Terrain Correction

Use the Gravity > Terrain Corrections >Terrain Correction menu option (geogxnet.dll(Geosoft.GX.Gravity.TerrainCorrection;Run)*) to calculate the gravity terrain effect. The terrain correction will be calculated for every station in the database, considering a correction area of 2 x correction distance by 2 x correction distance centered on the station, and saved in the output terrain correction channel.

Terrain Correction dialog options

Elevation channel	This is the survey instrument elevation relative to the reference datum. The axis is positive above the reference datum. The reference datum is generally, but not necessarily, set to the sea level. Script Parameter: GRTERAIN.ELEVCH
Topography (top of rock) grid	Specify the most detailed grid defining the boundary of the solid rock with air or water. If the survey area spans multiple bodies of water, this grid defines the contact of the solid material with air over bodies of water and the contact of the solid material with air everywhere else. The topography grid must extend beyond the survey area by at least the specified correction distance value. The extent of the topography grid depends on the topographic relief of the area. If there are significant masses or deficiencies of masses in the survey area, they will strongly contribute to the terrain effect, and the grid coverage should be extended further. For relatively flat areas, approximately a 25 Km extension beyond the survey area may suffice. In the case of pronounced topography, the grid should be extended further, not exceeding 167 Km beyond the survey area, where the curvature of the Earth has a stronger contribution than the topographic variability. Essentially, surface masses beyond this distance should produce negligible gravitational effects at the survey stations. If the topography grid does not extend at least as far as the correction distance beyond the survey area, the terrain is assumed to reflect on the opposite grid edges of the topography grid out to the correction distance (see the Application Notes section below). Script Parameter: GRTERAIN.DEMGRD
Correction distance	Specify the correction distance. This is the distance beyond the survey area to be used for calculating the terrain effect, and it depends on the degree of topographic relief (see the Application Notes section below). Script Parameter: GRTERAIN.DIST
Earth density	Specify the density of the earth in g/cm³ (the default is 2.67 g/cm³). Script Parameter: GRTERAIN.DENST
Water reference datum	If there are bodies of water in the survey area, you can specify the water level either as a constant or as a grid. Specify a constant when the survey area contains a single body of water or when all bodies of water are at the same elevation. However, for areas with high topographic relief and lakes at different elevations, provide a grid that defines the contact of the (water or solid) material with air (see the Application Notes section below). Script Parameter: GRTERAIN.WATEROPT
Water reference elevation or DEM (contact with air) grid	This is a contextual entry: Constant option: If you have selected the constant option as the Water reference datum, you will be prompted to specify a single Water reference elevation value on the elevation axis and in elevation units. Regardless of whether the survey area contains any bodies of water, the default is sea level (0.0). Script Parameter: GRTERAIN.WATERELEV Grid option: If you have selected the grid option as the Water reference datum, you will be prompted to enter a grid defining the contact between the material and air. This grid must coincide with the topography grid. The grid nodes located on solid material will have the same value in both the DEM (contact with air) grid and the Topography (top of rock) grid. Over water, however, this grid will consist of the elevation of the surface of the water (see Figure 1). Script Parameter: GRTERAIN.TOPOFROCK
Bathymetry channel	If surveying over water, select the bathymetry channel. This is the depth of the water column (positive down). If left blank and the channel “Water” is present in the database and contains values greater than zero, it will be used for calculating the terrain effect. Script Parameter: GRTERAIN.BATHYMETRY
Water density	Specify the water density in units of g/cm³ (the default is 1.00 g/cm³). Script Parameter: GRTERAIN.WATERDENS
Output terrain correction channel	Select the channel for the terrain correction effect. Script Parameter: GRTERAIN.TCORCH
Optimize process	Check this option to optimize the calculations. For large DEM grids, the terrain calculation can be quite time-consuming. The optimization option accelerates the calculation by desampling the outer zones to a coarser averaged grid and using 4x4 points spline interpolation to determine the elevation from the grid. In a test grid dimension of 2500x2500 cells, optimization improves performance 10 times at the cost of 3% accuracy compared to not optimizing the calculations. Script Parameter: GRTERAIN.OPT

Application Notes

Gravity terrain correction is a computationally intensive process. Initially, when the Oasis montaj gravity workflow was created, the concept of detailed local terrain contribution versus averaged regional contribution was introduced. The latter was computed once to speed up calculations. This workflow was a compromise between faster computation and the precision related to the contribution of the far field. In the original workflow, users had to ensure that the local and regional grid nodes aligned properly. With increasing computation speeds, the old dual-step model became unnecessary. A regional correction grid calculation was no longer needed as it no longer offered an advantage. As of version 2025.1, the terrain effect at each gravity station should be calculated using a single distance equivalent to the far distance.

Terrain correction accounts for the effects of topography variability. The gravitational attraction of a landmass above the observation station pulls away from Earth, decreasing the gravitational effect of the slab (Figure 1 - a) Solid rock). Similarly, a mass deficiency in the vicinity of the station results in a negative effect due to the lack of material and, consequently, the lack of attraction (Figure 1 - b) Air).

Figure 1: Schematic illustration of Bouguer slab, terrain, and variable water elevations

The magnitude of the terrain effect at each gravity station depends on the variability of the topography, with nearby topography exerting a stronger influence due to the inverse (distance) square law of gravity. Detailed information about nearby topography is necessary as it has a stronger impact on gravity measurements. Distant features, which have a smaller gravitational effect, can be represented more generally with larger cell sizes. The Terrain Correction tool will decimate the grid as it moves outwards from each gravity station for which it calculates the terrain effect.

If you have a detailed local DEM but only a coarse regional DEM, to account for an adequate correction distance, first invoke Boolean Operations and merge the two grids. Select the grid with the smaller cell size as “Grid 1”, select the “Or” logic, opt for the maximum grid size, and use the grid values of Grid 1 in the overlapping area. This will resample the regional grid to the smaller grid increment. The Terrain Correction tool will take care of decimating this finer DEM grid as necessary.

The graph below illustrates the gradual change in the magnitude of the terrain correction as a function of the correction distance for a given gravity survey in ragged topography (in red). The topography was then scaled to produce the other two profiles. The graphs asymptote (thin grey lines) at some distance away from the gravity station. Selecting a correction distance at 95% of the asymptote is reasonable. Asymptotes are indicated with thin grey lines, while the 95% mark is indicated with a dashed line, and the intersections are shown with grey bars.

Figure 2: Profiles of terrain correction versus correction distance for three DEM grids of varying reliefs.

The DEM grid used to produce the terrain effect of the red profile has a maximum vertical topographic range of 300 m with a standard deviation of 67 m. The graph asymptotes around 0.049 mGals. 95% of this amplitude is reached at a distance of 44 km, an adequate distance for this DEM.

The DEM grid used to produce the terrain effect of the blue profile has a maximum vertical topographic range of 660 m with a standard deviation of 135 m (about double the grid above). The graph asymptotes around 0.196 mGals. 95% of this amplitude is reached at a distance of 55 km, an adequate distance for this DEM.

The DEM grid used to produce the terrain effect of the green profile has a maximum vertical topographic range of 165 m with a standard deviation of 32.5 m (half of the first DEM grid). The graph asymptotes around 0.012 mGals. 95% of this amplitude is reached at a distance of 25 km, an adequate distance for this DEM.

Conclusion: There is no one-to-one relationship between the vertical relief of the DEM grid and the correction distance. Set the distance to the maximum distance of the available DEM. It is not necessary to go beyond 100 km for very rugged areas, while for relatively flat areas, much shorter distances would produce reasonable results.

At the edge of a cliff or gorge, the terrain correction is inevitably in error; therefore, it is recommended not to measure gravity at the edge of sharp relief.

In general, for relatively flat regions where the variability of the terrain is in the tens of meters, terrain corrections range from 0.1 to 1 mGal. In hilly regions with variability in the hundreds of meters, the terrain effect is in the order of 1 to 10 mGals, and in mountainous regions, the terrain effect is on the order of several tens of mGals. Bathymetric correction is similar to terrain correction; gravity corrections are determined by a combination of the thickness of the water column and the solid material.

Topography Grid

The topography grid is centered on the gravity survey area and should extend at least by the correction distance beyond the edges of the survey perimeter. Dummy terrain values are interpolated using a weighted average of the surrounding points. If the grid does not extend sufficiently beyond the survey area, and the specified correction distance is greater than the distance between the topography grid outline and the survey perimeter, then the grid is extended to meet this margin. The extension is simply the other edge of the topography grid reflected on the opposite side. This approach, however, is a fallback only and could introduce errors in the terrain effect calculation if the nature of the topography changes significantly or if the survey terrain has a regional slope. The correction distance should be chosen carefully to avoid introducing errors to stations located near the edge of the defined topography grid.

Figure 3: Reflection of terrain elevation on opposite sides

Digital gridded terrain models are often available from government sources and can be used to simplify the application of regional terrain corrections.

These grids should not be gridded to a cell size much smaller than the original sampling accuracy of the DEM data. If the topography grid is produced by gridding the elevation of the gravity survey, the grid cell size should be about one-half of the nominal gravity station spacing

Terrain Correction Methods

Terrain corrections are calculated using a combination of the methods described by Nagy (1966) and Kane (1962). The terrain effect is derived based on the annular ring segment approximation to square prisms.

To calculate the correction at each gravity station, the topography grid is resampled, centered on that gravity station, and extended to the correction distance (see Figure 3). The correction is calculated based on a series of square zones, the effects of which are added to produce the terrain correction:

• Near zone: Zone 0 covering a 1-cell radius ring centered on the station.
• Intermediate zones: Zone 1 covering a 2 to 8-cell flat-topped square prism in a square ring. Zone 2 at a distance of 9-16 cells and at double the cell size.
• Far zones: Zone 3 and beyond, covering concentric flat-top square rings beyond 16 cells. The number of far zones depends on the correction distance.

Each zone aligns with the next. For more processing efficiency, the far zones are progressively desampled by a factor of 2 and set to the average of the grid values they cover. In Zone 2 every 4 initial adjacent DEM cells are averaged; in Zone 3, every 16 initial cells, and so on.

Figure 4: Resampling of DEM for each gravity station by zones

Equations:

For shipborne and airborne surveys, corrections are calculated as follows: 

• Using the flat-topped square prism approach of [Nagy ,1966]³ for the near and intermediate zones.

• Using the rod formula [Telford et al.,1976]⁴ for the far zone.

Script Mode

The following parameters are only available when running the current GX from a script:

Terrain correction grid: The terrain correction grid contains the correction component beyond the survey areas extended by the correction distance. The magnitude of the correction in the terrain correction grid is normalized and scaled to the provided Earth density, and added to the calculated correction of the more highly sampled topography grid. Script Parameter: GRTERAIN.CORGRD

Local slope channel: The local slope of the grid is calculated on the fly; however, if local slopes have been measured at each station, you can specify the slope channel. (The slope is only applicable to Zone 0; see the Application Notes section.) Script Parameter: GRTERAIN.SLOPCH

References