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The eikonal equation is utilized across a wide spectrum of science and engineering disciplines. In seismology, it regulates seismic wave traveltimes needed for applications like source localization, imaging, and inversion. Several numerical…

Computational Physics · Physics 2021-07-07 Umair bin Waheed , Ehsan Haghighat , Tariq Alkhalifah , Chao Song , Qi Hao

Seismic tomography has long been an effective tool for constructing reliable subsurface structures. However, simultaneous inversion of P- and S-wave velocities presents a significant challenge for conventional seismic tomography methods,…

Geophysics · Physics 2024-07-24 Chao Song , Hang Geng , Umair bin Waheed , Cai Liu

Seismic traveltime tomography using transmission data is widely used to image the Earth's interior from global to local scales. In seismic imaging, it is used to obtain velocity models for subsequent depth-migration or full-waveform…

Computational Physics · Physics 2021-04-06 Umair bin Waheed , Tariq Alkhalifah , Ehsan Haghighat , Chao Song , Jean Virieux

The high cost of acquiring a sufficient amount of seismic data for training has limited the use of machine learning in seismic tomography. In addition, the inversion uncertainty due to the noisy data and data scarcity is less discussed in…

Geophysics · Physics 2023-08-09 Rongxi Gou , Yijie Zhang , Xueyu Zhu , Jinghuai Gao

In the study of subsurface seismic imaging, solving the acoustic wave equation is a pivotal component in existing models. The advancement of deep learning enables solving partial differential equations, including wave equations, by applying…

Machine Learning · Computer Science 2023-03-10 Bian Li , Hanchen Wang , Shihang Feng , Xiu Yang , Youzuo Lin

Simulating seismic first-arrival traveltime plays a crucial role in seismic tomography. First-arrival traveltime simulation relies on solving the eikonal equation. The accuracy of conventional numerical solvers is limited to a…

Geophysics · Physics 2025-05-09 Hang Geng , Chao Song , Umair bin Waheed , Cai Liu

Seismic velocity is one of the most important parameters used in seismic exploration. Accurate velocity models are key prerequisites for reverse-time migration and other high-resolution seismic imaging techniques. Such velocity information…

Geophysics · Physics 2019-02-19 Fangshu Yang , Jianwei Ma

In this study, we propose a Bayesian seismic tomography inference method using physics-informed neural networks (PINN). PINN represents a recent advance in deep learning, offering the possibility to enhance physics-based simulations and…

Geophysics · Physics 2023-07-19 Ryoichiro Agata , Kazuya Shiraishi , Gou Fujie

Real-time monitoring of induced seismicity is critical to mitigate operational risks, relying on the rapid and accurate classification of triggered data from continuous data streams. Deep learning models are effective for this purpose but…

Geophysics · Physics 2026-04-14 Ayrat Abdullin , Umair bin Waheed , Leo Eisner , Abdullatif Al-Shuhail

Physics-informed neural networks (PINNs) offer a powerful framework for seismic wavefield modeling, yet they typically require time-consuming retraining when applied to different velocity models. Moreover, their training can suffer from…

Geophysics · Physics 2025-06-03 Shijun Cheng , Tariq Alkhalifah

Physics-informed neural networks (PINNs) have great potential for flexibility and effectiveness in forward modeling and inversion of seismic waves. However, coordinate-based neural networks (NNs) commonly suffer from the "spectral bias"…

Geophysics · Physics 2025-06-19 Yi Ding , Su Chen , Hiroe Miyake , Xiaojun Li

Numerical simulations are essential tools to evaluate the solution of the wave equation in complex settings, such as three-dimensional (3D) domains with heterogeneous properties. However, their application is limited by high computational…

Machine Learning · Computer Science 2025-04-09 Fanny Lehmann , Filippo Gatti , Didier Clouteau

With the recent rise of neural operators, scientific machine learning offers new solutions to quantify uncertainties associated with high-fidelity numerical simulations. Traditional neural networks, such as Convolutional Neural Networks…

Machine Learning · Computer Science 2024-09-04 Fanny Lehmann , Filippo Gatti , Michaël Bertin , Didier Clouteau

Seismic wave forward and inverse modeling are fundamental tools for subsurface imaging and geological hazard assessment. Conventional grid-based numerical methods, such as finite-difference and finite-element approaches, often require dense…

Geophysics · Physics 2026-01-23 Chaohua Liang , Xingliang Peng , Jun Matsushima

High-fidelity direct numerical simulation of turbulent flows for most real-world applications remains an outstanding computational challenge. Several machine learning approaches have recently been proposed to alleviate the computational…

Model-based seismic inversion is a key technique in reservoir characterization, but traditional methods face significant limitations, such as relying on 1D average stationary wavelets and assuming an unrealistic lateral resolution. To…

Geophysics · Physics 2025-07-22 Marcus Saraiva , Ana Muller , Alexandre Maul

Structural failures are often caused by catastrophic events such as earthquakes and winds. As a result, it is crucial to predict dynamic stress distributions during highly disruptive events in real time. Currently available high-fidelity…

Machine Learning · Computer Science 2022-11-30 Hamed Bolandi , Gautam Sreekumar , Xuyang Li , Nizar Lajnef , Vishnu Naresh Boddeti

The precise simulation of turbulent flows is of immense importance in a variety of scientific and engineering fields, including climate science, freshwater science, and the development of energy-efficient manufacturing processes. Within the…

Fluid Dynamics · Physics 2024-06-10 Shengyu Chen , Peyman Givi , Can Zheng , Xiaowei Jia

There has been an increasing interest in integrating physics knowledge and machine learning for modeling dynamical systems. However, very limited studies have been conducted on seismic wave modeling tasks. A critical challenge is that these…

Geophysics · Physics 2022-11-03 Pu Ren , Chengping Rao , Su Chen , Jian-Xun Wang , Hao Sun , Yang Liu

This paper proposes a physics-informed neural operator (PINO) framework for solving inverse scattering problems, enabling rapid and accurate reconstructions under diverse measurement conditions. In the proposed approach, the dielectric…

Computational Physics · Physics 2026-03-27 Q. C. Dong , Zi-Xuan Su , Qing Huo Liu , Wen Chen , Zhizhang , Chen
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