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We study an inverse problem for the wave equation where localized wave sources in random scattering media are to be determined from time resolved measurements of the waves at an array of receivers. The sources are far from the array, so the…

Mathematical Physics · Physics 2016-07-18 Liliana Borcea , Ilker Kocyigit

We study inverse problems in anisotropic elasticity using tools from algebraic geometry. The singularities of solutions to the elastic wave equation in dimension $n$ with an anisotropic stiffness tensor have propagation kinematics captured…

Differential Geometry · Mathematics 2025-05-01 Maarten V. de Hoop , Joonas Ilmavirta , Matti Lassas , Anthony Várilly-Alvarado

We introduce a fully 3D, deep learning-based approach for the joint inversion of time-lapse surface gravity and seismic data for reconstructing subsurface density and velocity models. The target application of this proposed inversion…

Geophysics · Physics 2023-10-10 Adrian Celaya , Mauricio Araya-Polo

The concept of residual migration to zero offset is introduced for the case that a prestack migration and a subsequent residual moveout analysis have been performed for a seismic survey and a new depth model has not yet been determined.…

Geophysics · Physics 2021-11-19 Joerg F. Schneider

We study a class of statistical inverse problems with non-linear pointwise operators motivated by concrete statistical applications. A two-step procedure is proposed, where the first step smoothes the data and inverts the non-linearity.…

Statistics Theory · Mathematics 2016-11-08 Kolyan Ray , Johannes Schmidt-Hieber

Least-squares reverse time migration (LSRTM) is one of the classic seismic imaging methods to reconstruct model perturbations within a known reference medium. It can be computed in either data or image domain using different methods by…

Geophysics · Physics 2025-12-11 Pengliang Yang , Zhengyu Ji

Full waveform inversion (FWI) is used to reconstruct the physical properties of subsurface media which plays an important role in seismic exploration. However, the precision of FWI is seriously affected by the absence or inaccuracy of…

Geophysics · Physics 2024-04-29 Zheng Cong , Xintong Dong , Shaoping Lu , Shiqi Dong , Xunqian Tong

Neural-networks have seen a surge of interest for the interpretation of seismic images during the last few years. Network-based learning methods can provide fast and accurate automatic interpretation, provided there are sufficiently many…

Geophysics · Physics 2019-03-28 Bas Peters , Eldad Haber , Justin Granek

It is a very challenging task to identify the objectives on which a certain decision was based, in particular if several, potentially conflicting criteria are equally important and a continuous set of optimal compromise decisions exists.…

Optimization and Control · Mathematics 2021-03-05 Bennet Gebken , Sebastian Peitz

This paper is concerned with the inverse scattering problem which aims to determine the spatially distributed dielectric constant coefficient of the 2D Helmholtz equation from multifrequency backscatter data associated with a single…

Numerical Analysis · Mathematics 2020-02-25 Trung Truong , Dinh-Liem Nguyen , Michael Klibanov

Seismic full-waveform inversion (FWI) is a nonlinear computational imaging technique that can provide detailed estimates of subsurface geophysical properties. Solving the FWI problem can be challenging due to its ill-posedness and high…

Machine Learning · Computer Science 2021-03-25 Renán Rojas-Gómez , Jihyun Yang , Youzuo Lin , James Theiler , Brendt Wohlberg

Recent applications of machine learning algorithms in the seismic domain have shown great potential in different areas such as seismic inversion and interpretation. However, such algorithms rarely enforce geophysical constraints - the lack…

Geophysics · Physics 2019-08-22 Motaz Alfarraj , Ghassan AlRegib

In the workflow of Full-Waveform Inversion (FWI), we often tune the parameters of the inversion to help us avoid cycle skipping and obtain high resolution models. For example, typically start by using objective functions that avoid cycle…

Geophysics · Physics 2020-02-11 Bingbing Sun , Tariq Alkhalifah

Stochastic gradient descent (SGD) is a promising method for solving large-scale inverse problems, due to its excellent scalability with respect to data size. In this work, we analyze a new data-driven regularized stochastic gradient descent…

Numerical Analysis · Mathematics 2024-09-30 Zehui Zhou

This paper deals with the solution of Maxwell's equations to model the electromagnetic fields in the case of a layered earth. The integrals involved in the solution are approximated by means of a novel approach based on the splitting of the…

Numerical Analysis · Mathematics 2023-01-04 Eleonora Denich , Paolo Novati , Stefano Picotti

Travel time tomography is used to infer the underlying three-dimensional wavespeed structure of the Earth by fitting seismic travel time data collected at surface stations. Data interpolation and denoising techniques are important…

Optimization and Control · Mathematics 2020-01-08 Robert Baraldi , Carl Ulberg , Rajiv Kumar , Kenneth Creager , Aleksandr Aravkin

Unfitted mesh formulations for interface problems generally adopt two distinct methodologies: (i) penalty-based approaches and (ii) explicit enrichment space techniques. While Stable Generalized Finite Element Method (SGFEM) has been…

Numerical Analysis · Mathematics 2025-03-21 Yin Song , Wenkai Hu , Xin Li

In this paper we study the linearized inverse problem associated with imaging of reflection seismic data. We introduce an inverse scattering transform derived from reverse-time migration (RTM). In the process, the explicit evaluation of the…

Analysis of PDEs · Mathematics 2011-01-24 Tim J. P. M. Op 't Root , Christiaan C. Stolk , Maarten V. de Hoop

This paper considers downlink of reconfigurable intelligent surface (RIS) assisted cooperative non-orthogonal multiple access (CNOMA) systems. Our objective is to minimize the total transmit power by jointly optimizing the active…

Signal Processing · Electrical Eng. & Systems 2020-12-08 Jiakuo Zuo , Yuanwei Liu , Naofal Al-Dhahir

Drilling investment is pivotal to operational planning in oil and gas (O\&G) exploration. Conventional deployment relies heavily on fragmented expert assessments of geological and economic factors, with limited integration ability of…

Optimization and Control · Mathematics 2026-03-20 Chao Min , Junyi Cui , Stanisław Migórski , Yonglan Xie , Qingxia Zhang , Jun Peng
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