arXiv subjects

Hossein S. Aghamiry

Publications and source records attributed to Hossein S. Aghamiry.

26 records · Page 2Linked to original sources

arXiv2020

Complex-valued Imaging with Total Variation Regularization: An Application to Full-Waveform Inversion in Visco-acoustic Media

Full waveform inversion (FWI) is a nonlinear PDE constrained optimization problem, which seeks to estimate constitutive parameters of a medium such as phase velocity, density, and anisotropy, by fitting waveforms. Attenuation is an additional parameter that needs to be taken into account in viscous media to exploit the full potential of FWI. Attenuation is more easily implemented in the frequency domain by using complex-valued velocities in the time-harmonic wave equation. These complex velocities are frequency-dependent to guarantee causality and account for dispersion. Since estimating a complex frequency-dependent velocity at each grid point in space is not realistic, the optimization is generally performed in the real domain by processing the phase velocity (or slowness) at a reference frequency and attenuation (or quality factor) as separate real parameters. This real parametrization requires an a priori empirical relation (such as the nonlinear Kolsky-Futterman (KF) or standard linear solid (SLS) attenuation models) between the complex velocity and the two real quantities, which is prone to generate modeling errors if it does not represent accurately the attenuation behavior of the subsurface. Moreover, it leads to a multivariate inverse problem, which is twice larger than the actual size of the medium and ill-posed due to the cross-talk between the two classes of real parameters. To alleviate these issues, we present a mono-variate algorithm that solves directly the optimization problem in the complex domain by processing in sequence narrow bands of frequencies under the assumption of band-wise frequency dependence of the sought complex velocities.

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arXiv2020

Full Waveform Inversion with Adaptive Regularization

Regularization is necessary for solving nonlinear ill-posed inverse problems arising in different fields of geosciences. The base of a suitable regularization is the prior expressed by the regularizer, which can be non-adaptive or adaptive (data-driven). In this paper, we propose general black-box regularization algorithms for solving nonlinear inverse problems such as full-waveform inversion (FWI), which admit empirical priors that are determined adaptively by sophisticated denoising algorithms. The nonlinear inverse problem is solved by a proximal Newton method, which generalizes the traditional Newton step in such a way to involve the gradients/subgradients of a (possibly non-differentiable) regularization function through operator splitting and proximal mappings. Furthermore, it requires to account for the Hessian matrix in the regularized least-squares optimization problem. We propose two different splitting algorithms for this task. In the first, we compute the Newton search direction with an iterative method based upon the first-order generalized iterative shrinkage-thresholding algorithm (ISTA), and hence Newton-ISTA (NISTA). The iterations require only Hessian-vector products to compute the gradient step of the quadratic approximation of the nonlinear objective function. The second relies on the alternating direction method of multipliers (ADMM), and hence Newton-ADMM (NADMM), where the least-square optimization subproblem and the regularization subproblem in the composite are decoupled through auxiliary variable and solved in an alternating mode. We compare NISTA and NADMM numerically by solving full-waveform inversion with BM3D regularizations. The tests show promising results obtained by both algorithms. However, NADMM shows a faster convergence rate than Newton-ISTA when using L-BFGS to solve the Newton system.

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arXiv2020

Attenuation imaging by wavefield reconstruction inversion with bound constraints and total variation regularization

Wavefield reconstruction inversion (WRI) extends the search space of Full Waveform Inversion (FWI) by allowing for wave equation errors during wavefield reconstruction to match the data from the first iteration. Then, the wavespeeds are updated from the wavefields by minimizing the source residuals. Performing these two tasks in alternating mode breaks down the nonlinear FWI as a sequence of two linear subproblems, relaying on the bilinearity of the wave equation. We solve this biconvex optimization with the alternating-direction method of multipliers (ADMM) to cancel out efficiently the data and source residuals in iterations and stabilize the parameter estimation with appropriate regularizations. Here, we extend WRI to viscoacoustic media for attenuation imaging. Attenuation reconstruction is challenging because of the small imprint of attenuation in the data and the cross-talks with velocities. To address these issues, we recast the multivariate viscoacoustic WRI as a triconvex optimization and update wavefields, squared slowness, and attenuation factor in alternating mode at each WRI iteration. This requires to linearize the attenuation-estimation subproblem via an approximated trilinear viscoacoustic wave equation. The iterative defect correction embedded in ADMM corrects the errors generated by this linearization, while the operator splitting allows us to tailor $\ell{1}$ regularization to each parameter class. A toy numerical example shows that these strategies mitigate cross-talk artifacts and noise from the attenuation reconstruction. A more realistic synthetic example representative of the North Sea validates the method.

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arXiv2019

Robust Wavefield Inversion via Phase Retrieval

Extended formulation of Full Waveform Inversion (FWI), called Wavefield Reconstruction Inversion (WRI), offers potential benefits of decreasing the nonlinearity of the inverse problem by replacing the explicit inverse of the ill-conditioned wave-equation operator of classical FWI (the oscillating Green functions) with a suitably defined data-driven regularized inverse. This regularization relaxes the wave-equation constraint to reconstruct wavefields that match the data, hence mitigating the risk of cycle skipping. The subsurface model parameters are then updated in a direction that reduces these constraint violations. However, in the case of a rough initial model, the phase errors in the reconstructed wavefields may trap the waveform inversion in a local minimum leading to inaccurate subsurface models. In this paper, in order to avoid matching such incorrect phase information during the early WRI iterations, we design a new cost function based upon phase retrieval, namely a process which seeks to reconstruct a signal from the amplitude of linear measurements. This new formulation, called Wavefield Inversion with Phase Retrieval (WIPR), further improves the robustness of the parameter estimation subproblem by a suitable phase correction. We implement the resulting WIPR problem with an alternating-direction approach, which combines the Majorization-Minimization (MM) algorithm to linearise the phase-retrieval term and a variable splitting technique based upon the alternating direction method of multipliers (ADMM). This new workflow equipped with Tikhonov-total variation (TT) regularization, which is the combination of second-order Tikhonov and total variation regularizations and bound constraints, successfully reconstructs the 2004 BP salt model from a sparse fixed-spread acquisition using a 3~Hz starting frequency and a homogeneous initial velocity model.

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arXiv2019

ADMM-based multi-parameter wavefield reconstruction inversion in VTI acoustic media with TV regularization

Full waveform inversion (FWI) is a nonlinear waveform matching procedure, which suffers from cycle skipping when the initial model is not kinematically-accurate enough. To mitigate cycle skipping, wavefield reconstruction inversion (WRI) extends the inversion search space by computing wavefields with a relaxation of the wave equation in order to fit the data from the first iteration. Then, the subsurface parameters are updated by minimizing the source residuals the relaxation generated. Capitalizing on the wave-equation bilinearity, performing wavefield reconstruction and parameter estimation in alternating mode decomposes WRI into two linear subproblems, which can solved efficiently with the alternating-direction method of multiplier (ADMM), leading to the so-called IR-WRI. Moreover, ADMM provides a suitable framework to implement bound constraints and different types of regularizations and their mixture in IR-WRI. Here, IR-WRI is extended to multiparameter reconstruction for VTI acoustic media. To achieve this goal, we first propose different forms of bilinear VTI acoustic wave equation. We develop more specifically IR-WRI for the one that relies on a parametrisation involving vertical wavespeed and Thomsen's parameters delta and epsilon. With a toy numerical example, we first show that the radiation patterns of the virtual sources generate similar wavenumber filtering and parameter cross-talks in classical FWI and IR-WRI. Bound constraints and TV regularization in IR-WRI fully remove these undesired effects for an idealized piecewise constant target. We show with a more realistic long-offset case study representative of the North Sea that anisotropic IR-WRI successfully reconstruct the vertical wavespeed starting from a laterally homogeneous model and update the long-wavelengths of the starting epsilon model, while a smooth delta model is used as a passive background model.

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arXiv2019

Compound Regularization of Full-waveform Inversion for Imaging Piecewise Media

The nonlinear and ill-posed nature of full waveform inversion (FWI) requires us to use sophisticated regularization techniques to solve it. In most applications, the model parameters may be described by physical properties (e.g., wave speeds, density, attenuation, anisotropic parameters) which are piecewise functions of space. Compound regularizations are thus necessary to reconstruct properly such parameters by FWI. We consider different implementations of compound regularizations in the wavefield reconstruction inversion (WRI) method, a formulation of FWI that extends its search space and prevent the so-called cycle skipping pathology. Our hybrid regularizations rely on Tikhonov and total variation (TV) functionals, from which we build two classes of hybrid regularizers: the first class is simply obtained by a convex combination (CC) of the two functionals, while the second relies on their infimal convolution (IC). In the former class, the model of parameters is required to simultaneously satisfy different priors, while in the latter the model is broken into its basic components, each satisfying a distinct prior (e.g. smooth, piecewise constant, piecewise linear). We implement these types of compound regularizations in the WRI optimization problem using the alternating direction method of multipliers (ADMM). Then, we assess our regularized WRI in the framework of seismic imaging applications. Using a wide range of subsurface models, we conclude that compound regularizer based on IC leads to the lowest error in the parameter reconstruction compared to that obtained with the CC counterpart and the Tikhonov and TV regularizers when used independently.

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arXiv2019

Implementing bound constraints and total-variation regularization in extended full waveform inversion with the alternating direction method of multiplier: application to large contrast media

Full waveform inversion (FWI) is a waveform matching procedure, which can provide a subsurface model with a wavelength-scale resolution. However, this high resolution makes FWI prone to cycle skipping, which drives the inversion to a local minimum when the initial model is not accurate enough. Other sources of nonlinearities and ill-posedness are noise, uneven illumination, approximate wave physics and parameter cross-talks. All these sources of error require robust and versatile regularized optimization approaches to mitigate their imprint on FWI while preserving its intrinsic resolution power. To achieve this goal, we implement bound constraints and total variation (TV) regularization in the so-called frequency-domain wavefield-reconstruction inversion (WRI) with the alternating direction method of multipliers (ADMM). In the ADMM framework, WRI relies on an augmented Lagrangian function, a combination of penalty and Lagrangian functions, to extend the FWI search space by relaxing the wave-equation constraint during early iterations. Moreover, ADMM breaks down the joint wavefield reconstruction plus parameter estimation problem into a sequence of two linear subproblems, whose solutions are coordinated to provide the solution of the global problem. The decomposability of ADMM is further exploited to interface in a straightforward way bound constraints and TV regularization with WRI via variable splitting and proximal operators. The resilience of our regularized WRI formulation to cycle skipping and noise as well as its resolution power are illustrated with two targets of the large-contrast BP salt model. Starting from a 3Hz frequency and a crude initial model, the extended search space allows for the reconstruction of the salt and subsalt structures with a high fidelity.

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arXiv2018

Improving full waveform inversion by wavefield reconstruction with the alternating direction method of multipliers

Full waveform inversion (FWI) is an iterative nonlinear waveform matching procedure subject to wave-equation constraint. FWI is highly nonlinear when the wave-equation constraint is enforced at each iteration. To mitigate nonlinearity, wavefield-reconstruction inversion (WRI) expands the search space by relaxing the wave-equation constraint with a penalty method. The pitfall of this approach resides in the tuning of the penalty parameter because increasing values should be used to foster data fitting during early iterations while progressively enforcing the wave-equation constraint during late iterations. However, large values of penalty parameter lead to ill-conditioned problems. Here, this tuning issue is solved by replacing the penalty method by an augmented Lagrangian method equipped with operator splitting (IR-WRI as iteratively-refined WRI). It is shown that IR-WRI is similar to a penalty method in which data and sources are updated at each iteration by the running sum of the data and source residuals of previous iterations. Moreover, the alternating direction strategy exploits the bilinearity of the wave equation constraint to linearize the subsurface model estimation around the reconstructed wavefield. Accordingly, the original nonlinear FWI is decomposed into a sequence of two linear subproblems, the optimization variable of one subproblem being passed as a passive variable for the next subproblem. The convergence of WRI and IR-WRI are first compared with a simple transmission experiment, which lies in the linear regime of FWI. Under the same conditions, IR-WRI converges to a more accurate minimizer with a smaller number of iterations than WRI. More realistic case studies performed with the Marmousi II and the BP salt models show the resilience of IR-WRI to cycle skipping and noise.

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