A finite element method for computation of the regional gravity anomaly

Abstract

A regional gravity anomaly, based on element shape functions used in finite element analysis, is developed. The regional gravity is approximated by a weighted sum of discrete gravity values at eight stations coinciding with the eight nodes of a second‐order or at twelve stations coinciding with the twelve nodes of a third‐order isoparametric element superimposing the map space. The computations are carried out on a reference space with the shape functions acting as weighting factors, and subsequently translated to the real map space. In this technique, no observed gravity data lying inside the survey area enter into the regional computation. Tests on the gravity field in Harris County, Texas, a well known hydrocarbon prospect during the 1940s, and the Klamath Mountains and the Cascade Range in California confirmed the efficacy of this method.

A geophysical approach to the igneous rocks in the Biga Peninsula (NW Turkey) based on airborne magnetic anomalies: geological implications

“…Since this study deals with the shallow geologic structure of the Biga Peninsula, a FEM, based on the element shape functions, was applied to data-set in order to estimate the amplitude of the regional magnetic background. The amplitude of the regional background was estimated by a weighted sum of discrete magnetic values at eight stations coinciding with the eight nodes of a second-order isoparametric element superimposing the map space (Mallick & Sharma, 1999). A reference space which is defined by the non-dimensional coordinates (ξ and η) ranging between −1 and 1 was used for the computations with the shape functions acting as weighting factors (Mallick & Sharma, 1999).…”

“…The amplitude of the regional background was estimated by a weighted sum of discrete magnetic values at eight stations coinciding with the eight nodes of a second-order isoparametric element superimposing the map space (Mallick & Sharma, 1999). A reference space which is defined by the non-dimensional coordinates (ξ and η) ranging between −1 and 1 was used for the computations with the shape functions acting as weighting factors (Mallick & Sharma, 1999). The shape functions at the nodes 1-8 in reference space were computed by using following formulations (Cheung & Yeo, 1979):…”

“…Further, ∑ N i (ξ, η) = 1 (Mallick & Sharma, 1999). The regional anomaly computed on the reference space was translated to the real map space as shown in Figure 9 and then removed from the original total field anomaly map to estimate the residual anomalies, representing the short wavelength effects.…”

Application of the finite element method to gravity data case study: Western Turkey

“…2, changing the existing (x,y) plane coordinates to (ξ,η) plane coordinates is a necessary step. The new (ξ,η) plane coordinates can be expressed (Mallick and Sharma, 1999) as…”

Gravity Anomalies of 2.5-D Multiple Prismatic Structures with Variable Density: A Marquardt Inversion

“…Regional and residual anomaly separation plays an important role in the interpretation of gravity anomalies. In the recent past, techniques based on the minimum curvature (MICKUS et al, 1991), least-squares orthogonal polynomial fitting (AGARWAL and SIVAGI, 1992), Green's equivalent layer concept (PAWLOWSKI, 1994), fractals (CHAPIN, 1996), and finite elements (MALLICK and SHARMA, 1999) have gained importance in separating a regional gravity field from the Bouguer gravity anomalies. However, each method has its own merits and demerits in its application.…”