Some issues and insights for gravity and magnetic modelling at the region to continent scale

Abstract

The form of the Earth is much closer to a sphere than a flat slab, so why is gravity and magnetic modelling almost exclusively carried out within a flat Earth or Cartesian framework? The use of a Cartesian coordinate system can be attributed in part to the absence of alternatives in the commercial modelling and visualisation software packages and the need for additional computational resources if modelling is carried out in a spherical or ellipsoidal reference system. These are not sufficiently good reasons, however, to blindly continue with this practice. Gravity modelling is a particularly widespread activity, being used for basic gravity data processing (e.g., Bouguer and terrain corrections - e.g., LaFehr, 1991a, 1991b, 1998; Talwani, 1998; Hinze et al, 2005), geodesy applications (e.g., geoid calculations), and geological interpretation. To what degree are the outcomes of these activities affected by the choice of Earth representation? In the exploration geophysics community, there is a standard answer to the question ?when do curvature effects become significant? which is ?when the models are larger than 166.7 km in horizontal extent?. This criterion can be traced back to Hayford and Bowie (1912). What was the basis for choosing this distance? Is this a criterion that can be applied to all modelling applications or just the original application of Hayford and Bowie (1912)? Although there is general acknowledgment that the curvature of the Earth is important when performing gravity or magnetic modelling of long traverses or large regions, there are few studies of the errors involved if a Cartesian (or rectangular) coordinate reference system is used. Examples that demonstrate the magnitude of curvature effects on gravity response can be found in Hayford and Bowie (1912), Takin and Talwani (1966), Johnson and Litehiser (1972), Qureshi (1976), Miku?ka et al. (2006), and Çavsak (2008). In the following, results of simple calculations for a regular mesh of prismatic elements are presented to quantify the differences in vertical gravity and vertical gravity gradient response for equivalent representations of source elements in Cartesian or spherical coordinate reference systems. It is noted that outcomes for vertical gravity gradient response are the same as those that would be obtained for total magnetic intensity response (TMI). Although this work is based on models comprised of a regular array of prismatic mesh elements, the outcomes can be related to those that would be obtained for models based on arbitrary 3D polyhedra. There are clear extensions of methodology that would allow modellers to estimate the significance of curvature effects for any specific application. This will help to answer the question that is prompted by Figure 1, i.e., ?How significant are the differences if I carry out gravity or magnetic modelling for a portion of the Earth using a Cartesian framework rather than a spherical framework??