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On the Unique Solvability of Inverse Problems of Magnetometry and Gravimetry
Mathematics, 2023 This article deals with the question of the unique solvability of systems of linear algebraic equations, to the solution of which many inverse problems of geophysics are reduced as a result of discretization when applying the methods of integral ...
Inna Stepanova +4 more
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Numerical simulation of inverse geochemistry problems by regularizing algorithms
Cogent Engineering, 2022 Currently, methods and approaches of scientific visualization based on additional data analysis are being intensively developed due to the rapid development of computer technology in geology.
Nurlan Temirbekov +4 more
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Improved Primal–Dual Interior-Point Method Using the Lawson-Norm for Inverse Problems
IEEE Access, 2020 Electrical impedance tomography (EIT), geophysics and undersea target reconstruction are typical non-linear ill-posed inverse problems, and in many cases, the anomalous bodies feature with a clear boundary. Thus, it is suitable to obtain sharp boundaries
Wenjing Shang +3 more
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Automatic differentiation in geophysical inverse problems [PDF]
Geophysical Journal International, 2007 Summary Automatic differentiation (AD) is the technique whereby output variables of a computer code evaluating any complicated function (e.g. the solution to a differential equation) can be differentiated with respect to the input variables.
Sambridge, Malcolm +3 more
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Mathematical modeling of magnetotelluric field in one-dimensional piecewise gradient medium
Вестник Камчатской региональной ассоциации "Учебно-научный центр". Серия: Науки о Земле, 2020 The solution of forward problems of magnetotelluric sounding for a case of one-dimensional piecewise gradient environments is received. Two problems are considered: the problem of calculating the impedance on the Earth’s surface for a gradient model of ...
Александров П.Н. +1 more
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Majorization–Minimization Total Variation Solution Methods for Electrical Impedance Tomography
Mathematics, 2022 Inverse problems arise in many areas of science and engineering, such as geophysics, biology, and medical imaging. One of the main imaging modalities that have seen a huge increase in recent years is the noninvasive, nonionizing, and radiation-free ...
Eman Alruwaili, Jing Li
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Ensemble inference in geophysical inverse problems [PDF]
Geophysical Journal International, 1993 Non-invasive studies of the shallow Earth are an essential element in a broad range of earth science disciplines. Such studies are usually accomplished using geophysical techniques, which means that a geophysical inverse problem must be solved. Unfortunately, non-uniqueness is a basic property of almost all solutions to geophysical inverse problems. In
D. W. Vasco +2 more
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Arbitrary Sampling Fourier Transform and Its Applications in Magnetic Field Forward Modeling
Applied Sciences, 2022 Numerical simulation and inversion imaging are essential in geophysics exploration. Fourier transform plays a vital role in geophysical numerical simulation and inversion imaging, especially in solving partial differential equations.
Shikun Dai +4 more
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Optimal Solutions to a Linear Inverse Problem in Geophysics [PDF]
Proceedings of the National Academy of Sciences, 1971 This paper is concerned with the solution of the linear system obtained in the Backus-Gilbert formulation of the inverse problem for gross earth data. The theory of well-posed stochastic extensions to illposed linear problems, proposed by Franklin, is developed for this application.
Jordan, T. H., Franklin, J. N.
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MONTE CARLO METHODS IN GEOPHYSICAL INVERSE PROBLEMS [PDF]
Reviews of Geophysics, 2002 Monte Carlo inversion techniques were first used by Earth scientists more than 30 years ago. Since that time they have been applied to a wide range of problems, from the inversion of free oscillation data for whole Earth seismic structure to studies at the meter‐scale lengths encountered in exploration seismology.
Sambridge, M., Mosegaard, Klaus
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