scholarly journals Inverse problem for the gravimetric modeling of the crust-mantle density contrast

2013 ◽  
Vol 43 (2) ◽  
pp. 83-98
Author(s):  
Robert Tenzer
Keyword(s):  
Inverse Problem ◽  
Integral Equation ◽  
Gravity Data ◽  
A Priori ◽  
Density Contrast ◽  
Spherical Harmonic Analysis ◽  
Moho Interface ◽  
Isostatic Gravity ◽  
Gravity Disturbances ◽  
Moho Depths

Abstract The gravimetric inverse problem for finding the Moho density contrast is formulated in this study. The solution requires that the crust density structure and the Moho depths are a priori known, for instance, from results of seismic studies. The relation between the isostatic gravity data (i.e., the complete-crust stripped isostatic gravity disturbances) and the Moho density contrast is defined by means of the Fredholm integral equation of the first kind. The closed analytical solution of the integral equation is given. Alternative expressions for solving the inverse problem of isostasy are defined in frequency domain. The isostatic gravity data are computed utilizing methods for a spherical harmonic analysis and synthesis of the gravity field. For this purpose, we define various spherical functions, which define the crust density structures and the Moho interface globally.

scholarly journals Gravimetric recovery of the Moho geometry based on a generalized compensation model

2013 ◽  
Vol 43 (4) ◽  
pp. 253-269
Author(s):  
Robert Tenzer
Keyword(s):  
Inverse Problem ◽  
Integral Equation ◽  
Upper Mantle ◽  
Gravity Data ◽  
Theoretical Assumption ◽  
Moho Interface ◽  
Compensation Model ◽  
Gravity Disturbances ◽  
Moho Depths ◽  
Definition Of

Abstract Gravity data used for a recovery of the Moho depths should (optimally) comprise only the gravitational signal of the Moho geometry. This theoretical assumption is typically not required in classical isostatic models, which are applied in gravimetric inverse methods for a recovery of the Moho interface. To overcome this theoretical deficiency, we formulate the gravimetric inverse problem for the consolidated crust-stripped gravity disturbances, which have (theoretically) a maximum correlation with the Moho geometry, while the gravitational contributions of anomalous density structures within the lithosphere and sub-lithosphere mantle (including the core-mantle boundary) should be subtracted from these gravity data. In the absence of a reliable 3-D Earth’s density model, our definitions are limited to the crustal and upper mantle density structures. The gravimetric forward modeling technique is applied to compute these gravity data using available models of major known anomalous crustal and upper mantle density structures. The gravimetric inverse problem is defined by means of the (non-linear) Fredholm integral equation of the first kind. After linearization of the integral equation, the solution to the gravimetric inverse problem is given in a frequency domain. The inverse problem is formulated for a generalized crustal compensation model. It implies that the compensation equilibrium is (theoretically) attained by both, the variable depth and density of compensation. A theoretical definition of this generalized crustal compensation model and a formulation of the gravimetric inverse problem for finding the Moho depths are given in this study.

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.

Stable inversion of gravity anomalies of sedimentary basins with nonsmooth basement reliefs and arbitrary density contrast variations

Geophysics ◽  
1999 ◽  
Vol 64 (3) ◽  
pp. 754-764 ◽  
Author(s):  
Valéria C. F. Barbosa ◽  
João B. C. Silva ◽  
Walter E. Medeiros
Keyword(s):  
Gravity Anomaly ◽  
Gravity Data ◽  
A Priori ◽  
Bouguer Anomaly ◽  
Gravity Anomalies ◽  
Sedimentary Basins ◽  
Upper And Lower Bounds ◽  
Density Contrast ◽  
Good Precision ◽  
Rift Basins

We present a new, stable method for interpreting the basement relief of a sedimentary basin which delineates sharp discontinuities in the basement relief and incorporates any law known a priori for the spatial variation of the density contrast. The subsurface region containing the basin is discretized into a grid of juxtaposed elementary prisms whose density contrasts are the parameters to be estimated. Any vertical line must intersect the basement relief only once, and the mass deficiency must be concentrated near the earth’s surface, subject to the observed gravity anomaly being fitted within the experimental errors. In addition, upper and lower bounds on the density contrast of each prism are introduced a priori (one of the bounds being zero), and the method assigns to each elementary prism a density contrast which is close to either bound. The basement relief is therefore delineated by the contact between the prisms with null and nonnull estimated density contrasts, the latter occupying the upper part of the discretized region. The method is stabilized by introducing constraints favoring solutions having the attributes (shared by most sedimentary basins) of being an isolated compact source with lateral borders dipping either vertically or toward the basin center and having horizontal dimensions much greater than its largest vertical dimension. Arbitrary laws of spatial variations of the density contrast, if known a priori, may be incorporated into the problem by assigning suitable values to the nonnull bound of each prism. The proposed method differs from previous stable methods by using no smoothness constraint on the interface to be estimated. As a result, it may be applied not only to intracratonic sag basins where the basement relief is essentially smooth but also to rift basins whose basements present discontinuities caused by faults. The method’s utility in mapping such basements was demonstrated in tests using synthetic data produced by simulated rift basins. The method mapped with good precision a sequence of step faults which are close to each other and present small vertical slips, a feature particularly difficult to detect from gravity data only. The method was also able to map isolated discontinuities with large vertical throw. The method was applied to the gravity data from Reco⁁ncavo basin, Brazil. The results showed close agreement with known geological structures of the basin. It also demonstrated the method’s ability to map a sequence of alternating terraces and structural lows that could not be detected just by inspecting the gravity anomaly. To demostrate the method’s flexibility in incorporating any a priori knowledge about the density contrast variation, it was applied to the Bouguer anomaly over the San Jacinto Graben, California. Two different exponential laws for the decrease of density contrast with depth were used, leading to estimated maximum depths between 2.2 and 2.4 km.

Towards the Moho depth and Moho density contrast along with their uncertainties from seismic and satellite gravity observations

2017 ◽  
Vol 11 (4) ◽  
Author(s):  
M. Abrehdary ◽  
L.E. Sjöberg ◽  
M. Bagherbandi ◽  
D. Sampietro
Keyword(s):  
Inverse Problem ◽  
Density Contrast ◽  
Moho Depth ◽  
Standard Errors ◽  
Combined Method ◽  
Satellite Gravity ◽  
Global Models ◽  
Moho Depths ◽  
Vening Meinesz ◽  
Models Of Gravity

AbstractWe present a combined method for estimating a new global Moho model named KTH15C, containing Moho depth and Moho density contrast (or shortly Moho parameters), from a combination of global models of gravity (GOCO05S), topography (DTM2006) and seismic information (CRUST1.0 and MDN07) to a resolution of 1° × 1° based on a solution of Vening Meinesz-Moritz’ inverse problem of isostasy. This paper also aims modelling of the observation standard errors propagated from the Vening Meinesz-Moritz and CRUST1.0 models in estimating the uncertainty of the final Moho model. The numerical results yield Moho depths ranging from 6.5 to 70.3 km, and the estimated Moho density contrasts ranging from 21 to 650 kg/m

Fast numerical method of solving 3D coefficient inverse problem for wave equation with integral data

2018 ◽  
Vol 26 (4) ◽  
pp. 477-492 ◽  
Author(s):  
Anatoly B. Bakushinsky ◽  
Alexander S. Leonov
Keyword(s):  
Inverse Problem ◽  
Integral Equation ◽  
Wave Equation ◽  
Wave Field ◽  
A Priori ◽  
Three Dimensional ◽  
Simulated Data ◽  
Three Dimensions ◽  
Unknown Coefficient ◽  
Computational Resources

Abstract An inverse coefficient problem for time-dependent wave equation in three dimensions is under consideration. We are looking for a spatially varying coefficient of this equation knowing special time integrals of the wave field in an observation domain. The inverse problem has applications to the reconstruction of the refractive index of an inhomogeneous medium, as well as to acoustic sounding, medical imaging, etc. In the article, a new linear three-dimensional Fredholm integral equation of the first kind is introduced from which it is possible to find the unknown coefficient. We present and substantiate a numerical algorithm for solving this integral equation. The algorithm does not require significant computational resources and a long solution time. It is based on the use of fast Fourier transform under some a priori assumptions about unknown coefficient and observation region of the wave field. Typical results of solving this three-dimensional inverse problem on a personal computer for simulated data demonstrate high capabilities of the proposed algorithm.

scholarly journals Inverse problem for fractional diffusion equation

2011 ◽  
Vol 14 (1) ◽  
Author(s):  
Vu Tuan
Keyword(s):  
Inverse Problem ◽  
Diffusion Coefficient ◽  
Lower Bound ◽  
Diffusion Equation ◽  
Spectral Data ◽  
A Priori ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
One Dimensional ◽  
Initial Distributions

AbstractWe prove that by taking suitable initial distributions only finitely many measurements on the boundary are required to recover uniquely the diffusion coefficient of a one dimensional fractional diffusion equation. If a lower bound on the diffusion coefficient is known a priori then even only two measurements are sufficient. The technique is based on possibility of extracting the full boundary spectral data from special lateral measurements.

Assembly method in GIS INTEGRO and its usage for solving of gravitational inverse problem

2021 ◽  
pp. 36-47
Author(s):  
Sergey Mitsyn ◽  
Egor Bolshakov
Keyword(s):  
Inverse Problem ◽  
A Priori ◽  
Regional Scale ◽  
Original Formulation ◽  
Model Evolution ◽  
Assembly Method ◽  
Practice Methods

Various methods based on growing bodies are lately gaining attention in a context of inverse gravity problem that we call a family of “assembly methods”. A variant of method was adopted for GIS INTEGRO in original formulation that is fit for the problem of multiple bodies incorporated in an environment of varying density, in absolute densities (not density contrasts) that are however have to be a priori specified. Such formulation allowed the implementation of the method that is suitable for territory modeling in the regional scale. To workaround method’s instability a number of changes are proposed that consist of introduction of priority on atomic modifications, modification queue and assessment of model evolution instead of just the final result. The developed software allows processing of large grids (tens of millions of tiling elements) even on 5–8 year old desktops. Based on method approbation experience some insights and practice methods are presented. An application example is presented as part of work on modeling of Enisei-Khatanga regional depression territory.

scholarly journals An integral equation formulation of the N-body dielectric spheres problem. Part 1: Numerical analysis

2020 ◽  
Author(s):  
Muhammad Hassan ◽  
Benjamin Stamm
Keyword(s):  
Integral Equation ◽  
Numerical Analysis ◽  
Error Analysis ◽  
Convergence Rates ◽  
A Priori ◽  
Approximation Error ◽  
Spherical Particles ◽  
Integral Equation Formulation ◽  
Dielectric Spheres ◽  
The Stability

In this article, we analyse an integral equation of the second kind that represents the solution of N interacting dielectric spherical particles undergoing mutual polarisation. A traditional analysis can not quantify the scaling of the stability constants- and thus the approximation error- with respect to the number N of involved dielectric spheres. We develop a new a priori error analysis that demonstrates N-independent stability of the continuous and discrete formulations of the integral equation. Consequently, we obtain convergence rates that are independent of N.

scholarly journals Basement Mapping of the Fucino Basin in Central Italy by ITRESC Modeling of Gravity Data

Geosciences ◽  
2021 ◽  
Vol 11 (10) ◽  
pp. 398
Author(s):  
Federico Cella ◽  
Rosa Nappi ◽  
Valeria Paoletti ◽  
Giovanni Florio
Keyword(s):  
Seismic Activity ◽  
Site Response ◽  
Gravity Data ◽  
A Priori ◽  
Central Italy ◽  
Gravity Anomalies ◽  
Gravity Modeling ◽  
Ground Shaking ◽  
Sedimentary Evolution ◽  
Fucino Basin

Sediments infilling in intermontane basins in areas with high seismic activity can strongly affect ground-shaking phenomena at the surface. Estimates of thickness and density distribution within these basin infills are crucial for ground motion amplification analysis, especially where demographic growth in human settlements has implied increasing seismic risk. We employed a 3D gravity modeling technique (ITerative RESCaling—ITRESC) to investigate the Fucino Basin (Apennines, central Italy), a half-graben basin in which intense seismic activity has recently occurred. For the first time in this region, a 3D model of the Meso-Cenozoic carbonate basement morphology was retrieved through the inversion of gravity data. Taking advantage of the ITRESC technique, (1) we were able to (1) perform an integration of geophysical and geological data constraints and (2) determine a density contrast function through a data-driven process. Thus, we avoided assuming a priori information. Finally, we provided a model that honored the gravity anomalies field by integrating many different kinds of depth constraints. Our results confirmed evidence from previous studies concerning the overall shape of the basin; however, we also highlighted several local discrepancies, such as: (a) the position of several fault lines, (b) the position of the main depocenter, and (c) the isopach map. We also pointed out the existence of a new, unknown fault, and of new features concerning known faults. All of these elements provided useful contributions to the study of the tectono-sedimentary evolution of the basin, as well as key information for assessing the local site-response effects, in terms of seismic hazards.

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