Gravity Measurement and Corrections

Modern Gravimeters

• Can detect a change of 1/100,000,000th g or 0.01 mGal.
• Rely on a mass pivoted on a beam attached to a spring.
• A thermostat prevents thermal contraction or expansion.
• Must be carefully leveled before a reading (time-consuming).
• Some models have automatic leveling.
• Are delicate and need protective transport.
• Data is not directly useful; needs reduction to correct for various effects.
• Gravity anomalies are small, so corrections are similarly sized and important.

Gravity Corrections

• Measurements at different elevations need correction because distance to Earth's center affects gravity.
• Corrections needed to analyze raw data for anomalies
• Drift: Changes in readings even without movement, often due to spring creep or diurnal variations that are corrected using base station readings.
• Latitude correction accounts for Earth's shape (oblateness) and latitude.
• Eötvös Correction: Accounts for centrifugal force due to Earth's rotation, important for moving objects (vehicles).
• Topographic corrections adjust for variations in altitude and terrain features (free-air and Bouguer corrections).
  • Free-air correction: Accounts for changes in gravity with elevation.
  • Bouguer correction: Accounts for the mass of the terrain above the measurement point.
• Temporal variations:
  • Instrumental drift
  • Tidal effects
  • Latitude variations
  • Elevation variations
  • Slab effects
  • Terrain effects

Drift

• Drift is a change in readings that can occur even with a stationary device.
• The spring inside the gravimeter can slowly creep or stretch.
• Drift is corrected by periodically returning to a base station to measure the drift rate.
• The drift is subtracted from the rest of the data.

Drift Example

• Temporal drift variations must be corrected for land-based surveys.
• Base station readings are used to normalize and subtract the temporal variations to account for drift.

Field Procedure

• Establish the location of one or more base stations (e.g., station 9625).
• Establish locations (numbered 158-163) for gravity stations to collect readings over the survey area.
• Record base station relative gravity readings and time.
• Collect relative gravity readings at each gravity station.
• Return to the base station every hour, taking final readings after the last station.

Causes of Tides

• The variations of gravity due to the motion of the Earth and the moon are corrected for and accounted for in the Gravity calculations.

Effects of Earth's Shape: Latitudinal Gravity Variations

• Gravity varies with latitude due to Earth's oblate spheroid shape.
• Least at the Equator, most at the Poles.
• Variation is about 0.5%.
• Earth's rotation causes centrifugal force larger at the equator than the poles and causes Earth to bulge outward.
• This produces a difference in the observed gravity between the equator and the poles.

Theoretical Gravity: Normal Ellipsoid, Latitude Correction

• Gravity varies with latitude, this correction is determined using the International Gravity Formula (usually called a theoretical gravity formula).
• The observed gravity must have the theoretical gravity subtracted from it to obtain the anomaly.
• The formula accounts for the Earth's shape and latitude.
• Corrections are ~0.8 mGal/km.

Eötvös Correction

• Necessary when gravity readings are taken from a moving object.
• Gravity measurements are affected by centrifugal acceleration induced by movement.
• Your weight reduction due to centrifugal force is about 0.34% at the equator because of rotation

Topographic Corrections

• Measure gravity at the same elevation for accuracy.
• Free-air and Bouguer corrections needed when elevations differ; these correct for variation due to Elevation changes or Mass variations.

Free-Air Correction

• Accounts for change in gravity with altitude.
• Gravimeter readings are corrected for variations due to elevation using the Free-Air correction.
• The correction is approximately 0.3086 mGal/meter of elevation change.
• Positive h = Mountain range, negative h = Valley.

Bouguer Correction

• Accounts for the mass of the terrain above the measurement point.
• The difference between the observed gravity and the calculated gravity based on a uniform density slab is the Bouguer Anomaly..

Combined Elevation Correction

• The free-air and Bouguer corrections can be combined into one.
• It calculates the total change in observed gravity due to both elevation and the mass of the terrain (using density).

Selecting Reduction Density

• Standard Bouguer density used for consistency across surveys.
• Field measurements or geologic maps (data tables) can also be used for selecting appropriate density.

Bouguer Terrain Correction

• Bouguer correction assumes an infinite slab, reasonable around C. The Bouguer correction should be used.
• Necessary when topography is present to account for the localized effect of mass.
• Terrain and density are relevant for corrections.

Finally... The Bouguer Anomaly

• After applying all previous corrections to the observed gravity readings, the result is called a "Bouguer Anomaly."
• The Bouguer Anomaly reflects density variations below a datum level, aside from the effects from topography and latitude.

Bouguer Anomaly of Egypt

• Example map of the Bouguer Anomaly of Egypt.