GeologyRocks

About the author

Jon
Imperial College London

Introduction

Gravity surveying involves looking at the subsurface structure based on the differences in densities of the subsurface rocks. The idea is based around a causative body - one which produces a gravity anomaly. Assessment of gravity anomalies can give ideas about depth, size and shape of the causing body. Gravity anomalies are measured in ms^-2. As the anomalies are very small compared to the Earth's field (9.81ms^-2), they are commonly expressed in gravity units (g.u.), where 1 gu = 1μms^-2. However, some measurements are in milligals, where 10 milligals = 1 g.u.

Basic Theory and Measurement

The basic theory for gravity stems from Newton's Law of gravitation:

where G is the Universal Gravitational Constant (6.67x10^-11m³kg^-1s^-2), m₁ and m₂ are two masses, distance r apart.

The gravitational field is best described using the gravitational potential, U:

which is a scalar (magnitude, no direction). The derivative of U in any direction gives the component of gravity in that direction, which gives computational flexibility.

Measurements of the gravitational field are done using a very sensitive spring and mass system (in a LaCoste & Romberg gravimeter). In this type of instrument a weight is attached to a beam and a spring (Figure 1). As gravity increases, the weight is forced downwards, stretching the spring. Measurements are made by bringing the beam back to horizontal, the amount of movement required is proportional to the gravitational force.

Figure 1: The LaCoste-Romberg gravimeter. The original position is in bolder colours. When the gravity in creases the weight forces the beam to rotate. Adjusting the screw (top let) moves the beam back to horizontal. The amount the beam moves is proportional to the gravity. Redrawn from Keary and Brooks (1991).

The spring in these gravimeters is extremely sensitive and has to be specially manufactured. Thermal effects also have to be accounted for my using special materials in the beam. Most gravimeters are capable of measuring a change of 0.1 g.u.

Gravity Anomalies of Simple Bodies

Consider the gravitational attraction of a point mass, m at a distance r (Figure 2). The gravitational attraction in the direction of the mass is:

Since only the vertical component is measured, the anomaly caused by the mass is:

This equation can now be used to build up simple geometries by integrating. For example, to build a line which is infinite in the y-direction, integrating gives:

Integrating over the x-direction (to infinity) and then over the vertical direction between two limits will give us the anomaly of an infinite horizontal slab:

where p is the density of the slab and t is the thickness.

Figure 2: The gravity anomaly caused by a point source mass. Redrawn from Keary and Brooks (1991)

Corrections

There are several corrections that need to be made on gravity survey results. These are:

• Drift - correct for stretching in the spring by measuring a base point throughout the survey
• Latitude - correct for the location of the survey due to the shape of the Earth
• Elevation - correct for the height above sea-level of the survey area. This includes free air correcting for the height (without taking into account the rocks), the Bouger correction (as free air, but takes into account the rocks in the "extra" height) and the terrain correction to account for terrain away from the survey area.
• Tidal - correct for the change in tides, usually using the same method as drift correction
• Eötvös - correct for the Coriolis acceleration. For survey done using moving vehicles only

Interpretation

Interpretation can either be done using forward or inverse modeling. Forward modeling involves constructing a model from which you calculate the gravity anomaly and then compare it to the measured anomaly. The model is then altered until the match is acceptable. Inverse modeling uses the measured data and is inverted to provide various parameters, such as the maximum depth, excess mass and approximate thickness.

There is a major problem with interpretation all potential fields (magnetic, gravity and electric) in that there is no unique solution. For example if you consider the anomaly produced from a series of concentric spheres of constant mass, but differing density and radius. Each sphere acts as a point mass, each producing an identical anomaly. This mean the model needs to be constrained in some way, perhaps using other potential techniques or existing geological knowledge.

Limiting Depth

The limiting depth can be found using the half-width (the distance in the horizontal direction from the maximum anomaly value to the position where the anomaly is half the maximum. See Figure 2):

Other methods involve the first and second derivatives of the anomaly.

Excess Mass

The excess mass is the extra mass that is occupied a body compared to the same body made of the country rock. This involves a surface integration

Inflection Points

Locations of inflection points can give details of the bodies edge.

Approximate Thickness

If the density contrast between the country rock and the body is known then the thickness can be estimated using the infinite slab formula.

Conclusion

Gravity surveying uses the difference in densities to detect subsurface anomalies. It can detect the size, shape and depth of such an anomaly. Measurements are done with a gravimeter, typically a LaCoste-Romberg meter. Using the gravity anomaly produced by a point mass, simple structures can be built up and compared against any measured field anomalies. However, there are several corrections that need to be done on field measurements to remove the effects of topography, elevation and latitude.

References

P. Keary & M. Brooks, 1991. An Introduction to Geophysical Exploration.

W. Lowrie, 1997. Fundamentals of Geophysics.