Derivation of Free-Air and Bouguer Gravity Anomaly Maps

Gravity anomalies are differences between the observed acceleration of the earth’s (or any planet's) reaction to gravity and a value predicted from a model. A location with a positive anomaly exhibits more gravity than predicted, while a negative anomaly exhibits a lower value than predicted. The anomaly is the body or effect that causes the deviation from the "ideal" gravity model. Many data corrections must be made to the measured gravity value in order to extract the response of the local anomaly, or local geology, which is invariably the purpose of the survey.

Lateral variations in gravity anomalies are related to anomalous density distributions within the Earth. Gravity measurements help us to understand the internal structure of the planet. Calculations show that the gravity anomaly signature of a thickened crust (for example, in orogenic belts) is negative and larger in absolute value, relative to a case where thickening affects the entire lithosphere.

In geodesy and geophysics, the usual theoretical model is the gravity on the surface of a reference ellipsoid such as WGS84.To understand the nature of the gravity anomaly due to the subsurface, a number of corrections must be made to the measured gravity value: The theoretical gravity (smoothed normal gravity) should be removed in order to leave only local effects.

The elevation of the point where each gravity measurement was taken must be reduced to a reference datum to compare the whole profile. This is called the Free-air Correction, and when combined with the removal of theoretical gravity leaves the free-air anomaly.

Correction for the differing elevations of gravity stations is made in three parts. The free-air correction (FAC) corrects for the decrease in gravity with height in free air resulting from increased distance from the centre of the Earth. To reduce to datum an observation taken at height h. The FAC is positive for an observation point above datum to correct for the decrease in gravity with elevation.

The free-air correction accounts solely for variation in the distance of the observation point from the centre of the Earth; no account is taken of the gravitational effect of the rock present between the observation point and datum. Thus, apart from the free air correction, we need to correct for the effects of any material between the gravity station and the geoid. To do this we model the material in between as being made up of an infinite number of slabs of thickness t. These slabs have no lateral variation in density, but each slab may have a different density than the one above or below it. This is called the Bouguer correction.

The Bouguer correction (BC) removes this effect by approximating the rock layer beneath the observation point to an infinite horizontal slab with a thickness equal to the elevation of the observation above datum. If ρ is the density of the rock, then:

BC = 2πGρh = 0.4191 ρh gu          (h in metres ρ in Mg m-3)

 Fig 1: (a) The free-air correction for an observation at a height h above datum. (b) The Bouguer correction. The shaded region corresponds to a slab of rock of thickness h extending to infinity in both horizontal directions. (c) The terrain correction.

On land the Bouguer correction must be subtracted, as the gravitational attraction of the rock between observation point and datum must be removed from the observed gravity value. The Bouguer correction of sea surface observations is positive to account for the lack of rock between surface and sea bed. The correction is equivalent to the replacement of the water layer by material of a specified rock density ρw. In this case:

BC = 2πG (ρ1 - ρw) z

where z is the water depth and ρw the density of water.

The free-air and Bouguer corrections are often applied together as the combined elevation correction.

The Bouguer correction makes the assumption that the topography around the gravity station is flat. This is rarely the case and a further correction, the terrain correction (TC), must be made to account for topographic relief in the vicinity of the gravity station. This correction is always positive as may be appreciated from the figure above. The regions designated A form part of the Bouguer correction slab although they do not consist of rock. Consequently, the Bouguer correction has overcorrected for these areas and their effect must be restored by a positive terrain correction. Region B consists of rock material that has been excluded from the Bouguer correction. It exerts an upward attraction at the observation point causing gravity to decrease. Its attraction must thus be corrected by a positive terrain correction.

Terrain effects are low in areas of subdued topography, rarely exceeding 10 gu in flat-lying areas. In areas of rugged topography terrain effects are considerably greater, being at a maximum in steep-sided valleys, at the base or top of cliffs and at the summits of mountains.

Where terrain effects are considerably less than the desired accuracy of a survey, the terrain correction may be ignored. Sprenke (1989) provides a means of assessing the distance to which terrain corrections are necessary. However, the usual necessity for this correction accounts for the bulk of time spent on gravity reduction and is thus a major contributor to the cost of a gravity survey.

Free-Air and Bouguer Gravity Anomaly Maps:

The Bouguer anomaly forms the basis for the interpretation of gravity data on land. In marine surveys Bouguer anomalies are conventionally computed for inshore and shallow water areas as the Bouguer correction removes the local gravitational effects associated with local changes in water depth. Moreover, the computation of the Bouguer anomaly in such areas allows direct comparison of gravity anomalies offshore and onshore and permits the combination of land and marine data into gravity contour maps. These may be used, for example, in tracing geological features across coastlines. The Bouguer anomaly is not appropriate for deeper water surveys, however, as in such areas the application of a Bouguer correction is an artificial device that leads to very large positive Bouguer anomaly values without significantly enhancing local gravity features of geological origin. Consequently, the free-air anomaly is frequently used for interpretation in such areas. Moreover, the FAA provides a broad assessment of the degree of isostatic compensation of an area.

Gravity anomalies are conventionally displayed on profiles or as contoured (isogal) maps. Interpretation of the latter may be facilitated by utilizing digital image processing techniques similar to those used in the display of remotely sensed data. In particular, colour and shaded relief images may reveal structural features that may not be readily discernible on unprocessed maps.

The Bouguer anomalies are usually negative in mountains because of isostasy: the rock density of their roots is lower, compared with the surrounding earth's mantle. Typical anomalies in the Central Alps are −150 milligals (−1.5 mm/s²). Rather local anomalies are used in applied geophysics: if they are positive, this may indicate metallic ores. At scales between entire mountain ranges and ore bodies, Bouguer anomalies may indicate rock types. Salt domes are typically expressed in gravity maps as lows, because salt has a low density compared to the rocks the dome intrudes. Anomalies can help to distinguish sedimentary basins whose fill differs in density from that of the surrounding region.

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