scholarly journals A three-dimensional inverse gravimetry problem for ice with snow caps

2013 ◽  
Vol 7 (2) ◽  
pp. 523-544 ◽  
Author(s):  
Victor Isakov ◽  
◽  
Shingyu Leung ◽  
Jianliang Qian ◽  
Keyword(s):  
Three Dimensional ◽  
Inverse Gravimetry ◽  
Inverse Gravimetry Problem

Decorrelative Mollifier Gravimetry

2021 ◽  
Author(s):  
Willi Freeden
Keyword(s):  
Inverse Problems ◽  
Density Contrast ◽  
Disturbing Potential ◽  
Book Series ◽  
Inverse Gravimetry ◽  
Constructive Approximation ◽  
Vening Meinesz ◽  
Inverse Gravimetry Problem

<p>The lecture highlights arguments that, coming from multiscale mathematics, have fostered the advancement of gravimetry, as well as those that, generated by gravimetric problems, have contributed to the enhancement in constructive approximation and numerics. Inverse problems in gravimetry are delt with multiscale mollifier decorrelation strategies. Two examples are studied in more detail: (i) Vening Meinesz multiscale surface mollifier regularization to determine locally the Earth's disturbing potential from deflections of vertical, (ii) Newton multiscale volume mollifier regularization of the inverse gravimetry problem to derive locally the density contrast distribution from functionals of the Newton integral and to detect fine particulars of geological relevance. All in all, the Vening Meinesz medal  lecture is meant as an  \lq \lq appetizer'' served to enjoy the tasty meal "Mathematical Geoscience Today'' to be shared by geoscientists and mathematicians in the field of gravimetry. It provides innovative concepts and locally relevant applications presented in a monograph to be published by Birkhäuser in the book series “Geosystems Mathematics” (2021).</p>

A level-set method for imaging salt structures using gravity data

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. G27-G40 ◽  
Author(s):  
Wenbin Li ◽  
Wangtao Lu ◽  
Jianliang Qian
Keyword(s):  
Inverse Problem ◽  
Level Set Method ◽  
Level Set ◽  
Gravity Data ◽  
Density Contrast ◽  
Level Set Function ◽  
Salt Structure ◽  
Inverse Gravimetry ◽  
Set Function ◽  
Inverse Gravimetry Problem

We have developed a level-set method for the inverse gravimetry problem of imaging salt structures with density contrast reversal. Under such a circumstance, a part of the salt structure contributes two completely opposite anomalies that counteract with each other, making it unobservable to the gravity data. As a consequence, this amplifies the inherent nonuniqueness of the inverse gravimetry problem so that it is much more challenging to recover the whole salt structure from the gravity data. To alleviate the severe nonuniqueness, it is reasonable to assume that the density contrast between the salt structure and the surrounding sedimentary host depends upon the depth only and is known a priori. Consequently, the original inverse gravity problem reduces to a domain inverse problem, where the supporting domain of the salt body becomes the only unknown. We have used a level-set function to parametrize the boundary of the salt body so that we reformulated the domain inverse problem into a nonlinear optimization problem for the level-set function, which was further solved for by a gradient descent method. Both 2D and 3D experiments on the SEG/EAGE salt model were carried out to demonstrate the effectiveness and efficiency of the new method. The algorithm was able to recover dipping flanks of the salt model, and it only took 40 min in a 2.5 GHz CPU to invert for a 3D model of 97,000 unknowns.

Stability and the inverse gravimetry problem with minimal data

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Victor Isakov ◽  
Aseel Titi
Keyword(s):  
Inverse Problem ◽  
Gravitational Force ◽  
Three Dimensional ◽  
Minimal Amount ◽  
Algebraic Equations ◽  
Inverse Gravimetry ◽  
Reference Domain ◽  
Boundary Measurements ◽  
Minimal Data ◽  
Simple Systems

AbstractThe inverse problem in gravimetry is to find a domain 𝐷 inside the reference domain Ω from boundary measurements of gravitational force outside Ω. We found that about five parameters of the unknown 𝐷 can be stably determined given data noise in practical situations. An ellipse is uniquely determined by five parameters. We prove uniqueness and stability of recovering an ellipse for the inverse problem from minimal amount of data which are the gravitational force at three boundary points. In the proofs, we derive and use simple systems of linear and nonlinear algebraic equations for natural parameters of an ellipse. To illustrate the technique, we use these equations in numerical examples with various location of measurements points on \partial\Omega. Similarly, a rectangular 𝐷 is considered. We consider the problem in the plane as a model for the three-dimensional problem due to simplicity.

scholarly journals An improved fast local level set method for three-dimensional inverse gravimetry

2015 ◽  
Vol 9 (2) ◽  
pp. 479-509 ◽  
Author(s):  
Wangtao Lu ◽  
◽  
Shingyu Leung ◽  
Jianliang Qian ◽  
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Local Level ◽  
Three Dimensional ◽  
Inverse Gravimetry ◽  
Local Level Set
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