arXiv subjects

Ali Gholami

Publications and source records attributed to Ali Gholami.

At least 19 recordsLinked to original sources

arXiv2026

Surface Crevasse Evolution Observed Using Matched Field Processing and Source Relocation at Hansbreen, Svalbard

Crevasses control glacier dynamics through fracture and meltwater routing, yet their propagation rates remain observationally scarce and poorly constrained across brittle-to-viscous regimes. Cryoseismology offers a powerful means to capture dynamic processes within glacial ice, with recent advances in novel processing methods like Matched Field Processing (MFP) applicable to dense seismic arrays. However, precise localisation of cryoseismic sources remains challenging in sparse or irregular seismic arrays. We propose a two-step workflow for metres-scale resolution mapping of glacial seismic activity that integrates MFP and discrete arrival times relocation under a limited instrumentation constraint. We apply this approach to analyse seismic activity at the ice surface on the Hansbreen glacier, Svalbard. Using MFP, we detect surface icequakes and characterise meltwater noise regardless of the limited instrumentation. The relocation procedure increases the accuracy of surface icequakes localisation and reveals ongoing crevasse opening episodes. The precise locations of the icequakes allow for the estimation of the crevasse propagation rate and the determination of the diffusion coefficients of 0.47 to 0.55 m2 per s. Based on the obtained results, we discuss brittle-to-viscous regime transfer and interpret the crevassing mechanism as sustained subcritical crack propagation, where viscous stress relaxation governs rates of orders of magnitude below elastic limits.

physics.geo-ph↗

arXiv2026

Regularized Nonstationary Phase Estimation via Proximal Maximization of Skewness and Kurtosis

Wavelet phase is a critical parameter in seismic processing, where zero-phase wavelets are essential for maximizing temporal resolution and ensuring accurate interpretation of subsurface structures. In practice, however, the seismic wavelet is often nonstationary, exhibiting a phase that varies in space and time due to physical factors such as attenuation, dispersion, and thin-bed tuning effects. Higher-order statistical measures-specifically kurtosis and skewness-are traditionally maximized to drive the signal toward a maximally non-Gaussian or maximally asymmetric zero-phase state. This paper addresses the computational and stability challenges inherent in nonstationary estimation by casting the problem as a regularized non-convex optimization task. We propose a robust framework based on the Alternating Direction Method of Multipliers (ADMM) that eliminates the instability and artifacts associated with traditional piecewise-stationary windowed approaches. The core of our contribution is the derivation of the first closed-form proximity operators for the scale-invariant inverse kurtosis and inverse skewness functionals. By exploiting the signed permutation invariance of these statistical measures, we reduce the high-dimensional proximal subproblems to efficient one-dimensional root-finding tasks. We provide a detailed geometric interpretation of the optimality conditions, demonstrating that the global minimizer is governed by a branch-separation property. Furthermore, we derive an explicit critical threshold parameter which provides a theoretical rule for identifying the global minimum among multiple stationary points. Numerical validations on synthetic and real seismic data demonstrate that the proposed proximal algorithms achieve linear computational complexity and superior stability compared to traditional methods, effectively enabling nonstationary phase correction.

physics.geo-ph↗

arXiv2026

Scalable Bayesian full waveform inversion via dual augmented Lagrangian SVGD

Full waveform inversion is an ill-posed inverse problem whose solution non-uniqueness -- i.e., arising from band-limited, finite-aperture, noisy data -- calls for uncertainty quantification to avoid overconfident geological interpretations. Bayesian inference addresses this need by characterizing the solution as a posterior distribution rather than a single point estimate. Sampling from this distribution, however, remains computationally challenging: Markov chain Monte Carlo and non-amortized variational inference require repeated wave equation solves, while amortized variational inference approaches that avoid repeated solves rely on training data that are inherently scarce in geoscience and face unresolved generalization challenges in high dimensions. To address these limitations, we integrate Stein variational gradient descent with the alternating direction method of multipliers under a dual augmented Lagrangian formulation. By fixing the wave operator at a background model that is updated between frequency batches, it need only be factorized once per particle per frequency, eliminating per-iteration refactorization and reducing the total cost to that of a handful of deterministic inversions while inheriting the favorable conditioning of extended-space formulations. Applied to the Marmousi~II model, the proposed method provides well-calibrated uncertainty estimates and achieves inversion quality comparable to that of the standard augmented Lagrangian SVGD at a fraction of the computational cost.

physics.geo-ph↗

arXiv2026

Dual-space posterior sampling for Bayesian inference in constrained inverse problems

Inverse problems constrained by partial differential equations are often ill-conditioned due to noisy, incomplete data or inherent non-uniqueness. A prominent example is full waveform inversion (FWI), which estimates Earth's subsurface properties by fitting seismic measurements subject to the wave equation, where ill-conditioning stems from noisy, band-limited, finite-aperture measurements and complex geological structures. A Bayesian framework describes the solution more comprehensively: instead of a single estimate, a posterior distribution of plausible solutions characterizes the non-uniqueness and can be sampled to quantify uncertainty. However, no clear procedure exists for translating hard physical constraints, such as the wave equation, into priors amenable to existing sampling techniques. We address this by sampling the posterior in the dual space via an augmented Lagrangian formulation, which converts hard constraints into penalties suited to sampling algorithms while enforcing them progressively through multiplier updates, so they are satisfied in the limit. We integrate the alternating direction method of multipliers (ADMM) with Stein variational gradient descent (SVGD), a particle-based sampler: the constraint is relaxed at each iteration and the multiplier updates progressively enforce its satisfaction. This enables posterior sampling under hard constraints while inheriting the favorable conditioning of dual-space solvers, where partial constraint relaxation permits productive updates even when the current model is far from the true solution. We validate the method on a stylized Rosenbrock conditional inference problem and on frequency-domain FWI for a Gaussian anomaly model and the Marmousi II benchmark, demonstrating physically consistent uncertainty estimates and posterior contraction with increasing data coverage.

physics.geo-ph↗

arXiv2025

Direct inversion of data-space Hessian for efficient time-domain extended-source waveform inversion using the multiplier method

The augmented Lagrangian (AL) method has been successfully applied for solving the full waveform inversion (FWI) problem. In AL-based FWI, the Lagrange multipliers serve as source extensions, offering several advantages to the inversion, such as improved robustness to cycle skipping, faster convergence, and simplified penalty parameter tuning. Time-domain applications of this method have been enabled by reformulating the optimization problem in the data space, significantly reducing memory requirements by projecting source-side multipliers into the data space. These data-side multipliers act as data extensions, effectively expanding the data space. A key challenge in these methods lies in computing the data-side multipliers, which involves solving a linear system to deblur the data residuals using the data-space Hessian matrix before it serves as the adjoint source. This Hessian matrix is prohibitively large to construct and invert explicitly. Iterative Krylov methods can be applied to solve this system as inner iterations, but they require two PDE solves per inner iteration per source, leading to significant computational costs. In this work, we present a key improvement to extended waveform inversion based on multiplier methods. We propose a novel approach that significantly reduces the computational cost of Hessian inversion. The method computes receiver-side Green functions in the time domain and directly constructs frequency-domain Hessian matrices for all required frequencies. These Hessian matrices, with dimensions equal to the number of receivers, can be computed, inverted, and stored in memory. Once constructed, they can be used simultaneously for all sources, further enhancing efficiency. Numerical experiments demonstrate the substantial computational gains achieved by the proposed method, highlighting its effectiveness for extended-source FWI in the time domain.

physics.geo-ph↗

arXiv2025

Automatic Penalty Parameter Selection by Residual Whiteness Principle (RWP) and GCV for Full Waveform Inversion

Full-waveform inversion (FWI) is a powerful seismic imaging technique used to estimate high-resolution physical properties of subsurface structures by minimizing the misfit between observed and modeled seismic data. FWI is inherently a highly non-linear and ill-posed inverse problem. Extended-source approaches, such as the augmented Lagrangian (AL) method, are employed to improve solution convexity and robustness. A key component of this formulation is the penalty parameter, which controls the trade-off between data fitting and satisfaction of the wave-equation constraint, strongly influencing convergence in the presence of noise. The main challenge lies in selecting the penalty parameter. Traditional strategies such as the Discrepancy Principle (DP) require an accurate estimate of the noise level, which is often unknown or poorly characterized. Moreover, trial-and-error tuning requires repeatedly solving the inverse problem, making it computationally expensive. To overcome these limitations and develop a parameter-free, computationally efficient extended-source FWI algorithm, we integrate two data-driven parameter-selection strategies--the Residual Whiteness Principle (RWP) and a stable variant of Generalized Cross-Validation (RGCV)--within a multiplier-oriented AL framework. Specifically, we adopt a dual-space AL formulation, which allows the background wave-equation operator to remain fixed and requires only a single LU factorization per frequency, significantly improving efficiency. This design enables dynamic adjustment of the parameter at negligible cost during iterations, making the algorithm scalable for large-scale applications. Numerical experiments on acoustic and elastic FWI with white and colored noise show that, combined with the dual-space formulation, RWP provides strong noise robustness, resulting in a reliable automated solution for large-scale seismic inversion.

physics.geo-ph↗

arXiv2025

Earthquake body wave extraction using sparsity-promoting polarization filtering in the time-frequency domain

Seismic waves generated by earthquakes consist of multiple phases that carry critical information about Earth's internal structure as they propagate through heterogeneous media. These phases provide constraints from different regions of the Earth, such as the crust, mantle, and even the cores. The choice of phase depends on the study target and scientific objective: surface waves are suited for imaging shallow structures, whereas body waves yield higher-resolution information at depth. A key challenge in body-wave studies is that the low-amplitude P and S arrivals are often masked by surface waves overlapping in both time and frequency. Although body waves typically contain higher-frequency content, their spectral overlap with surface waves limits the effectiveness of conventional filtering approaches. Addressing this issue requires advanced signal-processing techniques. One such method, Sparsity-Promoting Time-Frequency Filtering (SP-TFF, Mohammadigheymasi et al., 2022), exploits high-resolution polarization information in the time-frequency domain. SP-TFF integrates amplitude, directivity, and rectilinearity to enhance phase discrimination. Here, we further develop SP-TFF by designing a filter set tailored to isolate body-wave arrivals otherwise masked by high-amplitude surface waves. The directivity filters are constructed from predicted seismic ray incidence angles, enabling focused extraction of body-wave energy and suppression of interfering phases. We evaluate the method on both synthetic tests and waveform data from the Mw 7.0 Guerrero, Mexico, earthquake of September 8, 2021, recorded by the United States National Seismic Network (USNSN). Our results show that SP-TFF provides a robust computational framework for automated body-wave extraction, integrating polarization-informed filtering into seismological data-processing pipelines.

physics.geo-ph↗

arXiv2025

Weighted Lagrange Multiplier Method for Robust Source-Independent Waveform Inversion

The Lagrange multiplier method has proven highly effective for mitigating the ill-conditioning of full waveform inversion (FWI), enabling robust and computationally efficient algorithms that converge to accurate velocity models even from poor initial estimates. Classical multiplier-based FWI methods optimize an augmented Lagrangian (AL) functional with a scalar penalty parameter that uniformly weights wave-equation constraint violations. While this balances data fit and wave-equation satisfaction, it applies uniform relaxation across the model, disregarding source locations and the natural decay of seismic energy. We propose a weighted proximal-point Lagrangian formulation that introduces spatially varying regularization, applying weaker enforcement near sources and progressively stronger enforcement with increasing distance. This compensates for the energy decay, promotes balanced wave-equation enforcement, and improves the convexity of the optimization landscape. The method also eliminates the need for explicit source signature estimation and relaxes the requirement for sources to lie on finite-difference grid points, increasing practical applicability. Enhanced computational efficiency is achieved through our dual-space ADMM implementation, which avoids repeated LU factorizations of the forward operator. Only a few LU factorizations are required, with all subsequent iterations solved via efficient forward-backward substitution, making the approach scalable to large-scale 2D and 3D problems. Numerical experiments on challenging synthetic benchmarks demonstrate that the proposed method broadens the basin of attraction of the AL objective, improves robustness to poor initial models and strong noise, and achieves faster, more stable convergence compared with standard multiplier-based methods.

physics.geo-ph↗

arXiv2025

Robust acoustic and elastic full waveform inversion by adaptive Tikhonov-TV regularization

Full Waveform Inversion (FWI) is a powerful wave-based imaging technique, but its inherent ill-posedness and non-convexity lead to local minima and poor convergence. Regularization methods stabilize FWI by incorporating prior information and enforcing structural constraints like smooth variations or piecewise-constant behavior. Among them, Tikhonov regularization promotes smoothness, while total variation (TV) regularization preserves sharp boundaries. However, in the context of FWI, we highlight two key shortcomings of these regularization methods. First, subsurface model parameters (P- and S-wave velocities, density) often exhibit complex geological formations with sharp discontinuities separating distinct layers, while parameters within each layer vary smoothly. Neither Tikhonov nor TV regularization alone can effectively constrain such piecewise-smooth structures. Second, and more critically, when the initial model is far from the true model, these regularization assumptions can lead to a local minimum. To address these issues, we propose adaptive Tikhonov-TV (TT) regularization, which decomposes the model into smooth and blocky components, enabling robust recovery of piecewise-smooth structures. Implemented within the ADMM framework, TT regularization incorporates an automated balancing strategy based on robust statistical analysis. Numerical experiments on acoustic and elastic FWI using benchmark geological models demonstrate that TT regularization significantly improves convergence and reconstruction accuracy compared to Tikhonov and TV regularization when applied separately. We show that for complex models and remote initial models, both Tikhonov and TV regularization tend to converge to local minima, whereas TT regularization effectively mitigates cycle skipping through its adaptive combination of the two regularization strategies.

physics.geo-ph↗

arXiv2025

Fast Azimuthally Anisotropic 3D Radon Transform by Generalized Fourier Slice Theorem

Expensive computation of the conventional sparse Radon transform limits its use for effective transformation of 3D anisotropic seismic data cubes. We introduce a fast algorithm for azimuthally anisotropic 3D Radon transform with sparsity constraints, allowing effective transformation of seismic volumes corresponding to arbitrary anisotropic inhomogeneous media. In particular, a 3D data (CMP) cube of time and offset coordinates is transformed to a 3D cube of intercept time, slowness, and azimuth. The recently proposed generalized Fourier slice theorem is employed for very fast calculation of the 3D inverse transformation and its adjoint, which are subsequently used for efficient implementation of the sparse transform via a forward-backward splitting algorithm. The new anisotropic transform improves the temporal resolution of the resulting seismic data. Furthermore, the Radon transform coefficients allows constructing azimuthally dependent NMO velocity curve at any horizontal plane, which can be inverted for the medium anisotropic parameters. Numerical examples using synthetic data sets are presented showing the effectiveness of the proposed anisotropic method in improving seismic processing results compared with conventional isotropic counterpart.

physics.geo-ph↗

arXiv2025

Optimal Space-Variant Anisotropic Tikhonov Regularization for Full Waveform Inversion of Sparse Data

Full waveform inversion (FWI) is a challenging, ill-posed nonlinear inverse problem that requires robust regularization techniques to stabilize the solution and yield geologically meaningful results, especially when dealing with sparse data. Standard Tikhonov regularization, though commonly employed in FWI, applies uniform smoothing that often leads to oversmoothing of key geological features, as it fails to account for the underlying structural complexity of the subsurface. To overcome this limitation, we propose an FWI algorithm enhanced by a novel Tikhonov regularization technique involving a parametric regularizer, which is automatically optimized to apply directional space-variant smoothing. Specifically, the parameters defining the regularizer (orientation and anisotropy) are treated as additional unknowns in the objective function, allowing the algorithm to estimate them simultaneously with the model. We introduce an efficient numerical implementation for FWI with the proposed space-variant regularization. Numerical tests on sparse data demonstrate the proposed method's effectiveness and robustness in reconstructing models with complex structures, significantly improving the inversion results compared to the standard Tikhonov regularization.

math.NA↗

arXiv2025

Hierarchical Gradient Coding: From Optimal Design to Privacy at Intermediate Nodes

Gradient coding is a distributed computing technique for computing gradient vectors over large datasets by outsourcing partial computations to multiple workers, typically connected directly to the server. In this work, we investigate gradient coding in a hierarchical setting, where intermediate nodes sit between the server and workers. This structure reduces the communication load received at the server, which is a bottleneck in conventional gradient coding systems. In this paper, the intermediate nodes, referred to as \textit{relays}, process the data received from workers and send the results to the server for the final gradient computation. Our main contribution is deriving the optimal communication-computation trade-off by designing a linear coding scheme, also considering straggling and adversarial nodes among both relays and workers. We propose a coding scheme which achieves both the optimal relay-to-server communication load and the optimal worker-to-relay communication load. We further extend our setting to incorporate privacy by requiring that relays learn no information about the computed partial gradients from the messages they receive. This is achieved by introducing shared randomness among workers, allowing each worker to encode its partial gradients such that the randomness cannot be canceled out at the relay. Meanwhile, the server can successfully decode the global gradient by eliminating this randomness after receiving the computations of the non-straggling relays. Importantly, this privacy guarantee is achieved without increasing the overall communication load.

cs.IT↗

arXiv2024

Fast and Automatic Full Waveform Inversion by Dual Augmented Lagrangian

Full Waveform Inversion (FWI) stands as a nonlinear, high-resolution technology for subsurface imaging via surface-recorded data. This paper introduces an augmented Lagrangian dual formulation for FWI, rooted in the viewpoint that Lagrange multipliers serve as fundamental unknowns for the accurate linearization of the FWI problem. Once these multipliers are estimated, the determination of model parameters becomes simple. Therefore, unlike traditional primal algorithms, the proposed dual method circumvents direct engagement with model parameters or wavefields, instead tackling the estimation of Lagrange multipliers through a gradient ascent iteration. This approach yields two significant advantages: i) the background model remains fixed, requiring only one LU matrix factorization for each frequency inversion. ii) Convergence of the algorithm can be improved by leveraging techniques like quasi-Newton l-BFGS methods and Anderson acceleration. Numerical examples from elastic and acoustic FWI utilizing different benchmark models are provided, showing that the dual algorithm converges quickly and requires fewer computations than the standard primal algorithm.

physics.geo-ph↗

arXiv2024

Robust Estimation of Structural Orientation Parameters and 2D/3D Local Anisotropic Tikhonov Regularization

Understanding the orientation of geological structures is crucial for analyzing the complexity of the Earths' subsurface. For instance, information about geological structure orientation can be incorporated into local anisotropic regularization methods as a valuable tool to stabilize the solution of inverse problems and produce geologically plausible solutions. We introduce a new variational method that employs the alternating direction method of multipliers within an alternating minimization scheme to jointly estimate orientation and model parameters in both 2D and 3D inverse problems. Specifically, the proposed approach adaptively integrates recovered information about structural orientation, enhancing the effectiveness of anisotropic Tikhonov regularization in recovering geophysical parameters. The paper also discusses the automatic tuning of algorithmic parameters to maximize the new method's performance. The proposed algorithm is tested across diverse 2D and 3D examples, including structure-oriented denoising and trace interpolation. The results show that the algorithm is robust in solving the considered large and challenging problems, alongside efficiently estimating the associated tilt field in 2D cases and the dip, strike, and tilt fields in 3D cases. Synthetic and field examples show that the proposed anisotropic regularization method produces a model with enhanced resolution and provides a more accurate representation of the true structures.

physics.geo-ph↗

arXiv2024

Automatic nonstationary anisotropic Tikhonov regularization through bilevel optimization

Regularization techniques are necessary to compute meaningful solutions to discrete ill-posed inverse problems. The well-known 2-norm Tikhonov regularization method equipped with a discretization of the gradient operator as regularization operator penalizes large gradient components of the solution to overcome instabilities. However, this method is homogeneous, i.e., it does not take into account the orientation of the regularized solution and therefore tends to smooth the desired structures, textures and discontinuities, which often contain important information. If the local orientation field of the solution is known, a possible way to overcome this issue is to implement local anisotropic regularization by penalizing weighted directional derivatives. In this paper, considering problems that are inherently two-dimensional, we propose to automatically and simultaneously recover the regularized solution and the local orientation parameters (used to define the anisotropic regularization term) by solving a bilevel optimization problem. Specifically, the lower level problem is Tikhonov regularization equipped with local anisotropic regularization, while the objective function of the upper level problem encodes some natural assumptions about the local orientation parameters and the Tikhonov regularization parameter. Application of the proposed algorithm to a variety of inverse problems in imaging (such as denoising, deblurring, tomography and Dix inversion), with both real and synthetic data, shows its effectiveness and robustness.

math.NA↗

arXiv2024

Robust elastic full-waveform inversion using an alternating direction method of multipliers with reconstructed wavefields

Elastic full-waveform inversion (EFWI) is a process used to estimate subsurface properties by fitting seismic data while satisfying wave propagation physics. The problem is formulated as a least-squares data fitting minimization problem with two sets of constraints: Partial-differential equation (PDE) constraints governing elastic wave propagation and physical model constraints implementing prior information. The alternating direction method of multipliers is used to solve the problem, resulting in an iterative algorithm with well-conditioned subproblems. Although wavefield reconstruction is the most challenging part of the iteration, sparse linear algebra techniques can be used for moderate-sized problems and frequency domain formulations. The Hessian matrix is blocky with diagonal blocks, making model updates fast. Gradient ascent is used to update Lagrange multipliers by summing PDE violations. Various numerical examples are used to investigate algorithmic components, including model parameterizations, physical model constraints, the role of the Hessian matrix in suppressing interparameter cross-talk, computational efficiency with the source sketching method, and the effect of noise and near-surface effects.

math.NA↗

arXiv2023

Full Waveform Inversion and Lagrange Multipliers

Full-waveform inversion (FWI) is an effective method for imaging subsurface properties using sparsely recorded data. It involves solving a wave propagation problem to estimate model parameters that accurately reproduce the data. Recent trends in FWI have led to the development of extended methodologies, among which source extension methods leveraging reconstructed wavefields to solve penalty or augmented Lagrangian (AL) formulations have emerged as robust algorithms, even for inaccurate initial models. Despite their demonstrated robustness, challenges remain, such as the lack of a clear physical interpretation, difficulty in comparison, and reliance on difficult-to-compute least squares (LS) wavefields. This paper is divided into two critical parts. In the first, a novel formulation of these methods is explored within a unified Lagrangian framework. This novel perspective permits the introduction of alternative algorithms that employ LS multipliers instead of wavefields. These multiplier-oriented variants appear as regularizations of the standard FWI, are adaptable to the time domain, offer tangible physical interpretations, and foster enhanced convergence efficiency. The second part of the paper delves into understanding the underlying mechanisms of these techniques. This is achieved by solving the FWI equations using iterative linearization and inverse scattering methods. The paper provides insight into the role and significance of Lagrange multipliers in enhancing the linearization of FWI equations. It explains how different methods estimate multipliers or make approximations to increase computing efficiency. Additionally, it presents a new physical understanding of the Lagrange multiplier used in the AL method, highlighting how important it is for improving algorithm performance when compared to penalty methods.

math.OC↗

arXiv2023

Fundamental Limits of Multi-Message Private Computation

In a typical formulation of the private information retrieval (PIR) problem, a single user wishes to retrieve one out of $ K$ files from $N$ servers without revealing the demanded file index to any server. This paper formulates an extended model of PIR, referred to as multi-message private computation (MM-PC), where instead of retrieving a single file, the user wishes to retrieve $P>1$ linear combinations of files while preserving the privacy of the demand information. The MM-PC problem is a generalization of the private computation (PC) problem (where the user requests one linear combination of the files), and the multi-message private information retrieval (MM-PIR) problem (where the user requests $P>1$ files). A baseline achievable scheme repeats the optimal PC scheme by Sun and Jafar $P$ times, or treats each possible demanded linear combination as an independent file and then uses the near optimal MM-PIR scheme by Banawan and Ulukus. In this paper, we propose a new MM-PC scheme that significantly improves upon the baseline schemes. In doing so, we design the queries inspired by the structure in the cache-aided scalar linear function retrieval scheme by Wan {\it et al.}, which leverages the dependency between linear functions to reduce the amount of communications. To ensure the decodability of our scheme, we propose a new method to benefit from the existing dependency, referred to as the sign assignment step. In the end, we use Maximum Distance Separable matrices to code the queries, which allows the reduction of download from the servers, while preserving privacy. By the proposed schemes, we characterize the capacity within a multiplicative factor of $2$.

cs.IT↗