This grid of the isostatic residual gravity anomalies shows variations in the gravity field caused by lateral variations in the density of the Earth's crust and upper mantle that reflect variations in composition and thickness. Systematic gravity mapping began in Canada in 1944 and is ongoing. All data are tied to the International Gravity Standardization Network 1971. Local gravity anomalies result from the juxtaposition of relatively high- and low-density rock types. Shorter wavelength anomalies, representing nearer surface density contrasts, are enhanced by removing the calculated effects of the isostatic roots that support topographic loads.

This grid represents isostatic residual Bouguer gravity anomalies. The data were compiled from the holdings of the Canadian Geodetic Information System maintained by the Geodetic Survey Division, Geomatics Canada. The data were collected to map the variation in gravitational attraction over the Canadian landmass and offshore areas. Variations in the force of gravity are due to variations in the mass of underlying materials. These data are useful for geological interpretation and have applications in oil, gas, and mineral exploration. The gravity field is also used to define the geoid, which is the ideal shape of the Earth, or mean sea level if the Earth were completely covered with water.

The data used to compile this grid consist of approximately 660 000 gravity observations, including 165 000 on land, acquired between 1944 and 2001. The data spacing ranges from less than 1 km to over 20 km, with an average spacing between 5 and 10 km. All measurements were reduced to the IGSN71 datum. Theoretical gravity values were calculated from the Geodetic Reference System 1980 (GRS80) gravity formula. Bouguer anomalies were calculated using a vertical gravity gradient of 0.3086 mGal·m^-1 and a crustal density of 2 670 kg·m^-3. All areas are represented by isostatic residual Bouguer anomalies.

The principle of isostasy states that mass excesses, represented by topographic loads at the surface, are compensated by mass deficiencies at depth which are referred to as isostatic roots. The effect of these mass deficiencies are not accounted for in the Bouguer reduction and there exists an inverse correlation between broad Bouguer anomaly lows and positive topography. The isostatic correction removes the gravity effect of the isostatic roots. The depth of the roots were estimated based on the Airy-Heiskanen model (Simpson et al., 1986). The depth of the root is defined for land areas by the formula

d = d_s + e (ρ_t/ δρ)

Figure 1 & 2 larger image [GIF, 39.9 kb, 597 X 821, notice]

where d = depth to the bottom of the root (m)
d_s = the depth of compensation for sea level compensations (30 000m)
e = elevation (m)
ρ_t = density of the topographic load (2670 kg·m^-3), and
δρ = density contrast between the root and underlying mantle material (600 kg·m^-3, see Figure 1). For oceanic areas, a negative topographic load exists, since lower density water replaces higher density rock. The depth of the root over oceanic areas is defined by the formula:

d = d_s - d_w ((ρ_t - ρ_w)/ δρ)

where d_w = depth of water and ρ_w = the density of water (1030 kg·m^-3).

Calculation of a grid of root depths was carried out using gridded topographic data with a 10 km interval. The gravitational effect of the compensating mass at a given point has been calculated by others (Simpson et. al., 1986, Goodacre et al., 1987) by combining the effect of roots on a flat earth within a 166.7 km radius and the effect of roots beyond this radius as derived by Heiskanen (1953). As Heiskanen's outer zone calculations account for the curvature of the Earth and since better topographic models are now available, Heiskanen's formula was applied to all areas to determine the gravitational effect of the roots. Heiskanen defines the gravitational effect of a root at a point, O, by the formula

g_c = G m ((a²/2R) + d cos α) / ( a² + d² - 2 ad sin α/2) ^3/2

where g_c = the gravitational effect (mGal), m = mass deficiency of the root (kg), R = radius (m) of the Earth, a = distance (m) between the observation point and the point at sea level above the root , d = the distance (m) between the centre of mass of the root and the point at sea level above the root and α = the angle between lines extending from the observation point and the point at sea level above the root through the centre of the Earth (see Figure 2).

For the calculation of g_c, the grid of root depths was converted to latitude, longitude and depth to root bottom with approximately 10 km spacing. These were considered as spherical coordinates and converted to X, Y, and Z coordinates in metres with the centre of the sphere at the origin. The volume of the root under each point was calculated by multiplying the square of the data spacing (10 km) by the depth of the root beneath the depth of compensation at sea level (30 km). The mass deficiency under each point was calculated by multiplying the volume by the density contrast between the root and the underlying mantle. The gravitational effect of each point's root was calculated at all data points. The isostatic correction at each point is the sum of these gravitational effects. The isostatic corrections are calculated for sea level observations and so were upward continued to the topographic surface on land and left at sea level for the offshore. The isostatic residual anomalies were calculated by adding the isostatic correction to Bouguer gravity anomalies.

Topographic data used in calculating the isostatic roots were a combination of GDCTOPO1 (a 1 km grid of Canadian land elevations ), ETOPO5, and Kalaallit Nunaat (Greenland) bedrock topography, surface topography and ice thickness data (Bamber et al., 2000). The Kalaallit Nunaat data were used to calculate equivalent rock topography for the Kalaallit Nunaat ice sheet. Equivalent rock topographies were also calculated for the water load in the Great Lakes, Great Bear Lake and Great Slave Lake.

The gravity data were gridded to a 2 km interval, with a blanking radius of 20 km. The isostatic residual map emphasizes the short wavelength components in the gravity field representing nearer surface sources by removing long wavelength features caused by predictable mass deficiencies at depth.

Bamber, J.L., Layberry, R.L., Gogenini, S.P. 2001: A new ice thickness and bedrock dataset for the Greenland ice sheet: part I. Journal of Geophysical Research.

ETOPO5: 1988. Data Announcement 88-MGG-02, Digital relief of the Surface of the Earth. NOAA, National Geophysical Data Center, Boulder, Colorado.

Goodacre, A.K. 1972: Generalized structure of the deep crust and upper mantle in Canada; Journal of Geophysical Research, v. 77, p. 3146-3161.

Heiskanen, W. 1953. Isostatic reductions of the gravity anomalies by the aid of high-speed computing machines. Annales Academiae Scientiarum Fennicae, Series A, III. Geologica - Geographica, number 33.

Innes, M.J.S., Goodacre, A.K., Argun-Weston, A., and Weber, J.R. 1968. Gravity and isostasy in the Hudson Bay Region; in Science, History and Hudson Bay, v.2, ed. C.S. Beals and D.A. Shenstone, p. 703-728.

Miles, W.F.,Roest, W.R. and Vo, M.P.. 2000: Gravity Anomaly Map, Canada; Geological Survey of Canada, Open File 3830a.

Shih, K.G., Macnab,R., McConnell, R.K., Hearty, D.B., Halpenny, J.F., and Woodside, J. 1991: Regional geology and geophysics 2: gravity anomaly; in East Coast Basin Atlas Series: Scotian Shelf; Atlantic Geoscience Centre, Geological Survey of Canada, p.11.

Simpson, R.W., Jachens, R.C. ,Blakely,R.J., and Saltus, R.W. 1986. A New Isostatic Residual Gravity Map of the Conterminous United States With a Discussion on the Significance of Isostatic Residual Anomalies. Journal of Geophysical Research. V. 91, No 138, p. 8348-8372.

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