Journal ArticleDOI
Analytical computation of the full gravity tensor of a homogeneous arbitrarily shaped polyhedral source using line integrals
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TLDR
In this article, an analytical computation of the full gravity tensor from a polyhedral source of homogeneous density is presented, with emphasis on its algorithmic implementation, based on the subsequent transition of the general expressions from volume to surface and from surface to line integrals, defined along the closed polygons building each polyhedral face.Abstract:
The analytical computation of the full gravity tensor from a polyhedral source of homogeneous density is presented, with emphasis on its algorithmic implementation. The theoretical development is based on the subsequent transition of the general expressions from volume to surface and from surface to line integrals, defined along the closed polygons building each polyhedral face. However, the accurate numerical computation of the obtained transcendental expressions is linked with the relative position of the computation point and its corresponding projections on the plane of each face and on the line of each segment with respect to the polygons defining each face. Depending on this geometric setup, the application of the divergence theorem of Gauss leads to the appearance of additional correction terms, valid only for these boundary conditions and crucial for the correct numerical evaluation of the polyhedral-related gravity quantities at those locations of the computation point. A program in Fortran is su...read more
Citations
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Journal ArticleDOI
Optimized formulas for the gravitational field of a tesseroid
TL;DR: In this paper, the authors proposed a tesseroid-based method for the estimation of the potential derivatives of a point mass and its derivatives up to second-order in terms of Cartesian coordinates.
Journal ArticleDOI
Analytical computation of gravity effects for polyhedral bodies
TL;DR: In this article, it was proved that only the off-diagonal entries of the second-order derivative of the potential do exhibit a non-eliminable singularity when the observation point is aligned with an edge of a face.
Journal ArticleDOI
On the evaluation of the gravity effects of polyhedral bodies and a consistent treatment of related singularities
TL;DR: In this paper, the singularities which can affect the computation of the gravity effects (potential, gravity and tensor gradient fields) can be systematically addressed by invoking distribution theory and suitable formulas of differential calculus.
Journal ArticleDOI
An accurate, robust, and easy-to-implement method for integration over arbitrary polyhedra: Application to embedded interface methods
TL;DR: This is the first article that compares both accuracy and computational efficiency of methods relying on volume decomposition and those based on the divergence theorem and the results show that the method is as accurate and generalized as the most widely usedVolume decomposition based methods.
Journal ArticleDOI
Gravity Anomalies of Arbitrary 3D Polyhedral Bodies with Horizontal and Vertical Mass Contrasts
TL;DR: In this article, the authors derived analytic formulae for gravity anomalies of arbitrary polyhedral bodies with complicated polynomial density contrasts in 3D space, where anomalous mass density is allowed to vary in both horizontal and vertical directions in a Polynomial form of =ax^m+by^n+cz^t$$�, where m, n, t are nonnegative integers and a, b, c are coefficients of mass density.
References
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Book
Table of Integrals, Series, and Products
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Journal ArticleDOI
The quickhull algorithm for convex hulls
TL;DR: This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull algorithm with the general-dimension Beneath-Beyond Algorithm, and provides empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it used less memory.
Journal ArticleDOI
The Rapid Calculation of Potential Anomalies
TL;DR: In this paper, it is shown how a series of Fourier transforms can be used to calculate the magnetic or gravitational anomaly caused by an uneven, non-uniform layer of material.
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