A contribution to the new Magnetic Anomaly Map of North America

by W.F. Miles, Geological Survey of Canada

The new 1-km grid of magnetic anomaly data for Canada has been compiled as part of a joint effort between the Geological Survey of Canada (GSC), U.S. Geological Survey (USGS), and Consejo de Recursos Minerales de México (CRM) to produce a digital magnetic anomaly database for the North American continent. This database represents a substantial upgrade from the previous compilation of magnetic anomaly data for North America produced in 1988, and involves the compilation of over 500 individual airborne and shipborne magnetic surveys.

Magnetic data is also available for the United States and Mexico.

In 1999, a joint effort by the Geological Survey of Canada, the United States Geological Survey, and the Consejo de Recursos Minerales de México produced a 1 km grid of the residual total magnetic field over North America. In order to fulfill Canada's commitment to this project, a 1 km grid was generated from levelled profile data to achieve maximum resolution. The levelling of aeromagnetic survey profile data to a common datum and to adjacent surveys is required to account for secular variations in the geomagnetic field, arbitrary magnetometer base levels, variable flight line spacing, differences in flying height and data quality. Although much of the Canadian Aeromagnetic Data Base had been previously levelled to a national datum and to adjacent surveys, there remained a number of older, low quality data sets and recent high quality data sets that required levelling. In addition, the long wavelength component of the national datum was suspect and required investigation.

The levelling of Canada's aeromagnetic data has taken place over the last 30 years in several phases. Most of the data collected before 1980 was recorded before the advent of digital acquisition and were only available as analogue profiles and contour maps. The contour maps, compiled at a scale of 1:63 360 (1 inch to 1 mile), were digitized at the intersection of contour lines and flight lines. This project began in the late 1970's and required the participation of a number of private companies. The digitization was accomplished in three years, under the supervision of the Geological Survey of Canada (GSC). The line data were archived on a sheet and survey basis, and these accumulated data resulted in the creation of the Canadian Aeromagnetic Data Base.

The first levelling of all Canadian aeromagnetic survey data was to produce gridded data for a national series of 1:1 000 000 scale maps. The digitized and digital data were interpolated to an 812.8 m interval grid and the International Geomagnetic Reference Field (IGRF) for the year of the survey was removed. Differences at the boundary of adjacent surveys were removed using a low-order polynomial. The remaining errors were locally smoothed out where required (Teskey et al.,1982). A continuous, seamless aeromagnetic grid extending from Alberta to the Atlantic Ocean and from the United States border to the Arctic Ocean was created using regional surveys [flown at a mean terrain clearance of 305m (1000 feet) with a line spacing of 800m (½ mile)]. Smaller grids using drape-flown surveys from British Columbia and the Yukon Territory were also assembled. These levelled grids served as the basis for future levelling of the survey profile data.

The first stage of the levelling of Canadian aeromagnetic survey digital profile data was initiated by the Ontario Geological Survey (OGS), in cooperation with the Geological Survey of Canada, in 1989. The project consisted of the production of a 'Single Master Aeromagnetic Grid for the province of Ontario at a uniform grid spacing of 200 m' (Reford et al., 1990). In order to achieve maximum resolution, it was required to interpolate the digitized line data to a 200 m grid interval and apply the levelling adjustment previously applied to the existing, regional 812.8 m grid. The 812.8 m interval levelled grid was re-gridded to match the unlevelled 200 m interval grid. The unlevelled grid was subtracted from the levelled grid to produce a grid of differences. A Naudy filter was applied to the difference grid to retain only the level adjustments. The grid of the level adjustments was then added to the original unlevelled total field grid to produce a levelled 200 m grid. The line data for the digitized surveys were extracted by interpolation from the 200 m levelled grid. The levelling adjustments for the digitally acquired surveys were interpolated from the adjustment grid and applied directly to the line data, preserving the high frequency content of the data. The project was realized by Paterson, Grant & Watson Ltd. on behalf of the OGS and the GSC. Subsequently, an identical procedure was applied to the aeromagnetic survey data of the Atlantic provinces, Manitoba and Saskatchewan. The procedure was slightly modified for the processing of the surveys for the province of Quebec and the Northwest Territories. For these surveys, the levelling adjustment was systematically calculated from the adjustment grid. The adjustment was then applied to both digitized and digitally acquired line data.

The levelling of aeromagnetic survey data west of Manitoba was performed in-house. Surveys were levelled to the national datum by inspection of areas of overlap, or more often, lines of contact. By applying constant level adjustments to modern, calibrated surveys, the national datum was propagated to the west coast and north to the Beaufort Sea. Lower quality surveys of arbitrary level and often with an arbitrary long wavelength component removed, were levelled to the calibrated data by fitting low-order polynomials to the differences at their boundaries with adjacent, levelled surveys.

A series of surveys were flown at constant barometric altitude over the Rocky Mountains and in other mountainous terrains. These surveys bridge the gap in the aeromagnetic coverage between the drape-flown surveys on each side of the Rockies. Linking of the drape-flown levelled aeromagnetic grids to the constant altitude aeromagnetic survey grids was accomplished by computational draping of the constant altitude surveys to an idealized mean terrain clearance flight surface. The method used for draping is based on a Taylor series expansion of the magnetic field on the measurement surface (Pilkington and Roest, 1992). This method compares well to the drape-flown data (Pilkington et al., 1995), validating their use in the levelling of the Rocky Mountain surveys.

The levelling of the profile data west of Manitoba and south of N60° was completed in 1997.

Some of the vintage aeromagnetic data over the Yukon Territory were acquired during periods of high diurnal activity, a hazard of surveying in the auroral zone. To reduce the effects of these secular variations in the Earth's magnetic field, it was decided to decorrugate or micro-level the Yukon survey grids. Decorrugation involves a frequency domain directional cosine filter that reduces anomalies in the flight line direction. The decorrugated data were then levelled to the national datum.

Three types of magnetic data remained to be levelled to the national datum and to adjacent surveys in order to generate a maximum resolution 1 km grid for Canada; modern high quality data recently added to the Canadian Aeromagnetic data base, older data requiring remediation, and data available in gridded form only.

Modern, high quality data recently added to the Canadian Aeromagnetic Data Base yet to be levelled to the national datum included five surveys on or adjacent to Victoria Island, NWT, three surveys in the NWT along the Mackenzie river, one survey over southern Ontario, and one south of the boundary between British Columbia and the Yukon (Fig. 1). All these surveys were calibrated at the national calibration site at Bourget, Ontario. The level between such surveys is found to be similar and assumed to be accurate. Previously levelled data tends to be approximately 100 nT higher than the recent calibrated data. The recent surveys have had a constant level adjustment applied to match the previously levelled data. The recent surveys generally have one kilometre of data outside the required limits of the survey allowing a certain amount of overlap with previously levelled data in which to determine a bulk adjustment value. High frequency mismatches between surveys at their boundaries exist due to differing survey specifications and qualities. In order to produce seamless gridded data sets free of boundary discontinuities, a high frequency correction was made in a narrow band along the boundary.

The older, lower quality data requiring remediation included fourteen surveys over and adjacent to Axel Heiberg Island and eight marine surveys in the west coast offshore (Fig. 1).

The Axel Heiberg area surveys were mostly digitized from contour maps along flight lines at the intersections with contour lines. The five surveys over the island itself were industry surveys from the early 1960's. The surveys were flown at five different constant barometric heights and required draping and decorrugation to improve the quality of the data and the levelling between surveys.

Draping for the Axel Heiberg Island surveys was improved over previous draping efforts by limiting low pass filtering roll-off and cut-off wavelengths to values close to the Nyquist wavelengths. In the case of surveys with an 800 m line-spacing, a cut-off wavelength of 800 m and a roll-off of 1600 m were used. This low pass filtering removed only the highest frequencies in the data and minimized the effect of discontinuities and spikes on the frequency domain processing. Also, limiting the Taylor series expansion to two terms decreased processing time without any meaningful loss of accuracy. The topography used to determine the distance from the barometric survey altitude to the idealized flying surface was derived from a 1 km elevation grid based on GTOPO30, a global 30 arc-second elevation data model available from the EROS Data Center, United States Geological Survey.

The draping of the surveys has produced a much better match in the amplitude and wavelength of anomalies that cross survey boundaries (Fig. 2). Draping also increased the amplitude of line-to-line levelling errors in the data. Decorrugation was required to reduce these effects. In areas with high amplitude, short wavelength, linear anomalies perpendicular to the flight line direction (such as those anomalies due to iron formation and other high magnetic susceptibility layered units), the directional cosine filtering procedure can produce artifact linear features in the flight line direction. To minimize this effect, the logarithm of the gridded data, which lowers the relative amplitude of the anomalies, was decorrugated. The procedure is described in Appendix A.

The final decorrugated grid was subtracted from the original total field grid to generate corrections that were applied to the profile data. The surveys of Axel Heiberg Island now have a much better fit, with anomalies crossing survey boundaries having matching amplitudes and wavelengths (Fig. 2).

As the Axel Heiberg Island surveys were not in contact with previously levelled data, the bulk adjustments were made by comparison with the existing, national 2 km residual total magnetic field grid. The IGRF was subtracted from each survey for the year and altitude of that survey. These residual grids were then regridded to a 2km interval and subtracted from the national 2 km grid. Depending on the nature of the difference grid, either a bulk adjustment constant was determined or a first-order surface was fitted to the difference grid, and the result was added to the residual grid. As a result, the long wavelength of these surveys matches that of the 2 km grid. High frequency boundary adjustments were also applied to generate seamless, discontinuity-free boundaries. This procedure is described in Appendix B.

The offshore data around Axel Heiberg Island is of two vintages: modern GPS located surveys to the north and older Decca navigation surveys to the west. The three GPS-positioned surveys were flown over three years in the early 1990s and control lines were flown over the entire area in the last year of surveying, although the data had not been levelled to these lines. Tie-line levelling was performed using the Regional Geophysics Section Contract Surveys group tie-line levelling software. This levelling and later decorrugation greatly improved the quality of the data.

Decca navigation is a low-frequency hyperbolic navigation system that compares the phase difference of radio signals emitted by several radio stations. This generates a series of hyperbolic lanes used as survey flight paths (Fig. 3). This method of navigation was used in aeromagnetic surveying, before the advent of Global Position System, over water and ice where visual flight path recovery methods were not reliable. In the Arctic, aeromagnetic surveys should have closely spaced control lines to reduce high diurnal variation in the magnetic field through tie-line levelling. However, many of the offshore surveys were flown with extremely wide control line spacing and must be decorrugated to reduce the diurnal effects. As standard decorrugation methods require that the flight lines be parallel, the Decca navigation hyperbolic flight paths had to be transformed. Hyperbolic flight lines were straightened by finding the intersection of the flight lines and a line perpendicular to those lines. The coordinates were then rotated so that the perpendicular line was oriented east-west and the flights approximately north-south. The x-coordinates of all data values along a line were set to the x-coordinate of the intersection. The y-coordinate was calculated as the distance from the intersection to the position of the data value along the original flight path. By subtracting the rotated x and y positions from the new x and y positions and gridding the x and y difference values, transformation grids were obtained. This allowed the transformation of fill-in and other partial lines that did not cross the perpendicular line. Interpolating the transformation to the profile data and gridding the transformed x, transformed y, and magnetic intensity generated the desired grid of parallel flight line data. The grids were decorrugated in the manner previously described and the corrections were interpolated to the profile data at the transformed x and y locations.

No further processing was required to transform the data back to the original positions as the original positions were carried along through each stage of the processing. The line-to-line levelling problems have been greatly reduced by this procedure (Fig. 4). Also, most of the surveys were digitized by map sheet so that profile data were ordered by map sheet and were not necessarily all digitized in the same direction. This required reordering and renumbering of the data into continuous lines. Furthermore, some of the surveys used more than one set of hyperbolic lanes. This required that the surveys be divided into two separate areas in order to decorrugate them.

The results of the decorrugation, digitizing error editing, and subsequent levelling to the national datum and adjacent surveys for the Axel Heiberg Island and adjacent offshore area is shown in Fig. 5.

The recent surveys over Victoria Island include four flown for the GSC and two flown for private industry (Fig. 6). Data flown for the GSC is of high quality and was levelled to previously levelled data by bulk adjustment and high frequency boundary adjustments. One of the industry surveys, DB #269, was flown before the survey that surrounds it, DB #262. A mutually exclusive boundary was determined and the two surveys were levelled to each other, with overlapping profile data being set to null values.

Three recent surveys in the Mackenzie Corridor (Fig. 1) area and one in southern Ontario (Fig. 1), flown for the GSC, are of high quality and were levelled to previously levelled data by bulk adjustment and high frequency boundary adjustments were made by the previously described method.

West coast offshore data consists of ten shipborne surveys acquired between 1973 and 1985 (Fig. 7). These data had been previously adjusted to each other at the Pacific Geoscience Centre (GSC Pacific). Overlap of ship tracks between surveys created high frequency noise in grids of these data. To avoid this noise, the surveys were assigned mutually exclusive boundaries. The IGRF was removed for each survey and the data were merged together to produced a seamless grid. The ship track spacing varies from about 5000 m near shore to about 15 000 m at the western edge of the data set. Most of the surveys were acquired over oceanic crust. Oceanic crust is characterized by linear magnetic anomalies corresponding to alternating normal and reversely magnetized areas. As a result of the wide line spacing, the minimum curvature gridding algorithm tends to produce relaxed gradients in the grid away from data points. This produces segmented anomalies in the grid (Fig. 8a), appearing a series of circular anomalies rather than a continuous linear anomaly. Trend reinforcement of the data was applied by two methods. First, the data were reinforced using the method of Verhoef et al. (1996). This time and computing intensive method was optimized for areas with the minimum ship track spacing. To trend reinforce anomalies in areas of wider ship track spacing, a routine developed from the method of Keating (1997) was employed. Several enhancements were made to the computer program to ensure the optimum result, including the pre-screening of local minima and maxima to avoid loss of reinforcement due to crossover by unlikely trends. The trend reinforcement procedures produce a more realistic representation of the magnetic field (Fig. 8b).

Figure 8a. larger image [JPEG, 188.8 kb, 508 X 596, notice]

Figure 8b. larger image [JPEG, 195.7 kb, 496 X 589, notice]

The west coast offshore data set was assumed to have a reasonable long wavelength component. Comparison of the oceanic data with anomalies at the contact with continental crust is probably of little use due to the difference in the nature of oceanic and continental crust. High frequency boundary adjustments were made by the method described previously.

The magnetic coverage of Hudson Bay consists of four shipborne surveys and one airborne survey (Fig. 1). The shipborne surveys were adjusted to each other and were processed as a single unit. The level between the shipborne surveys and the airborne survey was reasonable. Overlap between the data sets caused high frequency artifacts when gridded. To avoid this problem the surveys were limited to mutually exclusive boundaries. A high frequency boundary adjustment was performed.

The newly-levelled profile data were reformatted to a binary file of latitude, longitude, and residual total magnetic field value. All previously levelled data in the Canadian Aeromagnetic Data Base were retrieved in a similar format. Due to limits imposed by computer memory and the minimum curvature gridding software, the data were divided into 10 overlapping sub-areas for gridding to a 1 km interval. The sub-areas were British Columbia, Alberta, Saskatchewan and Manitoba, Ontario, Quebec and the Maritimes, the Yukon, the Northwest Territories, southern Nunavut, northern Nunavut, and Hudson Bay. The projection used for gridding the data was the same as for a previous 2 km North American compilation (Committee for the Magnetic Anomaly Map of North America, 1987) – a mercator projection with a central meridian at W100° referred to NAD27. The grids were trimmed at their edges by 7 grid cells to remove an extrapolated apron around profile data points due to a 10 km grid blanking radius.

The wide blanking radius was required due to widely spaced digitized data in several of the sub-areas. The resulting grids were extracted to mutually exclusive boundaries and merged into a single grid. The result is a grid of all publically-available profile data held by the Canadian Aeromagnetic Data Base (Fig. 9).

The existing 2 km residual total magnetic field grid for Canada contains areas north of N60° for which no profile data exists (Fig. 10). These data were compiled for the original DNAG 2 km magnetic compilation (Dods et al., 1986). These data were digitized from contour maps for the DNAG and earlier compilations. In the Mackenzie corridor, 812.8 m grids of these data are available while elsewhere, mostly the Arctic islands and channels, only a 2 km grid is available.

The 812.8m grids of the Mackenzie corridor were regridded to 1000 m and subtracted from the 1000 m grid of all levelled profile data. Overlap between the two grids was limited to one grid cell. Due to very steep gradients along the northeastern boundary of DB# 287, Fort Good Hope, the maximum difference in this area was limited to avoid an over-correction. The second order surface was inspected and added to the grid-only data. High frequency boundary adjustments were made by the previously described method.

The 2 km grid of the Arctic islands and channels was regridded to 1000 m and subtracted from the 1000m grid of all levelled profile data.

The overall difference was small, with most of the contact between the data sets in the north where the profile data had been levelled to the 2km grid and where the magnetic field was low and smoothly varying. High frequency boundary adjustments were made by the previously described method. A similar void in the profile data based 1000 m grid was found in the Gulf of St. Lawrence and was processed in a similar manner. Figure 11 shows the merged grid-only and profile data 1 km grid coverage.

The long wavelength of the 1 km grid was suspect due to the piece-meal method of compilation. Pilkington and Roest (1996) showed that a series of aeromagnetic surveys flown by the Earth

Physics Branch (EPB) between 1969 and 1976 at an average altitude of 4.5 km and at line spacings between 35 km and 70 km could be used to generate a realistic grid of the long wavelength component of the magnetic field and suggested that this wavelength component could replace a similar waveband in a higher resolution compilation to provide a more accurate representation of the magnetic field over Canada.

The EPB data coverage is shown in Figure 12. To generate a grid, these data were averaged over a 20 km interval in order to reduce aliasing.

The data were then gridded to a 20 km interval. The Canadian 1 km grid was also averaged over 20 km and regridded to a 20 km interval. Both data sets were low pass filtered in the frequency domain using a Butterworth filter with cut off at 400 km (Fig. 13). The EPB data were also downward continued by 3700 m to match the average altitude of the 1 km grid data. The latter was subtracted from the former and the difference grid inspected. Lack of EPB data over Lakes Superior and Huron led to unrealistic differences with the 1 km grid. Similar edge effects were seen along a large north-south gap in the coverage at approximately W100° from N48° to N68°. These anomalous areas were

removed and the difference grid was regridded across the gaps in two stages; first to a 5 km interval, then to a 1 km interval. This 1 km difference grid contained the correction to the long wavelength of the 1 km grid of levelled profile data. Adding the two grids together produced a 1 km residual total magnetic field map of Canada with a non-arbitrary long wavelength (Fig. 14).

East coast offshore shipborne data collected by the Atlantic Geoscience Centre (GSC Atlantic) were compiled and adjusted by Verhoef et al. (1996). The data were gridded to a 5 km interval and low pass filtered at 400 km to provide a better fit between sub-areas.

As the majority of these data are in the offshore over oceanic crust, it was decided to merge the filtered data set with the 1000 m grid of levelled profile data. The 5 km compilation was regridded to 1000 m and subtracted from the levelled profile data grid. High frequency boundary adjustments were made by the previously described method, however a 20 km null zone was employed to ensure a smooth fit between the two data sets (Fig. 15).

Two airborne magnetic surveys were added after the original 1 km compilation was completed. GSC Survey #291, Atlin, is located south of the British Columbia-Yukon border between W132° and W134° (Fig. 1). The IGRF was removed from the data and a 1 km grid was produced. Using a 2 km overlap, an average difference with adjacent levelled surveys was found to be -65 nT. The levelling of all previous modern high resolution surveys to the non-long wavelength corrected national datum required some amount (averaging about 100 nT) be added to, not subtracted from, the modern survey. A high frequency boundary adjustment was also applied. Another survey, GSC Survey #210, Lincoln Sea (Fig. 1), had been available and had been decorrugated, but was not in contact with any other previously levelled survey. Furthermore, the survey would replace an area covered by the east coast compilation of Verhoef et al. (1996) and would have to match the long wavelength of that data set. The Lincoln Sea survey was therefore levelled after all other data had been compiled and levelled. The Lincoln Sea data were gridded to 1 km and subtracted from the national 1 km compilation. The levels of the two data sets were very similar. A 1^st order surface was fitted to the difference and added to the Lincoln Sea data. A high frequency boundary adjustment was made and both the Atlin and Lincoln Sea survey grids were merged into the national compilation.

The final 1 km interval residual total magnetic field grid is presented in Figure 15. The grid, generated from levelled profile data, has a true 1 km resolution. Draping of surveys flown at constant barometric altitude to an idealized mean terrain clearance surface allowed the inclusion of these surveys in the grid. The levelling process applied to the data has made survey boundaries seamless. Correcting the long wavelength of the data to the long wavelength defined by the high-altitude EPB surveys addresses concerns about long wavelength errors due to the piecemeal nature of the survey-to-survey levelling. The result of this work is to produce an internally consistent, realistic representation of the residual total magnetic field over Canada.

Appendix A - Decorrugation Procedures

Decorrugation was required to reduce these effects. In areas with high amplitude, short wavelength, linear anomalies perpendicular to the flight line direction (such as those anomalies due to iron formation and other high magnetic susceptibility layered units), the directional cosine filtering procedure can produce artifact linear features in the flight line direction. To minimize this effect, the logarithm of the gridded data, which lowers the relative amplitude of the anomalies, was decorrugated. The procedure consisted of the following steps:

1. Add a constant to the grid values to make the minimum value equal zero.
2. Take the logarithm of the grid values.
3. High pass filter the data at four times the line spacing.
4. Smoothly limit the maximum and minimum values of the grid. Values greater than the maximum or less than the minimum are set to 1 + 2.303 * log of the grid value.
5. Apply a directional cosine filter in the direction of the flight lines, passing the result. Generates a grid of anomalies in the flight line direction.
6. Apply a directional cosine filter to the grid resulting from step 5 in the direction of the flight lines, rejecting the result. Generates a grid of anomalies NOT in the flight line direction.
7. Subtract the second directional cosine filtered grid from the first (step 5 - step 6). Minimizes the geologically significant signal removed in the decorrugation process.
8. Subtract the result from step 7 from the log grid (step 2) to generate a decorrugated grid.
9. Take the anti-logarithm of the decorrugated grid.
10. Subtract the constant added in step 1.

The final decorrugated grid was subtracted from the original total field grid to generate corrections that were applied to the profile data.

Appendix B - High Frequency Boundary Adjustments

High frequency boundary adjustments were also applied to generate seamless, discontinuity-free boundaries. This procedure involved the following steps.

1. Grid survey data with at least 25 grid cells of real or extrapolated values outside the survey boundaries.
2. Grid surrounding data and extract to mutually exclusive boundary with survey to be levelled.
3. Subtract the unlevelled data grid from the levelled data grid. Generates a difference grid with accurate differences at the border and spurious, but relatively reasonable, differences elsewhere.
4. Generate a grid of zero values whose boundaries are the survey boundaries trimmed back by 15 to 25 grid cells (3 km to 5 km on a 200m grid which would be equivalent to 3 to 6 flight line spacings).
5. Generate a correction grid using the difference and zero grids as input. A minimum curvature gridding method was used. Minimize the wavelength of corrections from the difference grid by:
   1. using a search radius equal to the grid interval.
   2. using very small grid tolerance adjustment (0.1 nT).
   3. using a high number of iterations (40).

The wide zone of overlap, although spurious, will have a more reasonable level than that generated by the minimum curvature algorithm. This will better constrain the values interpolated in the null zone between the difference and zero grids. If the spurious data contain high amplitude anomalies, it may be necessary to limit these features to avoid generating unrealistic corrections in the null zone.

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