GEOPHYSICS, VOL. 63, NO. 2 (MARCH-APRIL 1998); P. 446–453, 7 FIGS.
Removing varying directional trends in aeromagnetic data
Mark Pilkington∗ and Walter R. Roest∗ reconstructions (Park et al., 1995) and help in unravelling the deformation history of the intruded regions. Most dykes are tholeiitic in composition and therefore magnetic. Thus, anomalies caused by dykes are common in magnetic maps. For example, Tucker and Boyd (1987) estimate 30% of the 1:250,000 scale magnetic maps for onshore Australia show the presence of dykes. Schwarz et al. (1987) estimate those outcropping mafic dykes wider than 5 m should be detectable in regional aeromagnetic data. Indeed, aeromagnetic data have helped considerably to improve the continuity of previous geological mappings of individual swarms (e.g., West and Ernst, 1991). However, linear magnetic anomalies caused by mafic dykes can obscure useful lithological and structural information that could otherwise be determined in their absence. Such linear trends often truncate and interrupt magnetic anomalies caused by magnetization contrasts, making the tracing of such features ambiguous. Similarly, any subtle magnetic texture within lithological units may be obscured by the presence of dyke anomalies. Since detectable dyke anomalies are generally caused by sources at or near the ground surface, any enhancements (e.g., calculating gradients) of the measured field are likely to exacerbate the problem. In addition, automated methods for source parameter estimation such as Euler deconvolution (Reid et al., 1990) and 3-D analytic signal (Roest et al., 1992) may respond preferentially to the dyke sources at the expense of other, perhaps more useful source information. Thus, to improve the usefulness of magnetic data where the obscuring effects of dykes are significant, some method to remove their signature is needed. Directional filtering either in the spatial or frequency domain is one option that allows all spectral components within some range of azimuths to be removed from the data (Fuller, 1967; Bezdova et al., 1990; Geosoft, 1994). Examples of directional filtering used to emphasize certain structural trends are given in Chandler (1985) and Yarger (1985). Miller and Singh (1994) use simple statistical measures to identify the major directional trends in potential field data that are then progressively removed with standard filtering methods. Clearly, such filters should be designed
ABSTRACT
Both qualitative and quantitative interpretations of aeromagnetic data can be hindered by the presence of magnetic anomalies caused by mafic dykes. Such anomalies obscure the magnetic signatures due to basement lithology and structure, and their effects will often dominate when automated interpretation methods are applied to gridded data sets. Since dyke swarms are often nonparallel, simple frequency-domain strike-sensitive filtering based on a single directional trend is not a viable method for removing their signatures. We use a coordinate transformation to project anomalies of various strikes onto one direction, which is then suppressed using a standard decorrugation method. The resulting grid is subsequently transformed back to the original projection. This approach is illustrated by the removal of the magnetic signature of the Proterozoic Mackenzie dyke swarm occurring in the Slave structural province, Northwest Territories, Canada.
INTRODUCTION
Mafic dyke swarms are found in many different geological environments on Earth, including volcanic centers, compressional plate boundaries, spreading centers and ophiolite complexes, and continent-continent collision zones and in radial swarms originating from the sites of mantle plumes (Ernst et al., 1995a). Approximately 70 giant swarms have been identified worldwide that extend over distances of more than 300 km (Ernst et al., 1995b). Their pattern has been used to infer regional paleostress fields, postdyke deformation geometries, and the location of possible mantle plumes. Reconstructing now-deformed dyke swarms can help in interpreting the surrounding geological structure (Bird et al., 1996) and determining the timing of the deformation events. Paleomagnetic studies of dykes may also provide constraints on paleocontinental
Manuscript received by the Editor January 8, 1997; revised manuscript received June 23, 1997. ∗ Geological Survey of Canada, 1 Observatory Crescent, Ottawa, Ontario K1A 0Y3, Canada. E-mail:
[email protected];
[email protected]. gc.ca. ° c 1998 Society of Exploration Geophysicists. All rights reserved. 446
Removing Directional Trends
to reject only those trends that are unwanted, with little effect on anomaly components in other directions. Nevertheless, some distortion is to be expected since the rejection band in the frequency domain must be smoothly tapered off and wide enough to avoid ringing effects in the filtered data. Many dyke swarms are parallel or subparallel (especially at small scales) so that standard directional filtering is appropriate for removing their signature. However, 50% of swarms in North America exhibit a fanning pattern (Ernst et al., 1995a) over large enough angles so that applying directional filters with such a large rejection band will undoubtedly remove useful source information along with the unwanted anomalies. Furthermore, the removal of trends over a wide range of angles distorts the remaining anomaly distribution and possibly introduces new, false directional information. Overcoming these difficulties can be achieved by a coordinate transformation that can reproject the varying dyke directions onto a single azimuth (Figure 1). Anomalies along this single trend can then be removed by standard directional filtering. First, the focal point of the swarm (latitude α ◦ , longitude β ◦ ) is estimated from the dyke trends. The data grid is then rotated an angle of 90 − α ◦ , moving the focal point to the north pole and causing the dykes to lie on lines of longitude. If the data is regridded onto a cylindrical projection (e.g., Mercator), lines of longitude are then oriented along the columns of the grid, the focal point now being at infinity. So, with the dyke anomalies thus aligned, their effects can be removed with standard decorrugation techniques (e.g., Urquhart, 1988; Minty, 1991) developed for leveling grids, i.e., those grids containing striping due to residual flight-line problems. The need for filtering over a range of azimuths has been removed. Once the grid is
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decorrugated in the transformed coordinate system, the opposite rotations can be applied and the data values regridded at the original grid location and orientation. Using a coordinate transformation with unidirectional filtering results in a more selective removal of specified anomaly components. In contrast to the effects of frequency-domain directional filtering that are spatially invariant, this approach is location dependent in that a given trend will only be removed if it passes through the specified focal point. Trends along a given direction in different areas will be affected according to their location. MACKENZIE DYKE SWARM
We use the coordinate transformation approach to suppress the anomalous effects of the Mackenzie dyke swarm that contributes significantly to the magnetic field over the Slave structural province, Northwest Territories (N.W.T.), Canada. The Mackenzie dykes constitute the largest dyke swarm known on Earth, covering an area of 2.7 × 106 km2 (Figure 2) and ranging from the northern coast of Canada down to northern Ontario (Ernst et al., 1995b). Some dykes can be traced (not continuously) for over 2300 km. The dykes likely originated from a mantle plume whose location has been estimated visually at 70◦ N, 118◦ W by locating the focal point of the swarm that radiates up to a 100◦ angle centered on an average northnorthwesterly trend (Ernst et al., 1995a). Paleomagnetic work shows that there has been no postdyke deformation, so that the maximum regional stress field (along which dykes will usually trend) is known to be oriented north-northwest at the time of dyke injection. Deviations from this trend are minor and reflect
FIG. 1. Flow chart of coordinate transformation method for specific trend removal. Rotation on a sphere is involved in stages (b) and (e). Gridding takes place in stages (c) and (e).
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pre-existing structure and lithological changes. The Mackenzie swarm was emplaced over a short period of time [4 million years at 1267 Ma (Fahrig, 1987)] along with related intrusions (Muskox) and volcanics (Coppermine Lavas) that occur near the plume center. Most of the Mackenzie dykes have a quartztholeiitic composition and are clearly magnetic, with maximum amplitudes of over 100 nT. The average dyke width is about 30 m, but some reach thicknesses of more than 100 m (Fahrig, 1987). Also present in the Slave province are the 750 Ma, northeasterly trending Franklin dykes, which are less pervasive than the Mackenzie swarm and are concentrated mostly in the north and west. The Contwoyto (northeast trending) and the Lac de Gras (north-south) swarms occur in the eastern part of the Slave. These late Aphebian rocks are relatively minor again in terms of their extent (Fahrig, 1987). All these three additional sets of dykes appear less magnetic than the Mackenzie swarm, so that their presence is not considered important to our processing. REMOVAL OF DYKE EFFECTS
Figure 3 shows the observed magnetic field over the Slave province and the ubiquitous nature of the Mackenzie dykes. Within this area, the swarm radiates over an angle of more than 60◦ with an average north-northwesterly trend. The grid is first rotated 20◦ northward, so that the focal point is at 90◦ N and the dykes are oriented north-south along lines of longitude. We then regrid the data on a Mercator projection, resulting in the grid shown in Figure 4, where the meridians are now vertical and coincident with the columns in the grid. The departure of the dyke trends from a north-south orientation reflects both the inherent deviations of dyke directions from the regional stress field at the time of injection and the lack of perfect focus of the dyke azimuths at the chosen focal point. Varying the focal point ±1◦ in both latitude and longitude did not produce significantly different results from those in Figure 4, based on visual inspection. The transformed grid was then decorrugated using a directional cosine filter of degree one (Geosoft, 1994, 23) and a low-pass Butterworth filter of order 8 and cutoff wavelength of 20 km. Decorrugation, as developed for the removal of flight line leveling problems (Urquhart, 1988; Minty, 1991), attempts to remove anomalies that are elongate, i.e., having a predominantly long wavelength content along the flight lines (or the grid columns, in our case) and a short wavelength content perpendicular to this trend. The directional cosine filter removes all those long wavelength trends parallel to the grid columns. This filter also removes long wavelengths parallel to the grid rows, whereas the dyke anomalies have a predominantly short wavelength character perpendicular to strike. Hence, the low-pass filter is used to reject only the shorter wavelength components perpendicular to the dyke trends (grid columns). After decorrugation, the grid is rotated back to the true grid position and orientation, and regridded at the original grid interval of 400 m (Figure 5). The difference between the original and processed data is shown in Figure 6, which highlights the Mackenzie dyke anomalies. In addition, this difference map shows other short wavelength anomalies, that are mainly artifacts of the grid
manipulation. If the procedure outlined in Figure 1 is carried out with the exception of the decorrugation phase, the original data set would not be completely recovered because the regridding leads inevitably to a loss of short wavelength information. In addition, the decorrugation filter eliminates all wavelength components shorter than the cutoff wavelength and, as a result, some useful (nondyke) information will be lost in the process. Alternatively, a narrower filter would not remove all dyke-related anomalies. Therefore a trade-off exists between removing unwanted dyke signatures and keeping useful short wavelength geological information. The nature of the coordinate transformation processing is evident when considered in the frequency domain. For comparative purposes, Figure 7a shows the power spectral amplitude of the original data of Figure 3, whereas Figure 7b shows the results of filtering using a standard directional filter with a rejection band of ±30◦ oriented 150◦ E. These parameters were found to be appropriate for removing most of the dyke effects. As expected, a significant part of the spectrum has been attenuated along the chosen (average) trend. This also includes all those nondyke source anomalies lying in this portion of the spectrum. Figure 7c shows the power spectrum of the grid in Figure 5 using the coordinate transformation approach. A much less drastic attenuation of frequency components can be seen along the average dyke trend since these components have only been removed from the data if the trends line up with the specified focal point. Hence, more information has been retained in the transformed grid compared to the standard directionally filtered grid. CONCLUSIONS
The suppression of variable directional trends in aeromagnetic maps has been accomplished by use of a simple coordinate transformation. A combination of rotations on a sphere can be devised to position the unwanted trends onto meridians which, after regridding with a suitable map projection, can be made to coincide with the columns in the grid. In this fashion, techniques that exist for decorrugating gridded data sets may be used to remove the trends. The example of the radiating Mackenzie dyke swarm shows that this type of approach has advantages over standard directional filtering methods. When trends exist over a large range of azimuths, too much useful, nondyke, magnetic source information is lost using the latter technique. Additionally, this type of filtering is spatially invariant, and rejected frequency components are removed similarly from all points in the gridded data. The coordinate transform, on the other hand, is location dependent, removing only those trends passing through a specified focal point. Plots of the power spectra of grids processed using the two different methods highlight the advantages of the coordinate transform method. ACKNOWLEDGMENTS
We thank Tim West for providing the digitized dyke positions, and R. Bird, R. Grieve, and J. Tod for helpful comments on the manuscript. This is Geological Survey of Canada contribution 1996415.
Removing Directional Trends
FIG. 2. Mackenzie dyke swarm (digitized locations from Ernst et al., 1994). Estimated focal point of the swarm is 70◦ N, 118◦ W.
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FIG. 3. Grayscale aeromagnetic map of the Slave structural province, N.W.T., Canada. Grid interval, 400 m.
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FIG. 4. Grayscale aeromagnetic map of study area after transformation and regridding with Mercator projection. Dykes now trend north-south along grid columns.
FIG. 5. Grayscale aeromagnetic map of transformed and back-rotated grid after decorrugation filtering. Projection is now the same as the original grid in Figure 3.
Removing Directional Trends
FIG. 6. Shaded relief map of difference between processed (Figure 5) and original grid (Figure 3).
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FIG. 7. (a) Power spectrum of original data (Figure 3). (b) Power spectrum of original data directionally filtered with a passband of ±30◦ and orientation 150◦ E. (c) Power spectrum of data grid shown in Figure 5. A wavenumber of 1 radian is equivalent to a wavelength of ∼2500 m.
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