full-waveform inversion by model extension

Full-waveform inversion by model extension

On the use of nonlinear anisotropic diffusion filters for seismic imaging using the full waveform

Integrating Deep Neural Networks with Full-waveform Inversion: Reparametrization, Regularization, and Uncertainty Quantification

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