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.

Geodesy and Mathematics: Interactions in Multiscale Mollifier Regularization Methods

2020 ◽  
Author(s):  
Willi Freeden
Keyword(s):  
Research Field ◽  
Data Sampling ◽  
Disturbing Potential ◽  
Earthquake Modeling ◽  
Inverse Gravimetry ◽  
The Subject ◽  
Vening Meinesz ◽  
And Mathematics ◽  
Space Data ◽  
Novel Applications

<p>The lecture highlights arguments that, coming from Mathematics, have fostered the advancement of Geodesy, as well as those that, generated by geodetic problems, have contributed to the enhancement in Mathematics.</p><p>We particularly deal with novel applications to Geodesy in the context of multiscale approximation (MA). In fact, multiscale reconstruction and decorrelation methods are a research field originated in geophysics for, e.g., earthquake modeling some decades ago, in which today's Geodesy and Mathematics show mutual influences, especially on the subject of spectral and space data sampling.</p><p>We particularly focus the attention on inverse problems of Geodesy and multiscale mollifier regularization strategies. Two examples are studied in more detail:</p><p>(i) Vening Meinesz multiscale surface mollifier regularization to determine locally the Earth's disturbing potential from deflections of vertical,</p><p>(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.</p><p>Neither extreme depth to explain all facets of the geodetic observational situation nor penetrative handling of mathematical obligations and technicalities can be expected. The lecture is just an \lq \lq appetizer'' served to enjoy the tasty meal "Mathematical Geodesy Today'' to be shared by geodesists and mathematicians.</p>

Contribution of satellite altimetry in modelling Moho density contrast in oceanic areas

2019 ◽  
Vol 13 (1) ◽  
pp. 33-40 ◽  
Author(s):  
M. Abrehdary ◽  
L. E. Sjöberg ◽  
D. Sampietro
Keyword(s):  
Satellite Altimetry ◽  
Density Contrast ◽  
Contrast Model ◽  
Bathymetric Data ◽  
Crustal Model ◽  
Marine Gravity ◽  
Study Results ◽  
Vening Meinesz ◽  
Satellite Altimetry Data

Abstract The determination of the oceanic Moho (or crust-mantle) density contrast derived from seismic acquisitions suffers from severe lack of data in large parts of the oceans, where have not yet been sufficiently covered by such data. In order to overcome this limitation, gravitational field models obtained by means of satellite altimetry missions can be proficiently exploited, as they provide global uniform information with a sufficient accuracy and resolution for such a task. In this article, we estimate a new Moho density contrast model named MDC2018, using the marine gravity field from satellite altimetry in combination with a seismic-based crustal model and Earth’s topographic/bathymetric data. The solution is based on the theory leading to Vening Meinesz-Moritz’s isostatic model. The study results in a high-accuracy Moho density contrast model with a resolution of 1° × 1° in oceanic areas. The numerical investigations show that the estimated density contrast ranges from 14.2 to 599.7 kg/m3 with a global average of 293 kg/m3. In order to evaluate the accuracy of the MDC2018 model, the result was compared with some published global models, revealing that our altimetric model is able to image rather reliable information in most of the oceanic areas. However, the differences between this model and the published results are most notable along the coastal and polar zones, which are most likely due to that the quality and coverage of the satellite altimetry data are worsened in these regions.

Sign in / Sign up

Export Citation Format

Share Document