GRAVITY SURVEY (i)GRAVITY SURVEY (i)--Introduction-Introduction-

June, 2004

Gravity SurveyGravity Survey

Measurements of the gravitational field at a series of different locations Measurements of the gravitational field at a series of different locations over an area of interest. The objective in exploration work is to over an area of interest. The objective in exploration work is to associate variations with differences in the distribution of densities and associate variations with differences in the distribution of densities and hence rock types. Occasionally the whole gravitational field is measured hence rock types. Occasionally the whole gravitational field is measured or derivatives of the gravitational field, but usually the difference or derivatives of the gravitational field, but usually the difference between the gravity field at two points is measured between the gravity field at two points is measured

(From: (From: R. E. Sheriff; R. E. Sheriff; Encyclopedic Dictionary of Exploration Encyclopedic Dictionary of Exploration GeophysicsGeophysics, published by the , published by the Society of Exploration GeophysicsSociety of Exploration Geophysics ) )

In gravity prospecting, geophysicists measure minute In gravity prospecting, geophysicists measure minute variations in the force of gravity from rocks up to a variations in the force of gravity from rocks up to a few miles beneath the earth's surface. few miles beneath the earth's surface.

Different types of rocks have different densities, and Different types of rocks have different densities, and the denser rocks have the greater gravitational the denser rocks have the greater gravitational attraction. attraction.

Theory of gravityTheory of gravity

Use two of Newton’s laws:Use two of Newton’s laws:

Universal law of gravitation:Universal law of gravitation:

Where G=6.67 ´ 10-11 N mWhere G=6.67 ´ 10-11 N m22/kg/kg2 2 (m3/kg.s2) (m3/kg.s2)

Second law of motion:Second law of motion: F = mgF = mg

We can combine them to obtain the gravitational acceleration at the We can combine them to obtain the gravitational acceleration at the surface of the earth:surface of the earth:

221

R

mGmF =

RE

EGMg

2=

Gravity and potentialsGravity and potentials

g is a vector field:g is a vector field:

where r1 is the unit vector pointing toward the center of the Earthwhere r1 is the unit vector pointing toward the center of the Earth

Gravitational potential:Gravitational potential:

U is a scalar field which makes it easier to work with g is a vector field:U is a scalar field which makes it easier to work with g is a vector field:

DefinitionDefinition:: The gravitational potential, U, due to a point mass m, at a distance r from The gravitational potential, U, due to a point mass m, at a distance r from m, is the work done by the gravitational force in moving a unit mass from infinity m, is the work done by the gravitational force in moving a unit mass from infinity to to a position r from m.to to a position r from m.

r12

RE

EGMg =

r

GmU =

Relating g to URelating g to U

U is a scalar field which makes it easier to work with:U is a scalar field which makes it easier to work with:• • Potentials are additivePotentials are additive• • Gravity is a conservative forceGravity is a conservative force• • And gravitational acceleration can be easilyAnd gravitational acceleration can be easilydetermined from the potential…determined from the potential…

It follows that:It follows that:

For smaller scale problems we usually deal with g,For smaller scale problems we usually deal with g,and sum the vertical component of gand sum the vertical component of g

r

GmU =

rr

GmUg

∂∂

2- ==

Units for gUnits for gSI unit for g: m/s2SI unit for g: m/s2

1 cm/s2 = 1 Gal (for Galileo) = 0.01 m/s21 cm/s2 = 1 Gal (for Galileo) = 0.01 m/s2

milliGal or mGal = 10-3 Gal – typical unit for field milliGal or mGal = 10-3 Gal – typical unit for field studiesstudies

some text book uses the “gravity unit” (g.u.)some text book uses the “gravity unit” (g.u.)

1 g.u. = 0.1 mGal1 g.u. = 0.1 mGal

Normal value of g at the surface of the Earth:Normal value of g at the surface of the Earth:

gE = 9.8 m/s2 = 980 cm/s2 = 980 Gal = 980,000 mGal = gE = 9.8 m/s2 = 980 cm/s2 = 980 Gal = 980,000 mGal = 9800 g.u.9800 g.u.

Gravity MeterA gravimeter is any instrument designed to measure spatial variations in gravitational acceleration

Gravity 1/7

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