https://dspace.igf.edu.pl/xmlui/handle/123456789/5 2026-04-26T16:58:35Z 2026-04-26T16:58:35Z Gholami, Ali Gazzola, Silvia https://dspace.igf.edu.pl/xmlui/handle/123456789/135 2025-03-05T13:23:19Z 2024-11-01T00:00:00Z

Robust estimation of structural orientation parameters and 2D/3D local anisotropic Tikhonov regularization Gholami, Ali; Gazzola, Silvia Understanding the orientation of geologic structures is crucial for analyzing the complexity of the earths’ subsurface. For instance, information about geologic 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 uses the alternating direction method of multipliers within an alternating minimization scheme to jointly estimate orientation and model parameters in 2D and 3D inverse problems. Specifically, our 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. Our algorithmis tested across diverse 2D and 3D examples, including structure-oriented denoising and trace interpolation. The results indicate 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 our anisotropic regularization method produces a model with enhanced resolution and provides a more accurate representation of the true structures.

2024-11-01T00:00:00Z Aghazade, Kamal Gholami, Ali Aghamiry, Hossein S. Siahkoohi, Hamid Reza https://dspace.igf.edu.pl/xmlui/handle/123456789/134 2025-03-05T13:17:57Z 2024-05-01T00:00:00Z

Robust elastic full-waveform inversion using an alternating direction method of multipliers with reconstructed wavefields Aghazade, Kamal; Gholami, Ali; Aghamiry, Hossein S.; Siahkoohi, Hamid Reza 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.

2024-05-01T00:00:00Z Gholami, Ali https://dspace.igf.edu.pl/xmlui/handle/123456789/133 2025-03-05T13:09:46Z 2024-05-01T00:00:00Z

An extended Gauss-Newton method for full-waveform inversion Gholami, Ali Full-waveform inversion (FWI) is a large-scale nonlinear ill-posed problem for which computationally expensive Newton-type methods can become trapped in undesirable local minima, particularly when the initial model lacks a low-wavenumber component and the recorded data lack low-frequency content. A modification to the Gauss-Newton (GN) method is developed to address these issues. The standard GN system for multisource multireceiver FWI is reformulated into an equivalent matrix equation form, with the solution becoming a diagonal matrix rather than a vector as in the standard system. The search direction is transformed from a vector to a matrix by relaxing the diagonality constraint, effectively adding a degree of freedom to the subsurface offset axis. The relaxed system can be explicitly solved with only the inversion of two small matrices that deblur the data residual matrix along the source and receiver dimensions, which simplifies the inversion of the Hessian matrix. When used to solve the extended-source FWI objective function, the extended GN (EGN) method integrates the benefits of model and source extension. The EGN method effectively combines the computational effectiveness of the reduced FWI method with the robustness characteristics of extended formulations and offers a promising solution for addressing the challenges of FWI. It bridges the gap between these extended formulations and the reduced FWI method, enhancing inversion robustness while maintaining computational efficiency. The robustness and stability of the EGN algorithm for waveform inversion are demonstrated numerically.

2024-05-01T00:00:00Z Gholami, Ali Aghazade, Kamal https://dspace.igf.edu.pl/xmlui/handle/123456789/132 2025-03-05T12:12:06Z 2024-04-19T00:00:00Z

Full waveform inversion and Lagrange multipliers Gholami, Ali; Aghazade, Kamal 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 seen a renewed interest in extended methodologies, among which source extension methods leveraging reconstructed wavefields to solve penalty or augmented Lagrangian (AL) for mulations have emerged as robust algorithms, even for inaccurate initial models. Despite their demonstrated robustness on synthetic data, challenges remain, such as the lack of a clear physical interpretation and reliance on difficult-to-compute least-squares (LS) wavefields. Moreover, the literature lacks a general and through comparison of these source extension methods with each other and with the standard FWI. This paper is divided into three 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 use LS multipliers instead of wavefields. These multiplier-oriented variants appear as regularizations of the standard FWI, are suitable 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 associated non-linear 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 the 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. In the final section, the paper presents numerical examples that compare different methods within a unified iterative algorithm, utilizing benchmark Marmousi and 2004 BP salt models.

2024-04-19T00:00:00Z