Gravity

Measuring Gravity - Gravity must be measured very accurately (often to 0.00001 percent of average Earth's gravity). Elevation and Latitude also must be accurately known. Unit of measure is mGal (gravitational acceleration of 9.8 m/s is 980,000 mGals)

Pendulum - The period of oscillation of the pendulum can be used to determine gravity. It is a very cumbersome device. Each pendulum has a different constant based on the length of string and mass of weight at the end. Relative Measurements - difference in gravity between two points

Gravimeter - A weight attached to a series of springs. Gravity is measured by the length of the spring (Hook's law). Must be accurately leveled and not vibrating. Temperature also must be controlled as the spring expands with temperature. Relative Measurements - difference in gravity between two points

Absolute Measurements, IGSN71 - Using lasers, absolute gravity can be measured from the times that an object passes two points both on the way up and on the way down. IGSN71 over 1800 gravity sites around the world.

Corrections to Gravity
Latitude - Earth is not a stationary, perfect sphere. It is spinning. This produces centrifugal force and a flattening at the poles. Gravity is less at the equator than at the poles by 5.2 Gal. Gravity is corrected for latitude by using the Reference Ellipsoid (true, gross shape of the earth) to compute normal gravity. The difference between normal and observed gravity is the gravity anomaly. Geoid is the actual height of sea level

Free-Air - gravity decreases with distance from the center of the Earth (0.3086 mGal for every meter above sea-level). The Free-air correction adjusts gravity measurements to some datum, usually sea level.

Bouguer and Terrain - Free-Air correction only adjusts for elevation NOT the mass of material between the observation point and the datum. Simple Bouguer correction assumes that the mass of topography can be treated as an infinite slab. In mountainous regions, a more complex Terrain correction must be made.

Field Methods
Drift and Earth Tides - gravity measurements at the same location vary with time because of instrument drift and earth tides. These time variations are approximately linear if the time interval between repeat measurements at the same location is 2-3 hours or less. Intervening measurements at different locations can then be linearly interpolated to correct for time variations. Thus most gravity surveys use looping where the gravimeter is brought back to a base station every 2-3 hours for a repeat measurement.

Elevation and Horizontal Position - must be known accurately. For a survey with 0.1 mGal accuracy, elevation must be know to 0.33 m and latitude to 125 m. GPS is the best method. Topographic maps also are commonly used as well as barometers.

Rock Densities - rock density varies by about a factor of two from 1800 to 3400 kg/m^3 as a result of porosity and mineralogy. In areas where rock density is not measured, the Bouguer correction is made using a rock density that produces a gravity anomaly with the least correlation to topography.

Simple Geometric Shapes
Density contrast - difference in density (higher or lower) producing a gravity anomaly. A water filled void in limestone would have a density contrast of -1700 kg/m^3 (1000 kg/m^3 minus 2700 kg/m^3).

Sphere, Horizontal Cylinder (void, meteorite or fold) - Both produce a symmetry anomaly. The amplitude and wavelength of the anomaly is a function of depth. Shallow objects produce high amplitude, narrow anomalies. Deep objects produce low amplitude, broad anomalies. Because of the additional mass present for a given radius, a horizontal cylinder produces a wider, broader gravity anomaly. Unless density contrast is known, it is not possible to uniquely determine the radius of the sphere or cylinder.

Vertical Cylinder (salt dome)- Calculation at off axis locations is complex. A vertical rod is an acceptable approximation to a vertical cylinder when the diameter of the cylinder is less than its depth.

Inclined Rod, Horizontal Sheet (faults, dikes or sills) - An inclined rod produces an asymmetric gravity profile. The maximum anomaly is offset in the dip direction where there is more mass near the surface. Semi-infinite horizontal sheets at different depths (offset by a fault) produce a gravity couple (high and low) across the offset. The shape of the gravity couple depends on whether the fault is normal, vertical, or reverse.

Polygons - Can be used to compute gravity due to an arbitrary two-dimensional shape. The polygon is broken up into cells. The gravity anomaly for each cell depends on the depth and angle subtended as measured from the point of calculation.

Analysis of Gravity Anomalies
Regional and Residuals - In order to see local/shallow features it is often necessary to remove a regional trend and look at the residual gravity profile. A regional trend is determined by a least squares fit of the data to a low order polynomial. A truly local anomaly would go to zero on either side of the gravity profile.

Upward Continuation - gravity data can be mathematically manipulated to estimate gravity as if the survey was taken at high elevations (1 or 2 km). Upward continuation reduces the gravity effect of small/shallow objects.

Half-Maximum Technique - The depth to a sphere or horizontal cylinder can be estimated from the horizontal distance between the maximum value and a value one-half the maximum value.

Second Derivative Technique - can be estimated numerically. This emphasizes regions of rapid changes in gravity (edges of structures). However, it also emphasizes noise.

Applications - Any feature that has a density contrast with surrounding country rocks. Depth to Bedrock, Landfills, Voids, Salt Domes. Also may be used to estimate size of Mineral Deposits prior to mining.
 
 
 
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