Gravity - Geoscientific Measure:
The variations in the Earth’s gravitational field due to changes in density of
materials within the Earth.
Objective
• Map variation in gravitational field associated with distribution of densities
in different materials (rock types)
Note: Critical to this is not the absolute values of density but rather the
contrast in density between materials
Measurement of Gravity
• Falling body - measure falling object to calculate acceleration due to gravity
• Pendulum - measure period of oscillation of a pendulum to determine
acceleration due to gravity
• Mass on Spring - suspending a mass and observing deflection of spring under
force of gravity. This is the most commonly used principle in instrument
manufacture for the exploration geophysics industry.
Galileo Galilei
1564-1642
Father of Gravity
velocity is out, acceleration is in
objects fall with same acceleration under force of gravity at same
place on the Earth
Distribution of Mass within the Earth
How is mass distributed within the earth?
plum pudding
inside
Moment of Inertia/distribution of mass
outside
Fundamental Principles - Newton’s Universal Law of
Gravitation
The mutual attractive force (F)
between two point masses, m1
and m2 is proportional to the
square of the distance
between them.
Gm1m2
F?
2
r
m1
The constant of proportionality is
G the gravitational constant.
m2
r
Newton’s Second Law of Gravitation (motion)
However, when measuring the Earth’s gravity we measure the accel eration (g)
resulting from the gravitational attraction.
Newton’s Second Law
Force is proportional to acceleration
F ? m2 g
Thus from 1) and 2)
Gm1
g? 2
r
and Gravitational Potential U
GM
U?
r
Units of gravity are gu or micrometer per second per second. The c.g.s. units
are milligal where 1milligal = 10gu
G=6.67x10 -11Nm2kg-2
Gravitational Attraction
From Newton’s Laws, the gravitational
acceleration on a mass m2 can be shown
to be equal to the mass of attracting
object m1 over the squared distance
between the centre of the two masses.
Further, that the attracting mass is related
to the density of that mass and that an
increase in density will result in an
increase in gravitational acceleration.
Taken from T. Boyd at CSM
m1
m2
The “attractiveness of a body”!!!!
M ? ? ?v
Gm1m2
F?
2
r
? more dense, greater
the attraction
? greater the
gravitational pull or
anomaly
from Bouguer to Airy
Pierre Bouguer 1735
• Established height of Andes
with plumb bob
• Noticed deflection not what it
should be
• Postulated that density very
different
•
experience replicated in
Himalayas by George Everest
Sir George Airy, 1855
• Postulated that mountains had
huge roots to support weight
• These roots very very less
dense than surrounding mantle
• “Floated on Mantle”
Factors Influencing Gravity
Shape
The Geoid and Continental Scale Effects
Ellipse
Geoid - an equipotential surface
•
•
The Geoid - an equipotential surface - the sealevel surface if no tidal or
wind action
These long wave length effects can all be measured by satellite
The Geoid and Local Effects
• These short wave length
anomalies measured using
airborne, land and sea
techniques
Mass
Corrections for Gravity Measurements (noise)
A number of corrections must be made to gravity measurements but these are
beyond the scope of this introduction and will be covered during the
Honours modules. These corrections are to account for:
Instrument Drift - the variations in spring property with time
Tidal affects - the variation in observed gravity resulting from the attraction
of the moon and sun.
Latitude - shape and rotation of the Earth
Elevation - Free-Air corrections so all readings taken as if from the same
elevation
Mass - variations due to excess mass - Bouguer Slab Correction
Topography - Terrain Corrections
Note: precise surveying of station position (x, y, and z) is essential for gravity
and especially micro gravity
Note: field observations only estimate relative changes in gravity
Rock Properties and Gravity Measurements
Density of Common Materials
Material
Clay
Silt
Sand
Peat
Gravel
Sandstone
Chalk
Shale
Granite
Basalt
Density (Mg m-3)
1.6-2.6
1.8-2.2
1.7-2.3
1.1-2.4
1.7-2.4
1.6-2.7
1.5-2.6
1.7-3.2
2.5-2.8
2.7-3.3
Other Factors Influencing Gravity (density)
Factor and Approximate % change in density (after Reynolds, 1997)
• Composition - 35
• Cementation - 10
• Age and depth of Burial - 25
• Tectonic Processes - 10
• Porosity and Pore fluids - 10
Instrumentation
•
•
Stable (static) Gravimeters
– Boliden
– Gulf
Unstable (astatic) gravimeters
– LaCoste - Romberg
– Worden
Examples
Initial Equipment Cost
Productivity
Maintenance
Operation budget
Experience
£10K to£30K
Low
Low – but expensive when
it goes wrong
Low
Low for survey, high for
interpretation
Convergent - Destructive Margins
Ocean-Continent
Gravity Anomalies at Ocean-Continent
Collision
Gravity in the Wind River Basin
Gravity and the Wildcat discoveries in the
Gulf of Mexico
Salt less dense at depth than surrounding sediments
Gravity Anomalies over Sink holes
Gravity anomalies over abandoned mine
shafts
What caused the extinction of the dinosaurs?
Meteor impact theory – the Chiczulub Crater, Mexico
Terralog – solution feature mapping
Interpretation of Gravity Anomalies
•
there is no unique solution therefore other geologic knowledge is essential
to determine the correct solution
Removal of Regional Anomalies
regional
observed
Residual
Field Interpretation of Gravity Anomalies
-4
-2
0
2
4
2 x half width (x½)
1 / 2? g max
Total Anomaly (gmax)
Bouguer anomaly (gu)
For a Sphere
• depth to centre of sphere
z ? 1 .3 x1 / 2
For a Horizontal Cylinder
• depth to centre
z ? x1 / 2
Note: because a body has a finite size
and its mass is not concentrated at the
centre, any depth estimate will be an over
calculation
Gravitational Attraction
Sphere
?g ?
G 4 3 ? ? ? a3
h
h
a
Horizontal Cylinder
G 2?? ? a 2
?g ?
h
Vertical Cylinder
h
k
G?? ? a 2
?g ?
k
Horizontal Slab
? g ? 2? G? ? t
t