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We propose an iterative solution method for the 3D high-frequency Helmholtz equation that exploits a contour integral formulation of spectral projectors. In this framework, the solution in certain invariant subspaces is approximated by…

Numerical Analysis · Mathematics 2018-11-30 Xiao Liu , Yuanzhe Xi , Yousef Saad , Maarten V. de Hoop

In this paper we present an overview of recent progress on the development and analysis of domain decomposition preconditioners for discretised Helmholtz problems, where the preconditioner is constructed from the corresponding problem with…

Numerical Analysis · Mathematics 2016-06-24 I. G. Graham , E. A. Spence , E. Vainikko

Full-waveform inversion (FWI) is an accurate imaging approach for modeling velocity structure by minimizing the misfit between recorded and predicted seismic waveforms. However, the strong non-linearity of FWI resulting from fitting…

Geophysics · Physics 2021-10-04 Weiqiang Zhu , Kailai Xu , Eric Darve , Biondo Biondi , Gregory C. Beroza

Full waveform inversion (FWI) is a powerful tool for reconstructing material fields based on sparsely measured data obtained by wave propagation. For specific problems, discretizing the material field with a neural network (NN) improves the…

Machine Learning · Computer Science 2024-08-02 Divya Shyam Singh , Leon Herrmann , Qing Sun , Tim Bürchner , Felix Dietrich , Stefan Kollmannsberger

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)…

Optimization and Control · Mathematics 2019-10-29 Hossein S. Aghamiry , Ali Gholami , Stéphane Operto

Full Waveform Inversion (FWI) is a critical technique in subsurface imaging, aiming to reconstruct high-resolution subsurface properties from surface measurements. Acoustic FWI involves two physical modalities, seismic waveforms and…

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…

Geophysics · Physics 2024-02-23 Ali Gholami

We consider the high-resolution seismic imaging method called full-waveform inversion (FWI). FWI is a data fitting method aimed at inverting for subsurface mechanical parameters. Despite the large adoption of FWI by the academic and…

Full Wave Inversion (FWI) imaging scheme has many applications in engineering, geoscience and medical sciences. In this paper, a surrogate deep learning FWI approach is presented to quantify properties of materials using stress waves. Such…

Materials Science · Physics 2020-01-08 Reza Rashetnia , Mohammad Pour-Ghaz

This paper presents an efficient Krylov subspace iterative solver for the three-dimensional (3D) Helmholtz equation with non-constant coefficients and absorbing boundary conditions, combining high-resolution compact schemes with low-order…

Numerical Analysis · Mathematics 2026-02-10 Yury Gryazin , Ron Gonzales , Xiaoye Sherry Li

Full waveform inversion (FWI) can be expressed in a Bayesian framework, where the associated uncertainties are captured by the posterior probability distribution (PPD). In practice, solving Bayesian FWI with sampling-based methods such as…

Geophysics · Physics 2025-11-05 Shuhua Hu , Mrinal K Sen , Zeyu Zhao , Abdelrahman Elmeliegy , Shuo Zhang

The displacement field for three dimensional dynamic elasticity problems in the frequency domain can be decomposed into a sum of a longitudinal and a transversal part known as a Helmholtz decomposition. The Cartesian components of both the…

Computational Physics · Physics 2019-10-02 Evert Klaseboer , Qiang Sun , Derek Y. C. Chan

The quantitative reconstruction of sub-surface Earth properties from the propagation of waves follows an iterative minimization of a misfit functional. In marine seismic exploration, the observed data usually consist of measurements of the…

Full-waveform inversion (FWI) is known as a seismic data processing method that achieves high-resolution imaging. In the inversion part of the method that brings high resolution in finding a convergence point in the model space, a local…

Geophysics · Physics 2023-07-11 Jiahang Li , Hitoshi Mikada , Junichi Takekawa

Conventional frequency-domain full-waveform inversion (FWI) is typically implemented with an $L^2$ misfit function, which suffers from challenges such as cycle skipping and sensitivity to noise. While the Wasserstein metric has proven…

Optimization and Control · Mathematics 2025-10-10 Zhijun Zeng , Matej Neumann , Yunan Yang

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…

Geophysics · Physics 2024-12-13 Kamal Aghazade , Ali Gholami

Full waveform inversion (FWI) is crucial for reconstructing high-resolution subsurface models, but it is often hindered, considering the limited data, by its null space resulting in low-resolution models, and more importantly, by its…

Geophysics · Physics 2025-10-23 Xinquan Huang , Fu Wang , Tariq Alkhalifah

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…

Optimization and Control · Mathematics 2021-05-25 Hossein S. Aghamiry , Frichnel W. Mamfoumbi-Ozoumet , Ali Gholami , Stéphane Operto

In salt provinces, full-waveform inversion (FWI) is most likely to fail when starting with a poor initial model that lacks the salt information. Conventionally, salt bodies are included in the FWI starting model by interpreting the salt…

Geophysics · Physics 2023-04-07 Abdullah Alali , Tariq Alkhalifah

Change detection in remote sensing imagery plays a vital role in various engineering applications, such as natural disaster monitoring, urban expansion tracking, and infrastructure management. Despite the remarkable progress of deep…

Computer Vision and Pattern Recognition · Computer Science 2025-08-08 Xiaoyang Zhang , Guodong Fan , Guang-Yong Chen , Zhen Hua , Jinjiang Li , Min Gan , C. L. Philip Chen