Hossein S. Aghamiry

Charité Universitätsmedizin Berlin | Charité

Full Waveform Inversion can be made immune to cycle skipping by matching the recorded data arbitrarily well from inaccurate subsurface models. To achieve this goal, the simulated wavefields can be computed in an extended search space as the solution of an overdetermined problem aiming at jointly satisfying the wave equation and fitting the data in...

Frequency-domain simulation of seismic waves plays an important role in seismic inversion, but it remains challenging in large models. The recently proposed physics-informed neural network (PINN), as an effective deep learning method, has achieved successful applications in solving a wide range of partial differential equations (PDEs), and there is...

Full-waveform inversion (FWI) with extended sources first computes wavefields with data-driven source extensions, such that the simulated data in inaccurate velocity models match the observed counterpart well enough to prevent cycle skipping. Then, the source extensions are minimized to update the model parameters. This two-step workflow is iterate...

Frequency-domain full-waveform inversion (FWI) is potentially amenable to efficient processing of full-azimuth long-offset stationary-recording seabed acquisition carried out with a sparse layout of ocean-bottom nodes (OBNs) and broadband sources because the inversion can be performed with a few discrete frequencies. However, computing the solution...

Full waveform inversion (FWI) is a nonlinear optimization problem that addresses the estimation of subsurface model parameters by matching the predicted to the observed seismograms. We formulate FWI as a constrained optimization problem where the regularization term is minimized subject to the nonlinear data matching constraints. Unlike standard FW...

To stabilize an ill-posed inverse problem such as full waveform inversion (FWI), prior information must be added to the objective function in the frame of regularization techniques. Established regularization methods such as Tikhonov and total variation (TV) regularization assume certain statistical assumptions about the structural properties of th...

Full Waveform Inversion can be made immune to cycle skipping by matching the recorded data arbitrarily well from inaccurate subsurface models. To achieve this goal, the simulated wavefields can be computed in an extended search space as the solution of an overdetermined problem aiming at jointly satisfying the wave equation and fitting the data in...

Frequency-domain Full Waveform Inversion (FWI) is potentially amenable to efficient processing of full-azimuth long-offset stationary-recording seabed acquisition carried out with sparse layout of ocean bottom nodes (OBNs) and broadband sources because the inversion can be performed with a few discrete frequencies. However, computing efficiently th...

Frequency-domain simulation of seismic waves plays an important role in seismic inversion, but it remains challenging in large models. The recently proposed physics-informed neural network (PINN), as an effective deep learning method, has achieved successful applications in solving a wide range of partial differential equations (PDEs), and there is...

Efficient frequency-domain full-waveform inversion (FWI) of long-offset node data can be designed with a few discrete frequencies, which lead to modest data volumes to be managed during the inversion process. Moreover, attenuation effects can be straightforwardly implemented in the forward problem without the computational overhead. However, 3D fre...

Implementation of the standard full waveform inversion (FWI) poses difficulties as the initial model offsets from the true model. The wavefield reconstruction inversion (WRI) was proposed to mitigate these difficulties by relaxing the wave-equation constraint. In this abstract, working on the nonlinear term in the Hessian matrix of FWI, we develop...

This abstract proposes a unified matrix-based framework to mitigate the computational burden of PDE-constrained optimization like full-waveform inversion (FWI) with multiple source terms. The idea utilizes sketching matrices to transform the original problem into a lower dimension, leading to an efficient computation framework. The performance of t...

The extended full-waveform inversion (FWI) formulations is a reliable alternative to classical FWI to tackle the cycle skipping issue. Compared to classical FWI, these methods extend the inversion search space with extra degrees of freedom. However, most of these developments were restricted to the acoustic approximation, which is not acceptable in...

The wavefield reconstruction inversion (WRI) or its refined variant (IR-WRI) has provided outstanding results for imaging complex subsurface with rather remote initial models. The frequency-domain formulation of these methods requires solving iteratively a normal system of equations formulated as a weighted sum of the Gram matrices associated with...

In 3D, time-domain full-waveform inversion (FWI) is generally favored to solve the wave equation with explicit schemes. Furthermore, extended-space approaches such as wavefield reconstruction inversion (WRI) or extended-source FWI decrease the sensitivity of FWI to the initial model. However, their time-domain implementation is not straightforward...

Full-waveform inversion (FWI) is a high-resolution and computationally intensive imaging technique to reconstruct unknown parameters in the computational model in which the waves propagate; however, an accurate model of only part of this medium is required for some applications. To decrease the computational burden of such problems, target-oriented...

Efficient frequency-domain Full Waveform Inversion (FWI) of long-offset node data can be performed with a few frequencies. The seismic response of these frequencies can be computed with compact finite-difference stencils on regular Cartesian grid with direct or hybrid direct/iterative methods. Compactness, which is necessary to mitigate the fill-i...

Full-waveform inversion (FWI) is a seismic imaging method that provides quantitative inference about subsurface properties with a wavelength-scale resolution. Its frequency-domain formulation is computationally efficient when processing only a few discrete frequencies. However, classical FWI, which is formulated on the reduced-parameter space, requ...

My presentation about FWI, its challenges and our developments in WIND.

Partial differential equation (PDE) constrained optimization problems such as seismic full waveform inversion (FWI) frequently arise in the geoscience and related fields. For such problems, many observations are usually gathered by multiple sources, which form the right-hand-sides of the PDE constraint. Solving the inverse problem with such massive...

Efficient frequency-domain Full Waveform Inversion (FWI) of long-offset node data can be designed with a few discrete frequencies hence allowing for compact volume of data to be managed. Moreover, attenuation effects can be straightforwardly implemented in the forward problem without computational overhead. However, 3D frequency-domain seismic mode...

Extended full-waveform inversion by wavefield reconstruction inversion (WRI) requires estimation of the so-called data-assimilated wavefields (DAW). DAWs are the solution of an ill-conditioned symmetric positive definite linear system, which is built by augmenting the wave equation weighted by a penalty parameter with the observation equation relat...

Augmented Lagrangian (AL) based full-waveform inversion (FWI) has shown promising results for accurate estimation of subsurface parameters when the initial models are not sufficiently accurate. Applying this method in the time domain, however, is limited because of the challenge of estimating data-assimilated wavefield and the need to store the La...

The augmented Lagrangian (AL) method allows an efficient solution of full-waveform inversion (FWI). It is robust with respect to the initial model while being general (in the sense of dealing which non-differentiable (e.g., TV) regularizers) and decomposable (which makes it suitable for dealing with large scale problems). The method, however, beha...

The augmented Lagrangian (AL) method provides a flexible and efficient framework for solving extended-space full-waveform inversion (FWI), a constrained nonlinear optimization problem whereby we seek model parameters and wavefields that minimize the data residuals and satisfy the wave equation constraint. The AL-based wavefield reconstruction inver...

Full waveform inversion (FWI) requires an accurate estimation of source signatures. Indeed, the coupling between the source signatures and the subsurface model can make small errors in the former to translate into significant errors in the latter. When direct methods are used to solve the forward problem, classical frequency-domain FWI efficiently...

Full waveform inversion (FWI) is a multivariate PDE-constrained optimization problem, which jointly updates the wavefields and model parameters from partial measurements of the wavefields. A classical technique to solve such problems is the method of Lagrange multipliers where the wave-fields, the Lagrange multipliers, and the model parameters are...

The search space of Full Waveform Inversion (FWI) can be extended via a relaxation of the wave equation to increase the linear regime of the inversion. This wave equation relaxation is implemented by solving jointly (in a least-squares sense) the wave equation weighted by a penalty parameter and the observation equation such that the reconstructed...

This study clarifies some theoretical aspects of extended FWI (FWI_e) based on source extension. Our analysis revolves around the scattered-field wave equation. In both reduced-space FWI (FWI_r) and FWI_e , the parameters are updated by correlation of the scattering source of the partial derivative wavefield and the adjoint wavefields computed by b...

Full waveform inversion (FWI) is a constrained optimization problem that draws inferences about high-resolution subsurface parameters by matching the recorded and the simulated seismograms, the latter being obtained by solving the wave equation. The difference between the two sets of seismograms (data residuals) is minimized in a least-squares sens...

The full-waveform inversion (FWI) addresses the computation and characterization of subsurface model parameters by matching predicted data to observed seismograms in the frame of nonlinear optimization. We formulate FWI as a nonlinearly constrained optimization problem, for which a regularization term is minimized subject to the nonlinear data matc...

Efficient frequency-domain Full Waveform Inversion (FWI) of long-offset/wide-azimuth node data can be designed with a few discrete frequencies. However, 3D frequency-domain seismic modeling remains challenging since it requires solving a large and sparse linear indefinite system per frequency. When such systems are solved with direct methods or hyb...

Full waveform inversion (FWI) is beginning to be used to characterize weak seismic events at different scales, an example of which is microseismic event (MSE) characterization. However, FWI with unknown sources is a severely underdetermined optimization problem, and hence requires strong prior information about the sources and/or the velocity model...

Partial differential equation (PDE) constrained optimization problems such as seismic full wave-form inversion (FWI) frequently arise in the geoscience and related fields. For such problems, many observations are usually gathered by multiple sources, which form the right-hand-sides of the PDE constraint. Solving the inverse problem with such massiv...

The augmented Lagrangian (AL) method provides a flexible and efficient framework for solving extended-space full-waveform inversion (FWI), a constrained nonlinear optimization problem whereby we seek model parameters and wavefields that minimize the data residuals and satisfy the wave equation constraint. The AL-based wavefield reconstruction inver...

Full waveform inversion (FWI) requires an accurate estimation of source signatures. Due to the coupling between the source signatures and the subsurface model, small errors in the former can translate into large errors in the latter. When direct methods are used to solve the forward problem, classical frequency-domain FWI efficiently processes mult...

Full waveform inversion (FWI) is beginning to be used to characterize weak seismic events at different scales, an example of which is microseismic event (MSE) characterization. However, FWI with unknown sources is a severely underdetermined optimization problem, and hence requires strong prior information about the sources and/or the velocity model...

Full waveform inversion (FWI) requires an accurate estimation of source signatures. Due to the coupling between the source signatures and the subsurface model, small errors in the former can translate into large errors in the latter. When direct methods are used to solve the forward problem, classical frequency-domain FWI efficiently processes mult...

Full-waveform inversion (FWI) is a nonlinear PDE constrained optimization problem which seeks to estimate the constitutive parameters of a medium by fitting waveforms. Among these parameters, attenuation needs to be taken into account in viscous media to exploit the full potential of FWI. Attenuation is easily implemented in the frequency domain by...

Efficient frequency-domain Full-Waveform Inversion (FD-FWI) of wide-aperture data is designed by limiting inversion to few frequencies and by solving the Helmholtz equation with a direct solver to process multiple sources efficiently. Some variants of FD-FWI, which process the wave-equation as a weak constraint, were proposed to increase the comput...

Extended full-waveform inversion (FWI) has shown promising results for accurate estimation of subsurface parameters when the initial models are not sufficiently accurate. Frequency-domain applications have shown that the augmented Lagrangian (AL) method solves the inverse problem accurately with a minimal effect of the penalty parameter choice. App...

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), smooth or non smooth, variational-based or not. Nevertheless, tailoring a suitable and easy-to-...

Ultra-long offset node acquisition are beneficial for full waveform inversion (FWI) because the wide variety of wave types recorded by these geometries are suitable for broadband velocity model building. However, long propagation distances induced by long offsets exacerbate cycle skipping and the sparsity of the acquisition can inject wraparound ar...

Full waveform inversion (FWI) has recently received lots of attention for microseismic event characterization. However, FWI with unknown sources becomes severely underdetermined, hence requiring strong prior information about them. The frequency-domain wavefield inversion method (WRI) has shown promising results to mitigate the FWI nonlinearity gen...

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. Attenu...

Accurate subsurface imaging by full-waveform inversion (FWI) often requires to account for attenuation. Attenuation can be implemented in frequency-domain FWI with complex-valued velocities. FWI is however traditionally performed in the real domain to update separately real-valued phase velocities and attenuation factor. One reason is that the comp...

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 an alternating mode...

We propose a double iteration refinement approach for wavefield reconstruction inversion (WRI). The first is a refinement loop based on the alternating direction method of multipliers (ADMM), which solves the full waveform inversion (FWI), which is formulated as a PDE-constrained biconvex optimization problem, known as iteratively refined (IR)-WRI....

We propose efficient algorithms to solve non-linear inverse problems with non-smooth regularizations using proximal-Newton methods. The difference with the traditional Newton methods is that here the step direction is determined in a particular way to involve the gradients/subgradients of the non-differentiable regularization function. It requires...

Ultra-long offset OBN acquisitions are suitable for deep offshore subsalt imaging by full waveform inversion. However, these sparse long-offset acquisitions increase the risk of cycle skipping and can downsample the FWI kernel below the Nyquist rate leading to wraparound artefacts. The first issue has been recently mitigated with the wavefield reco...

Regularization is necessary for full-waveform inversion (FWI). The basis of a good regularization is the prior expressed by the regularizer, which can be non-adaptive or adaptive (data-driven). However, tailoring a suitable and easy to implement prior to describe geophysical models is a nontrivial task. In this abstract, we propose a general black-...

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 inv...

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...

Full Waveform Inversion (FWI) is a PDE-constrained optimization which reconstructs subsurface parameters from sparse measurements of seismic wavefields. FWI generally relies on local optimization techniques and a reduced-space approach where the wavefields are eliminated from the variables. In this setting, two bottlenecks of FWI are nonlinearity a...

Wavefield reconstruction inversion (WRI) mitigates cycle skipping in Full Waveform Inversion (FWI) by computing wavefields that do not exactly satisfy the wave-equation to match data with inaccurate velocity models. We refer these wavefields to as "data assimilated wavefield" because they are obtained by combining the physics of wave propagation an...

Full waveform inversion (FWI) is an iterative nonlinear waveform matching procedure, which seeks to reconstruct unknown model parameters from partial waveform measurements. The nonlinear and ill-posed nature of FWI requires sophisticated regularization techniques to solve it. In most applications, the model parameters may be described by physical...

Our slides that were presented in the SEG Annual Meeting 2019 by Stephane Operto.

Our poster about "Robust ADMM-based wavefield reconstruction inversion with phase retrieval" that was presented in SEG Annual Meeting 2019 by Stephane Operto.

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 br...

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 br...

Classical full waveform inversion (FWI) is an unconstrained data fitting/parameter estimation problem where the exact solution of the wave equation is enforced in the objective function, leading to highly non-linear problem prone to cycle skipping. To extend the linear regime of FWI, the wavefield reconstruction inversion (WRI) computes wavefields...

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 fi...

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...

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 fi...