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The gravityThe gravity method involves measuring the earth’s gravitational field at specific locations on the earth’ssurface to determine the location of subsurface density variations. The gravity method works when buriedobjects have different masses, which are caused by the object having a greater or lesser density than thesurrounding material.

However, the earth’s gravitational field measured at the earth’s surface is affected also by topographic changes, the earth’s shape and rotation, and earth tides. These factors must be removed before interpreting gravity data for subsurface features

THEORYTo appreciate the gravity method, one must understand Newton’s law of gravity, which describes the forcebetween two masses separated by a specific distance. In the gravity method, we are concerned withacceleration at the earth’s surface. To obtain the gravitational acceleration, g, we can use Newton’s law,F=mg, where m is mass, to obtain g on the earth’s surface:

where Me is the mass of the earth, G is the universal gravitational constant and Re is the radius of the earth.The units for g are cm/s2 in the c.g.s system and are commonly known as Gals, where the averageacceleration of gravity at the earth’s surface is 980 Gals. Most applied gravity studies are involved withvariations in the acceleration of gravity ranging from 10-1 to 10-3 Gals, so most workers use the term milliGal(mGal). In some detailed work involving engineering and environmental applications, workers are dealing withmicroGal (μGal) variations.

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The theoretical value of gravity

It is a value of gravity at any point on the earth when:

1-The earth is homogenous.

2- The earth is sphere.

It is measured from sea level by the following formula:

Latitudeis

galsequatoratGravityisg

gravityofvaluelTheoriticaisg

SinSingg

o

o

:

0318.978:

:

)20000059.00052884.01( 22

EquatorPole

Pole

r3

r1

r2

r1

r2r3

r1>r2>r3

r1=r2=r3

6371 km

63

51

km

2

1

rg

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Shape of the Earth : Spheroid

eR

pRR

Sphere Spheroid

• Spherical earth with R= 6371 km is an approximation

• Rotation creates an ellipsoid or a spherical.

247.298

1

e

pe

R

RR

Deviation from a spherical model

kmRR

kmRR

p

e

3.14

2.7

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Observed Gravity

It is a measurement of gravity at any point on the earth surface by using a gravimeter.

The measurements have to be corrected for the following corrections:

1- Drift correction.

2- Free air correction.

3- Bouguer correction.

4- Terrain correction.

5- Latitude correction.

6- Tidal correction.

7- Isopstacy correction.

1-Drift correction.

All the gravimeters change null reading with time when set up on the same station, due to:

1- Creep in the spring.

2- Variation in temperature.

3- Earth tide. 4- Sudden motion during transportation.

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Calculation of drift correction:

1- Select a station as a base station.

2- Repeated readings taken in the base station over certain period of time.

3- The readings plotted in the table:StationStation ReadingReading TimeTime

BaseBase 5555 9:009:00

11 6565 9:109:10

22 178178 9:219:21

BaseBase 6060 9:289:28

33 7575 9:359:35

44 6666 9:399:39

BaseBase 5252 9:459:45

55 5858 9:529:52

66 9999 9:569:56

BaseBase 4949 10:0010:00

Base 1 2 3 4 5 6

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4- Draw drift curve between the readings of base station and their times.

Time

Readin

gBase line

Dri

ft T

ime

St.1 St.2 St.3 St.4

Tidal and Drift Corrections: A Field Procedure

Let's now consider an example of how we would apply this drift and tidal correction strategy to the acquisition of an exploration data set. Consider the small portion of a much larger gravity survey shown in Figure 1. To apply the corrections, we must use the following procedure when acquiring our gravity observations:

1- Establish the location of one or more gravity base stations.2- Establish the locations of the gravity stations appropriate for the particular survey, in this case 158 through 163.3- starting to make gravity observations at the gravity stations.

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4- We now proceed to move the gravimeter to the survey stations numbered 158 through 163. At each location we measure the relative gravity at the station and the time at which the reading is taken.5- After recording the gravity at the last survey station, or at the end of the day, we return to the base station and make one final reading of the gravity.

Using observations collected by the looping field procedure, it is relatively straight forward to correct these observations for instrument drift and tidal effects. The basis for these corrections will be the use of linear interpolation to generate a prediction of what the time-varying component of the gravity field should look like. Shown in Figure 19 is a reproduction of the spreadsheet used to reduce the observations collected in the survey defined on the last page.

The first three columns of the spreadsheet present the raw field observations; column 1 is simply the daily reading number (that is, this is the first, second, or fifth gravity reading of the day), column 2 lists the time of day that the reading was made (times listed to the nearest minute are sufficient), column 3 represents the raw instrument reading (although an instrument scale factor needs to be applied to convert this to relative gravity, and we will assume this scale factor is one in this example).

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A plot of the raw gravity observations versus survey station number is shown in Figure 20. Notice that there are three readings at station 9625.This is the base station which was occupied three times. Although the location of the base station is fixed, the observed gravity value at the base station each time it was reoccupied was different. Thus, there is a time varying component to the observed gravity field. To compute the time-varying component of the gravity ¯eld, we will use linear interpolation between subsequent reoccupations of the base station. For example, the value of the temporally varying component of the gravity field at the time we occupied station 159 (dark gray line) is computed using the expressions given in Figure 3.

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Figure 4: Linear interpolation equations to compute time-varying component of the gravity field.

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One check to make sure that the corrections have been applied correctly is to look at the gravity observed at the base station. After application of the corrections:1- All of the gravity readings at the base station should all be zero. 2- The uncorrected observations show a trend of increasing gravitational acceleration toward higher station number. After correction, this trend no longer exists. The apparent trend in the uncorrected observations is a result of tides and instrument drift.

Gravity data (mgal) after tide/drift correction