Gravity methods

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Autograv CG5 gravimeter used to measure changes in the acceleration due to gravity.

Gravity is a versatile geophysical technique used to detect and identify subsurface bodies and anomalies within the Earth. It is based on the density changes of rock bodies and their effect on the acceleration of gravity. Its theory is based on Newton's Law of Gravitation which states that two mass points will exert an attractive force on each other. Geophysicists use gravity to identify both small-scale and large-scale changes in the Earth to identify certain features such as intrusions, ores, basin fills, faults and other geologic features. In surveying, corrections are an important part of gravity measurements due to their dynamic behavior to the constant motion of the Earth and its celestial bodies.

Fundamentals

Gravity analysis is based on Newton's Law of Gravitation which states that an attractive force between two mass points will be proportional to the product of their masses, a gravitational constant, and inversely proportional to the square of the distance between the mass points. The gravitational constant, denoted by capital G, has a value of 6.67408 × 10^-11 m³ kg^-1 s^-2

Small everyday objects exert a small force on each other, while larger celestial objects exert a noticeable pull on other objects. This pull is a force which can be simplified to a product of mass and acceleration. Acceleration can cancel out the need to calculate a second mass for a gravity measurement. In order to measure the acceleration of gravity, three methods are generally accepted. One method involves the timing of a falling object. This timing captures the acceleration of an object as it is pulled downward by gravity. The second method involves the period of a pendulum, as the period is susceptible to the effects of gravity. The final and most useful method involves using a spring as the displacement can be measured precisely and is subject to changes in the acceleration of gravity. This is the system most gravimeters use, which has the ability to measure changes in the acceleration due to gravity as precise as a hundredth of a mGal. A modern gravimeter uses an adjusting screw, a beam, a mass, and a spring. The spring rotates the beam at an angle, and this angle controls the sensitivity of the springs reaction to gravity changes. Gravimeters used in surveys must usually be placed on a level, solid surface in order to obtain the most accurate measurements. In order to obtain accurate measurements, factors such as temperature and drift changes should be compensated for. Gravimeters are delicate instruments that should be handled with care to avoid disruption of the spring within the gravimeter.

In taking measurements, the Earth acts as set of mass points separated by its radius of 6371 km. However, the Earth isn't a perfect sphere. There are two general shapes which have been accepted to represent the shape of the Earth. One is a reference spheroid which approximates mean sea level and has flattening at the poles. Another is a geoid, which is the actual mean sea level accounting for the effect of gravity anomalies. These two are a vital part of surveying with gravity.

Surveys

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Gravity anomaly contour map showing changes in gravity measurements measured in mGal. (USGS)

Gravity surveys require delicate attention to detail in order to obtain accurate measurements. In order to begin a survey, there must be an estimate of the target to be measured in order to identify the best survey to cover the area and determine a path or grid at points in which measurements are to be taken. Surveys can generally be taken as marine, land, or airborne surveys. Land surveys are accurate but require more time in order to set up the gravimeter at various areas and are also hard to cover large areas. Marine surveys are common but tend to offer challenges due to the effect of the sway of the ship and the velocity of the ship. Marine surveys usually require a specially adapted platform which must be stabilized and its motion averaged over a short period of time in order to cancel out motion. Sea-bottom gravimeters are occasionally used and offer a greater degree of accuracy but are harder to set up. GPS may be used to track a ship's motion and account for its velocity. In marine surveys, a correction for sea depth must be included and added to the observed acceleration of gravity. Airborne surveys are commonly used due to their rapid coverage of a target area. They also allow for a steadier ride for the gravimeter when taken in calm conditions. Much like marine surveys, GPS positioning is used to account for the velocity of the plane and a gyro-stabilizer is used to keep the gravimeter level. All of these require the use of a base station in order to correlate changes in the acceleration due to gravity to a constant "known" value and can be used to calculate changes in a survey due to the effects of the Earth's motion or the pull of celestial bodies.

Corrections

Gravity requires many corrections in order to adjust the observed value of gravity to an absolute value and to take the effects of topography, terrain, elevation, motion, and other factors into account.

Drift Correction

Drift corrections adjust for changes that occur through a time interval and account for the changes of the Earth's motion and the motion of celestial bodies. A drift correction bases the assumption that a reading should appear as if were taken at the same position throughout the day. Drift correction also adjusts for small changes in a spring due to the elasticity of the spring. In order to adjust for spring, a gravimeter should periodically be returned to a base station in order to re-calibrate the instrument and return it to its original value.

Latitude Correction

A latitude correction is required due to the changes that arise from the differences in the observed gravity taken at different latitudes, or at distances from the equator. Due to the Earth's rotation, the centrifugal force exerted results in an outward maximum at the equator and minimum at the poles. The equatorial bulge also caused by rotation results in the acceleration due to gravity to also be less at the equator. These two effects vary at the Earth's latitudes. N-S distance is only taken in to account in latitude correction. This correction is added for every km that a station lies towards the equator of the base station.

$$gn=978031.85(1.0+0.005278895sin^{2}(lat)+0.000023462sin^{4}(lat))(mGal)$$

Eötvös Correction

The Eötvös correction is only needed when a survey is conducted on a mobile vehicle, where the velocity of the vehicle must be taken into account. This motion produces a centrifugal force that should be taken into account. The only need to this correction is when motion is in an E-W traverse, with positive being in this respective direction.

Topographic Corrections

Because not all measurements are taken on level surfaces with even altitudes, a series of topographic corrections must be taken into account. Topographic corrections have three parts which account for rock density changes, elevation, and the non-homogeneous effect of terrain. The first of these corrections is the free-air correction which adjusts for changes in elevation. For every meter of height change, the observed value of g decreases by 0.3086 mGal. The Bouguer correction adjusts for height change caused by the thickness of a rock unite. The pull of a thicker rock section increases the observed value of g. The free-air correction is added and the Bouguer correction is subtracted from the observed value of gravity. A terrain correction is used to adjust for the effects of real world terrain. This can include a mountain having a different force magnitude on the sides of the slopes as compared to the peak. When all of these corrections are made, the anomaly that is corrected value is known as the Bouguer anomaly. The terrain correction is often omitted due to the difficulty of its calculation when it is minor compared to the Bouguer correction, leading to a 'simple Bouguer anomaly'.

$$gfreeair=gobs-gn+0.3086h(mGal)$$

$$gbouguer=gobs-gn+0.3086h-0.04193rh(mGal)$$

$$gterrain=gobs-gn+0.3086h-0.04193rh+TerrainCorrection(mGal)$$

Modelling and Interpretation

A challenge with gravity modelling arises in its inversion challenge, the ability to deduce a model of subsurface densities which are representative of the actual subsurface structure. This challenge arises due to the non-uniqueness trait of gravity anomalies. Non-uniqueness is defined by the ability of various subsurface structures to appear to have the same identical signal. In order to overcome this challenge, other constraints on data must be used such as resistivity, magnetism, seismic or other geophysical techniques. In order to deduce a buried body shape, various models are often used. These models account for the differences in the gravity that occur from shapes such as spheres, cylinders, and other common shapes. Knowing the gravity distribution of these shapes is vital for developing an accurate model. Interpreting the gravity of a buried body involves using all available data to create an accurate model of the subsurface.

External Links

• OpenEI - Ground Gravity Survey
• The National University of Malaysia - Gravity Lecture
• AAPG Wiki - The Gravity Method

References

Mussett, A. E., Khan, M. A., & Button, S. (2009). Looking into the Earth: an introduction to geological geophysics. Cambridge: Cambridge University Press.