Applications of the Gravity Method

- Shape of the Earth (Geodesy)
- Basin geometry
- Bedrock depths
- Fault locations
- Subsurface voids
- Location of local density changes

Gravimeters-use a zero length spring

A zero length spring is a spring which when all turns are touching has a given tension still present which is equal to the tension required to extend the spring a distance equal to its original length,i.e. tension is proportional to actual length of the spring

This condition is met by pre-stressing the spring in winding so an initial force is required to separate the coils.

**Gravity Corrections**

The difference in gravity between two stations is in part due to other factors in addition to the attraction of unknown anomalous masses, i.e.:

- variations in latitude
- elevation
- topography

The process of correcting for these factors is known as gravity reduction and most often we reduce our data as if taken on the geoidal surface, this is the most convenient equipotential surface.

The difference between observed gravity (g_{obs}) and theoretical gravity (g_{th}) at any point on the Earth's surface after reducing the gravity readings to the geoidal surface (i.e., making the Free Air, Bouguer slab, and terrain corrections) is known as the Bouguer gravity anomaly or Bouguer gravity and results due to lateral variations in density in the subsurface.

**Corrections to Gravimeter Reading**

1.) Correct for drift in terms of dial units

2.) Calculate difference between stations and base ( Rdg)

3.) Convert difference to units of gravity ( g) by multiplying Rdg values by the gravimeter scale constant

4.) Calculate g_{obs} at the station by adding g to observed gravity at base

5.) Calculate the Free Air (C_{FA}) correction (below reference surface h is negative, above h is positive) and add to g_{obs} of the station

6.) Calculate Bouguer slab (C_{BS}) correction and subtract from g_{obs} + C_{FA} of the station.

7.) Calculate terrain (C_{TC}) correction if necessary and add to g_{obs} + C_{FA} - C_{BS}

8.) Calculate g_{th} for the station and subtract from g_{obs} + C_{FA} - C_{BS} + C_{TC}. This is the complete Bouguer anomaly.

9.) The simple Bouguer anomaly is g_{obs} + C_{FA} - C_{BS} - g_{th}.

10.) The Free Air anomaly is g_{obs} + C_{FA} - g_{th}.

Density determinations

1. Assume =2.67 Mg/m^{3} or 2.67 g/cm^{3}.

2. Assign density based on literature search.

3. Measurements on hand samples, cuttings, and core.

4. Gamma-Gamma density logs.

5. Seismic velocities.

6. Borehole gravity:

- g
_{1}is increased by the downward attraction due to sheet, h - g
_{2}is decreased by upward attraction of sheet, h - g
_{2}is also increased by Free-Air gradient - g
_{2}- g_{1}= 3.086h - 4 G h or 3.086h - 0.8382 h; where is in Mg/m^{3}and h is in meters

7. Nettleton’s method of gravity (density) profiling.

8. Accounting for porosity: = P _{fluid} + (1-P) _{ dry}; where P = fractional porosity