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Three-dimensional gravity modeling in all space

✍ Scribed by Xiong L.I., Michel Chouteau

Tongue
English
Leaves
30
Category
Library
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✦ Synopsis

Surveys in Geophysics, Vol. 19: P.339–368, 1998.

Abstract. We review available analytical algorithms for the gravity effect and gravity gradients especially the vertical gravity gradient due to a right rectangular prism, a right polygonal prism, and a polyhedron. The emphasis is placed on an investigation of validity, consistency, and especially singularities of different algorithms, which have been traditionally proposed for calculation of the gravity effect on ground (or outside anomalous bodies), when they are applied to all points in space.
The rounding error due to the computer floating point precision is estimated. The gravity effect and vertical gradient of gravity in three dimensions caused by a cubic model are calculated by different types of algorithms. The reliability of algorithms for the calculation of gravity of a right polygonal prismand a polyhedron is further verified by using a regular polygonal prism approximating a vertical cylinder and a regular polyhedron approximating a sphere, respectively. By highlighting Haáz-Jung-Plouff and Okabe-Steiner-Zilahi-Sebess’ formulae for a right rectangular prism, Plouff’s algorithm for a right polygonal prism, and Götze and Lahmeyer’s algorithm for a polyhedron and removing their singularities, we demonstrate that these formulae and algorithms can be used to model the gravity anomaly and its vertical gradient at all possible computation positions.
Keywords: three-dimensional body, gravity, gravity gradient, forward modeling, all space, singularity, rounding error
Авторы рассматривают доступные аналитические алгоритмы для расчета гравитационного эффекта и гравитационных градиентов, особенно вертикальных градиентов силы тяжести правых прямоугольных призм, правых многогранных призм, и произвольных многогранников. Акцентируется внимание на изучении различных вычислительных алгоритмов, их методике применения и, особенно, обсуждение особенностей различных алгоритмов, которые традиционно предлагаются для расчета гравитационного эффекта на земле (или за пределами аномальных тел), когда они применяются ко всем точкам в пространстве.
Оценивается точность расчета гравитационного эффекта.
Ключевые слова: трехмерное тело, гравитация, градиент силы тяжести, моделирования, все пространство, сингулярность, ошибка округления

✦ Subjects

Горно-геологическая отрасль;Матметоды и моделирование в геологии

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<img height="34" width="91" src="http://media.wiley.com/assets/7143/33/agu_logo.jpg" /></p><h6 xmlns="http://www.w3.org/1999/xhtml">About The Product</h6><p xmlns="http://www.w3.org/1999/xhtml">Published by the American Geophysical Union as part of the <i>Coastal and Estuarine Sciences Series</i>. <