Gravity and isostasy

1
Gravity and isostasy

• Ref Musset and Kahn, 2000

2
Gravity surveys
Gravity surveys measure the acceleration due to
gravity, g. Average value of g at Earths surface
is 9.80 ms-2. Gravitational attraction depends on
density of underlying rocks, so value of g varies
across surface of Earth. Density, r, is physical
parameter to which gravity surveys are sensitive.
3
Examples

• Micro-gravity location of subsurface cavities,
  location of tombs (low density of air relative to
  soil/rock)
• Small scale mapping bedrock topography (high
  density bedrock relative to soil), mineral
  exploration (high density massive ore body
  relative to host rock)
• Medium scale location of salt domes in oil
  exploration (low density salt relative to
  sediments)
• Large scale estimation of crustal thickness (low
  density crust over higher density mantle)

4
Newtons Universal Law of Gravitation
The force of attraction between two bodies of
known mass is directly proportional to the
product of the two masses and inversely
proportional to the square of the distance
between them
where M and m are the masses of the two bodies, r
the distance separating them, and G6.67 x 10-11
Nm2kg-2 is the gravitational constant.
5
Extended body
The gravitational pull on m2 is the sum of the
forces given by each block as they were acting
separately
6
Spherical shell
A shell acts like a point mass located in its
centre, and a superimposition of shells acts like
a superimposition of point masses located at the
centre. For a body far away from the Earth, we
can consider the Earth as a point mass.
7
Units of Gravity
In honour of Galileo, the c.g.s. unit of gravity
is called the Gal. 1 Gal 1 cm s-2 Modern
gravity meters are extremely sensitive and can
measure g to within 1 part in 109. So the c.g.s
unit commonly used in gravity measurement is the
milliGal 1 mGal 10-3 Gal 10-3 cm s-2 In
m.k.s. SI units, gravity is commonly measured in
mm s-2 or g.u. (gravity unit). 10 g.u. 1
mGal Both mGal and g.u. are commonly utilised in
gravity surveying.
8
Accuracy of gravity measurements
On land 0.1 g.u. ( 0.01 mgal) At sea 10
g.u. (due to motion of ship) LaCoste-Romberg
0.02 mgal (nominal) 0.9 mgal/month (drift)
9
Variation of Gravity with Latitude
Gravity is 51860 g.u. greater at the poles than
at the equator. The acceleration due to gravity
varies with latitude due to two effects
Earths shape radius is 21 km greater at equator
so g is less
Earths rotation Centrifugal acceleration
reduces g. Effect is largest at equator where
rotational velocity is greatest, 1674 km/h. Zero
effect at poles.
10
International Gravity Formula
In 1743, Clairaut deduced a formula that
expressed the variation of gravity with latitude
where g0 is the gravity at sea level at the
equator and f the latitude. The most recent
standard derived from the IGF is the 1967
Geodetic Reference System (GRS67), given by
Where g0 9.78031846 m s-2 a
0.005278895 b 0.000023462
11
Density of geological materials
12
Density of geological materials
13
Measuring gravity
14
Relative instruments Pendulum

• T2?(L/g)1/2 or gK/T2
• where K4?2L. Since K doesnvary, it can measure
  changes in g
• g1T12g2T22
• Used to establish worldwide gravity network in
  early 60s.

15
Mass on spring
kxmg, or k??xm??g 0.1 mgal accuracy requires
?x10-7 m readings not easy. We can use
periods T2?(m/k)1/2 ?x/?gm/kT2/4?2 Sensitivit
y increase with T. But to get T20s, we need
springs 100 m long...
16
LaCoste RombergZero-lenght spring gravimeter
17
LaCoste RombergZero-lenght spring gravimeter
18
LaCoste Romberg zero-length spring

• Fk?(s-z) where k spring constant and
  zunstretched lenght
• Moment balance about pivot gives
• mga?cos(?)F?b?sin(?)k(s-z)?b?y?cos(?)/s
• g(k/m)?(b/a)?(1-z/s)?y
• ?g/?s(k/m)?(b/a)?(z/s2)?y

We want ?g/?s to be small, so a spring with zero
unstretched length (z0) gives, in theory,
infinite sensitivity.
19
LaCoste Romberg
20
LaCoste-Romberg Earth-tide meter
System Resolution 0.0001 mGal System Accuracy
0.001 mGal or better System Noise 0.006 mGal/Hz
or better Drift 1.5 mGal (or better) per month
when new, with aging drift values are usually
less than 0.5 mGals per month
21
Gravity anomalies
22
Buried sphere
??0.3 Mg/m3 d100 m r50 m ?g1.048x10-6 m/s2
??
23
Gravity anomaly of a buried sphere
24
Irregular body
25
Irregular body
26
Sphere and horizontal cylinder
27
Narrow sheet or plate
28
Horizontal sheet
Only if there is a lateral variation in density
is there a gravity anomaly. We need the stratum
not to be infinite, in order to observe the
background value.
29
Half sheet
Shallower density anomalies give a shorter
wavelength
30
Faulting
31
Data correction
32
Data correction

• Latitude correction
• Eötvös correction (when moving)
• Topographic correction
• Free air
• Bouguer
• Terrain

33
Topographic correction
34
Terrain correction
Bouguer correction assumes subdued topography.
Additional terrain corrections must be applied
where measurements near to mountains or valleys.
If station next to mountain, there is an upward
force on gravimeter from mountain that reduces
reading.
If station is next to valley, there is an absence
of the downward force on gravimeter assumed in
Bouguer correction, which reduces free-air
anomaly too much.
In both cases, terrain correction is added to
Bouguer Anomaly
35
Hammer charts
Terrain corrections can be computed using
transparent template, called a Hammer Chart,
which is placed over a topgraphic map
36
Hammer charts

• Chart is centred on gravity station and
  topography read off at centre of each segment.
• Contribution to terrain correction is obtained
  from tabulated values for each segement and then
  summed to obtain total correction. (See Table 2.8
  in Reynolds).
• Based on formula for gravitational attraction of
  cylindrical segment.
• Considered an additional part of Bouguer
  correction, i.e. results in Bouguer Anomaly.

37
SAR image of topography
38
(No Transcript)
39
Bouguer anomaly

• Bouguer anomalyobserved value of g free-air
  correction Bouguer correction terrain
  correction latitude correction Eötvös
  correction

40
Regional and residual anomaly
41
Modeling and interpretation
42
Different bodies giving identical anomalies
43
Different bodies giving identical anomalies
44
Different bodies giving identical anomalies
45
(No Transcript)