Synthetic Modelling of Bouguer Gravity Horizontal-gradient Vector Data

Darran J. Edwards
Department of Geology and Geophysics, The University of Calgary
2500 University Dr. N.W., Calgary, Alberta, T2N 1N4
e-mail: edwards@geo.ucalgary.ca
and
Henry V. Lyatsky
Lyatsky Geoscience Research and Consulting Ltd.
4827 Nipawin Cr. N.W., Calgary, Alberta, T2K 2H8
e-mail: lyatskyh@cadvision.com
Mapping the horizontal gradient of magnetic and gravity data enhances the images of anomaly-causing geologic discontinuities such as steep body edges (Hood and Teskey, 1989). Source-body edge detection is a useful tool in mapping, for example, basement grain, fault patterns and intrusive igneous bodies. The horizontal gradient is a two-component vector quantity, having magnitude and direction. A horizontal gradient vector (HGV) is displayed as an arrow whose orientation represents the direction of the gradient and whose length is proportional to the magnitude of the gradient. Arrows originate at grid nodes and can be generated either to point away from local maxima in the potential field (``downhill'') or toward the local maxima (``uphill''). A detailed discussion of HGV computation methods was provided by Lyatsky et al. (1992) and Thurston and Brown (1994).

In order to constrain or guide the interpretation of HGV maps, it is useful to carry out modelling studies incorporating some simple geologic bodies. Models were created using Sierra's MIMIC geologic modelling software package and then loaded into LCT's S3MOD, an interactive 3-D potential-field modelling program. Computation of the field utilizes a modified 3-D Talwani method. HGV data were then computed from the synthetic Bouguer gravity data. A prism and a dome are the two main model geometries presented here, but several variations on these and other models have also been tested. The models have been simplified to represent topography on the basement surface. Average densities of 2.5 and 2.7 g/cucm were used for the ``cover'' and ``basement'' rocks, respectively. Model dimensions were taken from an examination of typical potential-field HGV lineament patterns found in east-central Alberta (Edwards et al., 1996).

The prism model represents a basement block that may have been created by orthogonally-trending faults, heterogeneous basement rock lithology, or a combination of these two geologic scenarios. The aim of such synthetic modelling is to show that gravity and magnetic HGV maps can accurately and easily detect the edges of such blocks. The model consists of a 100 km by 100 km prism centered in a survey area of 1000 km by 1000 km and raised 200 m above a reference plane located at a depth of 1.8 km (Figure 1). Using a grid spacing of 5 km to simulate the common parameters of Geological Survey of Canada gravity data, the entire survey area contains 201 by 201 grid nodes. Figures 1C and 1D show that prism boundaries are easily defined by a zone of longer vector arrows that represent greater gradient magnitudes. In order to determine whether consistent HGV lineament patterns emerge regardless of data-grid orientation, a series of rotated prism models were generated. Figure 2 shows a prism oriented at 30 degrees relative to north. The lateral extent of the rotated prism is again delineated by a zone of longer arrow lengths, with no apparent artifacts introduced.

figure ed1.gif
figure ed2.gif
figure ed3.gif

Another common geometric shape is the dome, which may represent a pluton or intrusive body in the basement. In contrast to the near-vertical sides and flat top of the prism, the flanks of the dome slope gradually away from its apex. The dome has relief of 200 m above the reference plane and the radius of its circular projection, as seen in map view, of 50 km (Figure 3). The dome can easily be located on HGV data, particularly when vector arrows are plotted away from local maxima (``downhill''). The radiating HGV arrow pattern seen in Figure 3C indicates that the gradient is constantly changing from the apex to the boundary, hence the well-defined diverging pattern when arrows are plotted away from local maxima.

Modelling studies serve to illustrate the aptitude of the HGV method for edge detection. Basement structure and lithology may be distinguished on the basis of consistent orientations and lengths of vector arrows, often bounded by sharp breaks in the arrow pattern. Work is now under way, in conjunction with the Geological Survey of Canada, to assess the relative merits of logarithmic versus linear scaling of HGV arrows. It seems the use of linear scaling avoids a number of artifacts introduced by the logarithmic procedure. This issue will be addressed in upcoming publications.

References