Download Gravity Methods I - West Virginia University

Environmental and Exploration Geophysics I
Gravity Methods I
tom.h.wilson
[email protected]
Department of Geology and Geography
West Virginia University
Morgantown, WV
Tom Wilson, Department of Geology and Geography
Shallow borehole logs for near-surface characterization:
Upshur Co. WV
The kind of
constraint
that is useful
if affordable
Tom Wilson, Department of Geology and Geography
The SP (spontaneous potential log) resistivity and gamma
ray logs for geological correlations.
Tom Wilson, Department of Geology and Geography
Gravity
Passive source & non-invasive
LaCoste Romberg Gravimeter
Tom Wilson, Department of Geology and Geography
Worden Gravimeter
Hooke’s Law
F  ms g  kx
ms g
x
k
x spring extension
ms spring mass
k Young’s modulus
g acceleration due to gravity
Colorado School of Mines web sites -
Mass and spring
Pendulum measurement
Tom Wilson, Department of Geology and Geography
kx
g
ms
The spring inside the gravimeter
The spring is designed in such a way that small
changes in gravity result in rather large
deflections of the movable end of the beam.
Early gravimeters read the mechanical
movement of the spring.
Today’s gravimeters use electrostatic feedback
systems that hold the movable end of the beam
at a fixed position between the plates of the
capacitor. The voltage needed to hold the beam
at a fixed position is proportional to the
changes in gravity.
Tom Wilson, Department of Geology and Geography
Newton’s Universal Law of Gravitation
F12  G
m1m2
m1
2
r12
r12
F12 Force of gravity
G Gravitational Constant
m2
Newton.org.uk
Tom Wilson, Department of Geology and Geography
F12
mE
gE 
G
2
ms
RE
ms spring mass
mE mass of the earth
RE radius of the earth
gE represents the acceleration of gravity at
a particular point on the earth’s surface. The
variation of g across the earth’s surface
provides information about the distribution
of density contrasts in the subsurface since
m = V (i.e. density x volume).
Like apparent conductivity and resistivity g, the
acceleration of gravity, is a basic physical
property we measure, and from which, we infer
the distribution of subsurface density contrast.
Tom Wilson, Department of Geology and Geography
Units
The milliGal
Most of us are familiar with the units of g as
feet/sec2 or meters/sec2, etc.
F12
mE
gE 
G
ms
RE2
From Newton’s law of gravity g also has units of
newtons
g E  

kilogram
Tom Wilson, Department of Geology and Geography
Using the metric system, we usually think of g as being
9.8 meters/sec2.
This is an easy number to recall. If, however, we were on
the Martian moon Phobos, gp is only about
0.0056meters/sec2. [m/sec2] might not be the most useful
units to use on Phobos.
We experience similar problems in geological
applications, because changes of g associated with
subsurface density contrasts can be quite small.
Some unit names used in detailed gravity applications include
9.8 m/sec2
980 Gals (or cm/sec2)
980000 milliGals (i.e. 1000th of a Gal & 10-5m/s2)
10-6m/sec2=the gravity unit (gu) (1/10th milliGal)
Tom Wilson, Department of Geology and Geography
If you were to fall from a height of 100 meters on Phobos,
you would hit the ground in
a.
10 seconds
b.
1 minute
c.
3 minutes
t
2s
a
=189s
You would hit the ground with a velocity of
a.
1 m/s
b.
5 m/s
c.
30 m/s
v  at
=1m/s
How long would it take you to accelerate to that
velocity on earth?
a.
10 seconds
b.
1 second
c.
1/10th of a second
Tom Wilson, Department of Geology and Geography
v
t
a
=0.1s The velocity you would reach
after jumping off a brick.
3km
If you could jump up about ½ meter on earth you could probably jump
up about 1.7 kilometers on Phobos. (It would be pretty hard to take a
running jump on Phobos).
Tom Wilson, Department of Geology and Geography
3km
That would give you a velocity of 4.43 m/s and on Phobos that would keep you
off the surface for 26 minutes (13 up and 13 down). With a horizontal
component of about 2 meters per second you’d come down on the opposite rim.
Tom Wilson, Department of Geology and Geography
Diameter 12,756 km
F12  G
78 x 106 km
m1m2
2
r12
Diameter 6794 km
Tom Wilson, Department of Geology and Geography
1 milligal = 10 microns/sec2
1 milligal equals 10-5 m/sec2
or conversely 1 m/sec2 = 105 milligals.
The gravity on Phobos is 0.0056m/s2 or 560
milligals.
Are such small accelerations worth
contemplating? Can they even be measured?
Tom Wilson, Department of Geology and Geography
Spring sensitivity
Today’s gravimeters measure changes in g in the
Gal (10-9cm/s2) range. If spring extension in
response to the Earth’s gravitational field is 1 cm,
a Gal increase in acceleration will stretch the
spring by 10-11m – less than the radius of a
hydrogen atom.
The spring response in today’s modern field
portable gravimeters is amplified so that
detection of these small changes is possible….
for the modest price of
$80,000 to $90,000
Tom Wilson, Department of Geology and Geography
Calculated and observed
gravitational accelerations
are plotted across a major
structure in the Valley and
Ridge Province,
Note that the variations in g
that we see associated with
these large scale structures
produce small but detectable
anomalies that range in scale
from approximately 1 - 5
milliGals.
Tom Wilson, Department of Geology and Geography
We usually think of the acceleration due to gravity
as being a constant - 9.8 m/s2 - but as the forgoing
figures suggest, this is not the case. Variations in g
can be quite extreme.
For example, compare the gravitational
acceleration at the poles and equator.
The earth is an oblate spheroid - that is, its
equatorial radius is greater than its polar radius.
Rp = 6356.75km
RE= 6378.14km
Tom Wilson, Department of Geology and Geography
21.4km difference
Difference in polar and equatorial gravity
Rp = 6356.75km
RE= 6378.14km
gP=9.83218 m/s2
gE=9.780319 m/s2
Substitute for the
different values of R
mE
gE  G 2
RE
This is a difference of 5186 milligals.
If you weighed 200 lbs at the poles you would
weigh about 1 pound less (199 lbs) at the equator.
Tom Wilson, Department of Geology and Geography
Significant gravitational effects are also
associated with earth’s topographic features.
R. J. Lillie, 1999
Tom Wilson, Department of Geology and Geography
Isostatic compensation and density
distributions in the earth’s crust
R. J. Lillie, 1999
Tom Wilson, Department of Geology and Geography
Does water flow downhill?
Tom Wilson, Department of Geology and Geography
• Keep reading Chapter 6.
• Look over the three problems handed out in
class today.
• Resistivity paper summaries will be due
October 19th.
• Gravity papers will be available in the
mailroom next week.
Tom Wilson, Department of Geology and Geography