Fast randomized full-waveform inversion with compressive sensing

Geophysics ◽  
2012 ◽  
Vol 77 (3) ◽  
pp. A13-A17 ◽  
Author(s):  
Xiang Li ◽  
Aleksandr Y. Aravkin ◽  
Tristan van Leeuwen ◽  
Felix J. Herrmann
Keyword(s):  
Compressive Sensing ◽  
Waveform Inversion ◽  
Nonlinear Least Squares ◽  
Seismic Inversion ◽  
Full Waveform Inversion ◽  
Sampling Strategies ◽  
Computational Costs ◽  
Full Waveform ◽  
Nonlinear Least Squares Problem ◽  
Marine Data

Wave-equation-based seismic inversion can be formulated as a nonlinear least-squares problem. The demand for higher-resolution models in more geologically complex areas drives the need to develop techniques that exploit the special structure of full-waveform inversion to reduce the computational burden and to regularize the inverse problem. We meet these goals by using ideas from compressive sensing and stochastic optimization to design a novel Gauss-Newton method, where the updates are computed from random subsets of the data via curvelet-domain sparsity promotion. Two different subset sampling strategies are considered: randomized source encoding, and drawing sequential shots firing at random source locations from marine data with missing near and far offsets. In both cases, we obtain excellent inversion results compared to conventional methods at reduced computational costs.

FULL-WAVEFORM INVERSION WITH SOURCE AND RECEIVER COUPLING EFFECTS CORRECTION

Geophysics ◽  
2021 ◽  
pp. 1-37
Author(s):  
Xinhai Hu ◽  
Wei Guoqi ◽  
Jianyong Song ◽  
Zhifang Yang ◽  
Minghui Lu ◽  
...  
Keyword(s):  
Waveform Inversion ◽  
Nonlinear Least Squares ◽  
Real Data ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Linear Inversion ◽  
Near Surface ◽  
Model Parameter ◽  
Full Waveform ◽  
Coupling Factors

Coupling factors of sources and receivers vary dramatically due to the strong heterogeneity of near surface, which are as important as the model parameters for the inversion success. We propose a full waveform inversion (FWI) scheme that corrects for variable coupling factors while updating the model parameter. A linear inversion is embedded into the scheme to estimate the source and receiver factors and compute the amplitude weights according to the acquisition geometry. After the weights are introduced in the objective function, the inversion falls into the category of separable nonlinear least-squares problems. Hence, we could use the variable projection technique widely used in source estimation problem to invert the model parameter without the knowledge of source and receiver factors. The efficacy of the inversion scheme is demonstrated with two synthetic examples and one real data test.

scholarly journals Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. R43-R62 ◽  
Author(s):  
Yunan Yang ◽  
Björn Engquist ◽  
Junzhe Sun ◽  
Brittany F. Hamfeldt
Keyword(s):  
Least Squares ◽  
Optimal Transport ◽  
Waveform Inversion ◽  
Transportation Cost ◽  
Velocity Model ◽  
Seismic Inversion ◽  
Full Waveform Inversion ◽  
Wasserstein Metric ◽  
Full Waveform ◽  
Adjoint State

Conventional full-waveform inversion (FWI) using the least-squares norm as a misfit function is known to suffer from cycle-skipping issues that increase the risk of computing a local rather than the global minimum of the misfit. The quadratic Wasserstein metric has proven to have many ideal properties with regard to convexity and insensitivity to noise. When the observed and predicted seismic data are considered to be two density functions, the quadratic Wasserstein metric corresponds to the optimal cost of rearranging one density into the other, in which the transportation cost is quadratic in distance. Unlike the least-squares norm, the quadratic Wasserstein metric measures not only amplitude differences but also global phase shifts, which helps to avoid cycle-skipping issues. We have developed a new way of using the quadratic Wasserstein metric trace by trace in FWI and compare it with the global quadratic Wasserstein metric via the solution of the Monge-Ampère equation. We incorporate the quadratic Wasserstein metric technique into the framework of the adjoint-state method and apply it to several 2D examples. With the corresponding adjoint source, the velocity model can be updated using a quasi-Newton method. Numerical results indicate the effectiveness of the quadratic Wasserstein metric in alleviating cycle-skipping issues and sensitivity to noise. The mathematical theory and numerical examples demonstrate that the quadratic Wasserstein metric is a good candidate for a misfit function in seismic inversion.

Modified Gauss-Newton full-waveform inversion explained — Why sparsity-promoting updates do matter

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. R125-R138 ◽  
Author(s):  
Xiang Li ◽  
Ernie Esser ◽  
Felix J. Herrmann
Keyword(s):  
Phase Retrieval ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Nonlinear Least Squares ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Retrieval Problem ◽  
To Come ◽  
The One ◽  
Descent Directions

Full-waveform inversion (FWI) can be formulated as a nonlinear least-squares optimization problem. This nonconvex problem can be computationally expensive because it requires repeated solutions of the wave equation. Randomized subsampling techniques allow us to work with small subsets of (monochromatic) source experiments, reducing the computational cost. However, this subsampling may weaken subsurface illumination or introduce subsampling-related incoherent artifacts. These subsampling-related artifacts — in conjunction with the desire to obtain high-fidelity inversion results — motivate us to come up with a technique to regularize this inversion problem. Following earlier work, we have taken advantage of the fact that curvelets represent subsurface models and model perturbations parsimoniously. At first impulse, promoting sparsity on the model directly seemed the most natural way to proceed, but we have determined that in certain cases it can be advantageous to promote sparsity on the Gauss-Newton updates instead. Although constraining the one norm of the descent directions did not change the underlying FWI objective, the constrained model updates remained descent directions, removed subsampling-related artifacts, and improved the overall inversion result. We have empirically observed this phenomenon in situations where the different model updates occurred at roughly the same locations in the curvelet domain. We have further investigated and analyzed this behavior, in which nonlinear inversions benefit from sparsity-promoting constraints on the updates, by means of a set of carefully selected examples including the phase retrieval problem and time-harmonic FWI. In all cases, we have observed a faster decay of the residual and model error as a function of the number of iterations.

scholarly journals Elastic Full-Waveform Inversion Using Migration‑Based Depth Reflector Representation in the Data Domain

2020 ◽  
Author(s):  
Vladimir Cheverda
Keyword(s):  
Seismic Data ◽  
Optimization Problem ◽  
Waveform Inversion ◽  
Nonlinear Least Squares ◽  
Model Space ◽  
Full Waveform Inversion ◽  
Brute Force ◽  
Data Inversion ◽  
Full Waveform ◽  
Least Squares Optimization

Full-waveform seismic data inversion has given rise to hope for the simultaneous and automated execution of tomography and imaging by solving a nonlinear least-squares optimization problem. As previously recognized, brute force minimization by classical methods is hopeless if the data lacks low temporal frequencies. The article developed a reliable numerical method for recovering smooth velocity using model space decomposition. We present realistic synthetic examples to test the presented algorithm.

scholarly journals Optimal full-waveform inversion strategy for marine data in azimuthally rotated elastic orthorhombic media

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. R307-R320 ◽  
Author(s):  
Ju-Won Oh ◽  
Tariq Alkhalifah
Keyword(s):  
High Resolution ◽  
Reservoir Characterization ◽  
Waveform Inversion ◽  
Horizontal Layer ◽  
Full Waveform Inversion ◽  
Radiation Patterns ◽  
Trade Off ◽  
Full Waveform ◽  
Gradient Direction ◽  
Marine Data

The orthorhombic (ORT) anisotropic description of earth layers can allow the capture of much of the earth’s anisotropic complexity. The inversion for high-resolution azimuthal variation of anisotropy is important for reservoir characterization, among other applications. A high-resolution description of the azimuth of fractures can help us to predict flow preferences. To verify the feasibility of multiparameter full-waveform inversion (FWI) for marine data assuming azimuthally rotated elastic ORT media, we have analyzed the radiation patterns and gradient directions of ORT parameters to the reflection data. First, we express the gradient direction of the ORT parameters considering the azimuthal rotation of the symmetric planes. Then, to support our observations in the gradient direction, the radiation patterns of the partial derivative wavefields from each parameter perturbation are also derived under the rotated elastic ORT assumption. To find an optimal parameterization, we compare three different parameterizations: monoclinic, velocity-based, and hierarchical parameterizations. Then, we suggest an optimal multistage update strategy by analyzing the behavior of the rotation angle as a FWI target. To analyze the trade-off among parameters in different parameterizations, we calculate the gradient direction from a hockey-puck model, in which each parameter is perturbed at the different location on a horizontal layer. The trade-off analysis supports that the hierarchical parameterization provides us with more opportunities to build up subsurface models with less trade-off between parameters and less influence of the azimuthal rotation of ORT anisotropy. The feasibility of the proposed FWI strategy is examined using synthetic marine streamer data from a simple 3D reservoir model with a fractured layer.

scholarly journals A dual formulation of wavefield reconstruction inversion for large-scale seismic inversion

Geophysics ◽  
2021 ◽  
pp. 1-81
Author(s):  
Gabrio Rizzuti ◽  
mathias louboutin ◽  
Rongrong Wang ◽  
Felix J. Herrmann
Keyword(s):  
Large Scale ◽  
State Of The Art ◽  
Finite Difference Methods ◽  
Waveform Inversion ◽  
Seismic Inversion ◽  
Full Waveform Inversion ◽  
Dual Formulation ◽  
Full Waveform ◽  
Inversion Techniques ◽  
3D Applications

Many of the seismic inversion techniques currently proposed that focus on robustness with respect to the background model choice are not apt to large-scale 3D applications, and the methods that are computationally feasible for industrial problems, such as full waveform inversion, are notoriously limited by convergence stagnation and require adequate starting models. We propose a novel solution that is both scalable and less sensitive to starting models or inaccurate parameters (such as anisotropy) that are typically kept fixed during inversion. It is based on a dual reformulation of the classical wavefield reconstruction inversion, whose empirical robustness with respect to these issues is well documented in the literature. While the classical version is not suited to 3D, as it leverages expensive frequency-domain solvers for the wave equation, our proposal allows the deployment of state-of-the-art time-domain finite-difference methods, and is potentially mature for industrial-scale problems.

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