2.2 Gravity surveys. Gravity survey

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1 2.2 Gravity surveys Gravity survey The effect of latitude The effect of elevation The Bouguer effect Topographic effect The effect of tides Summary of corrections Gravity in boreholes Gravity survey In all gravity surveys the vertical component of g, g z, is measured. The instrument used to measure g z is called a gravimeter. Standard gravimeters have a precision of approximately 0.01 x 10-3 cm s -2. Gravimeter precision is thus 0.01 mgal or roughly 1 part in 10 8 in the measurement of g z. A gravity survey will show variation in g z caused by the following: a) changes in latitude b) changes in elevation c) local topography f) earth tides g) variation in subsurface density -1-

2 A profile of observations of g z may be dominated by a) and b) making it difficult to see a desired anomaly from a subsurface feature (the anomaly might be smaller than the line width of the curve plotting g z vs. distance along profile.) Since position and elevation can be known accurately it is customary to correct for or remove the first order variations due to elevation and latitude. The effect of latitude Equation 2.1 may be used to derive a formula for the change in g z as one moves from north to south along a line of latitude. For a change in distance ds the approximate expression is: dg/ds 1 x dg/d sin 2 mgal/mile or sin 2 mgal/km At a latitude of 45, dg/ds.817 mgal/km If the measurement accuracy of 0.01 mgal is to be useful the N-S position must be known to about 12 m. The effect of elevation In changing elevation, g z changes because of the change in distance from the center of mass of the earth. From Newton's Law we have that -2-

3 so dg dr 2GM 3 R GM gz 2 R 2g = mgal/m or mgal/ft at the equator R This is called the free air effect or free air correction. If the measurement accuracy is 0.01 mgal then we must know our elevation to 3.2 cm or 1.25 in. It is evident that accurate surveying of gravity stations, especially elevation, is important. The Bouguer effect Surveys are usually conducted on the land surface. As one changes elevation there are changes in g caused by the added (or subtracted) layer of material that has been included. Thus in moving up from a valley to a plateau the gravity decreases due to the increasing distance from the center of mass but is also increased by the attraction of the slab of rock whose thickness is the change in elevation. The effect is large. The gravitational attraction of an infinite slab of thickness z and density is: g z = 2 G z = z, when is in g cm -3 and z is in meters If we assume a typical density of 2.67 g cm -3, this becomes: g z = mgal/m or mgal/ft -3-

4 The effect of this intervening slab is called the Bouguer effect or Bouguer correction. It is the opposite sign to the free air correction. This effect may be difficult to calculate because one does not know the density. Further if the elevation change is confined to a small region, like going up a hill, then the infinite slab is an inappropriate description of the intervening mass. Under this circumstance the actual topography must be considered and another effect, the topographic effect, is included. This is discussed below. Conventional practice is to apply the Bouguer correction and then the topographic correction. For gradual topography where the Bouguer correction is appropriate an incorrect choice of density will yield a corrected set of gravity data whose surface (or profile line) mimics (if the density chosen was too low) or mirrors (if the density was too high) the topography. A method for estimating the density (after Nettleton, 1976) is then to vary the density in repeat calculations until a corrected profile is obtained which is uncorrelated with the topography. A tricky procedure because it requires a further assumption that the density of the topographic feature is uniform. The major effects, latitude variation, the free air effect and the Bouguer effect are shown schematically in Figure for a topographic section in which a cave is the target of a gravity survey. We will find below that the cave anomaly is about 0.4 mgals. The Bouguer effect is about 50 mgals overall along the profile, the free air effect changes by more than 100 mgals and the latitude effect is almost 10 mgals over the 10 km profile. The task is to plot the data in a way that shows a 0.4 mgal -4-

5 anomaly (with a resolution of 0.01 mgal) on a profile which varies up to 100 mgal. The dynamic range of such a plot is too large for visual or graphic presentation. Since the latitude and free air effects, and to a good approximation the Bouguer effect, are accurately predictable it is common practice to correct the data to a reference level. This essentially removes the large first order variations along the profile and permits the ready identification of the anomaly due to the buried density inhomogeneity or mass deficit in the case of the cave. If topographic effects are appreciable, they must be addressed as discussed next. Topographic effect In regions with considerable topographic relief the infinite Bouguer slab is not a good model for the intervening mass between the reference elevation and the point of observation. The actual gravitational effects must be calculated numerically for the masses above and below the slab surface. M 1 Observation point Ref. level Bouguer slab M 2 M 1 is a mass excess adjacent to the observation point which reduces the value of g z. -5-

6 M 2 is a mass deficit adjacent to the observation point which also reduces the value of g z. If it is reasonable to assume values for then the effects of the topography can be removed. The topographic corrections are difficult to do in very rugged terrain because the nearest features have the biggest effect but they are often the most poorly mapped. Choosing the density is also a problem but an iterative process such as that described for the Bouguer correction is used until the corrected data shows no correlation with the topography. The effect of tides The Earth, like the oceans, is distorted by the gravitational attraction of the sun and moon and the resulting bulges in the surface have diurnal periodicity which is predictable to first order at any point on the Earth. The tidal variations can be on the order of mgal and so to use the full sensitivity of the gravimeter these variations must be removed. In some small scale surveys it may be reasonable to assume that the tidal variations are linear with time during the intervals between the times that a base or reference station is reoccupied. In this case the tidal variations are included and treated in the same manner as the slow drift in gravimeter readings caused by inherent strain in the sensing element. -6-

7 Summary of corrections The corrections are applied with respect to a reference station which defines a reference level and a reference latitude. Following the sign convention for the corrections the observed gravity values at points of measured elevation and latitude, expressed as differences from the reference station, have the following corrections applied step by step: 1) Subtract the latitude correction for stations to the North of the reference and add it for stations to the South. 2) Add the free air correction. 3) Subtract the Bouguer slab correction. 4) Add the topographic correction. 5) Apply the tidal correction. The anomaly (if there is one) that remains after these corrections have all been applied is the Bouguer anomaly. The Bouguer anomaly reflects the subsurface inhomogeneities in density. It should also be noted here that the Bouguer anomaly is caused by the excess mass associated with a volume of density 2 enclosed by a medium of density 1. g z 2 1 Excess mass = volume ( 2-1 ) = volume x -7-

8 from which one can obtain the actual mass via: Actual mass = Excess mass 2 / ( 2-1 ) Gravity in boreholes Borehole gravimeters can be used to obtain very accurate measurements of the density of horizontally layered rocks. In the following sketch the interval between two depths can be thought of as a Bouguer slab. At z 1 the gravity field due to the slab of thickness h = + 2 G z At z 2 the gravity field due to the slab of thickness h = - 2 G z The change in g in going from z 1 to z 2 is therefore 4 G z. But there is also an increase in g due to going closer to the center of the Earth, the free air effect, which we have seen is h, so the total observed change across the interval is: g z = h h The objective of the exercise is to find so rearranging: (g cm -3 ) = h - g z / h = g z / h where h is in meters and g z is in mgals. -8-

Gravity data reduction

Gravity data reduction REDUCTION: raw data à gravity anomaly data Temporal corrections tides and instrument drift Spatial corrections latitude and elevation GRS67 = gravity variation with latitude at sea