Computational Basis for GM-SYS
The methods used to calculate the gravity and magnetic model response are based on the methods of Talwani et al., 1959, and Talwani and Heirtzler, 1964, and make use of the algorithms described in Won and Bevis, 1987. Two and one-half-Dimensional calculations are based on Rasmussen and Pedersen, 1979.
Methods proprietary to Geosoft have also been used to improve the efficiency and speed of the calculations and to make them better suited to an interactive environment. The results from GM-SYS have been verified by comparing them to other published results such as those by Campbell, 1983.
The GM-SYS Profile inversion routine utilizes a Marqardt inversion algorithm (Marqardt, 1963) to linearize and invert the calculations. GM-SYS Profile uses an implementation of that algorithm for gravity and magnetics developed by the USGS and used in their computer program, SAKI (Webring, 1985).
GM-SYS Profile uses a two-dimensional, flat-earth model for the gravity and magnetic calculations:
- Each structural unit or block extends to plus and minus infinity in the direction perpendicular to the profile.
- The earth is assumed to have topography but no curvature.
- The model also extends plus and minus 30,000 kilometres along the profile to eliminate edge effects.
In GM-SYS Profile, stations (points at which gravity or magnetic values are observed and calculated) should be outside of the source material (ie. in an area of the model with a density, magnetization and susceptibility equal to zero).
Computational Basis for GM-SYS 3D
The forward calculations used in GMSYS-3D are based on the frequency-domain techniques published by Parker (1972) and Blakely (1995).
The gravity structural and lateral density inversion schemes are based on unpublished algorithms developed by Bill Pearson.
The magnetic structural and the lateral susceptibility inversion schemes are based on the papers by Parker and Huestis (1974) and Oldenburg (1974).
Blakely (1995) advances these techniques and provides code examples of some of the key elements. The lateral susceptibility inversion also incorporates Geosoft's “Apparent Susceptibility” filter.
Difference Between Draped Survey and a Flat Survey
We divide the draped calculations into two realms; those layers that extend above the Minimum Survey Elevation (MSE), and those that are completely below it. The layers that extend above the MSE are computed as many vertical prisms in the (slow) space domain. Layers that are completely below are calculated using the grid-based FFT routines.
We have some optimizations to speed the space-domain calculations: beyond a certain distance/elevation, the space domain calculations are performed using spherical approximations, rather than the precise geometry of each prism. Also, where layers are coincident (zero thickness), the calculations are skipped.
References:
- Blakely, R.J., 1995, Potential Theory in Gravity & Magnetic Applications: Cambridge University Press, pp.441.
- Chavarria et al., 2006, Modeling gravity and tensor gravity data using Poisson's Equation for airborne, surface and borehole applications: US Patent No. 6,993,433 B2, ConocoPhillips Company.
Oldenburg, D. W., 1974, The inversion and interpretation of gravity anomalies: Geophysics, v.39:526-536 - Parker, R.L., 1972, The rapid calculation of potential anomalies: Geophysical Journal of the Royal Astronomical Society, v.42:315-334.
- Parker, R.L. and Huestis, S.P., 1974, The Inversion of Magnetic Anomalies in the Presence of Topography: JGR, v.79:1587-1593.