Transcript No Slide Title

Environmental and Exploration Geophysics II
Tie up Gravity methods & begin
Magnetic methods
tom.h.wilson
[email protected]
Department of Geology and Geography
West Virginia University
Morgantown, WV
Tom Wilson, Department of Geology and Geography
We make simplifying assumptions about the geometry of
complex objects such as dikes, sills, faulted layers, mine
shafts, cavities, caves, culminations and anticline/syncline
structures by approximating their shape using simple
geometrical objects - such as horizontal and vertical
cylinders, the infinite sheet, the sphere, etc. to estimate
the scale of an anomaly we might be looking for or to
estimate maximum depth, density contrast, fault offset,
etc. without the aid of a computer.
Burger gets into a lot of the
details in Section 6.5 of the text
Tom Wilson, Department of Geology and Geography
Recall our earlier discussions of the gravity anomaly
produced by a roughly spherical or equidimensional
distribution of density contrast -
Go to 31
Tom Wilson, Department of Geology and Geography
Two term solution with one of the terms
describing the shape of the anomaly


4

 GR 3 
1


3
gv 
3 
 2
z2
 2
 x
  z 2  1 
 

4
GR3
gv  3 2
z
z
Tom Wilson, Department of Geology and Geography
g directly over the
center of the
sphere is gmax
Shape term and maximum g directly over the
sphere




1


gv  K 
3 
2
 2
 x
  z 2  1 
 

gmax
Tom Wilson, Department of Geology and Geography
4
GR3
K3 2
 gmax
z
We recognize the shape term as this ratio
gv
1

3
g max  x 2  2
 2  1
z

Divide through by gmax
gmax contains information about
volume, density and radius
Tom Wilson, Department of Geology and Geography
The shape of the curve gv/gmax is scale independent.
It is not affected by the depth or size of the
sphere.
Tom Wilson, Department of Geology and Geography
Shape of the anomaly is independent of
the size of the sphere that produced it.
The shape, the variation as a function of
x/z is the same for all spheres regardless
of their depth or size.
Tom Wilson, Department of Geology and Geography
At what point does the anomaly fall
off to one-half of its maximum value?
gv
1
1


3
g max  x 2  2 2
 2  1
z

Tom Wilson, Department of Geology and Geography
Let the ratio g/gmax = ½ and solve for X/Z
Tom Wilson, Department of Geology and Geography
X1/2 /Z = 0.766 implies that Z can
be expressed in terms of X1/2
X1/2
½
½
Tom Wilson, Department of Geology and Geography
Diagnostic position and depth index multiplier
X1/2
½
½
In the above, the “diagnostic position” is X1/2, or the X
location where the anomaly falls to 1/2 of its maximum value.
The value 1.31 is referred to as the “depth index multiplier.”
This is the value that you multiply the reference distance
X1/2 by to obtain an estimate of the depth Z.
Tom Wilson, Department of Geology and Geography
A table of diagnostic positions and depth index multipliers
for the Sphere (see your handout).
Diagnostic Position
3/4 max
2/3 max
1/2 max
1/3 max
1/4 max
Depth Index Multiplier
1/0.46 = 2.17
1/0.56 = 1.79
1/0.77 = 1.305
1/1.04 = 0.96
1/1.24 = 0.81
Note that regardless of which diagnostic position you use, you
should get the same value of Z. Each depth index multiplier
converts a specific reference X location distance to depth – to Z.
G  (4 / 3 R 3 )
Z2
R3
 0.02793 2  for meters
Z
R3
 0.00852 2  for feet
Z
g max 
1/ 3
 g max Z 2 
R

 0.00852 
g max Z 2
 
0.00852 R 3
Tom Wilson, Department of Geology and Geography
(feet)
(feet)
Note that these constants
(e.g. 0.02793) assume that
depths and radii are in the
specified units (feet or
meters), and that density is
always in gm/cm3.
An estimate of z opens the possibility of solving for other
parameters in the relationship
For the sphere
G  (4 / 3 R 3 )
g max 
Z2
R3
 0.02793 2  for meters
Z
R3
 0.00852 2  for feet
Z
1/ 3
 g max Z 2 
R

 0.00852 
g max Z 2
 
0.00852 R 3
Tom Wilson, Department of Geology and Geography
(feet)
(feet)
Since we know Z we could
solve for R assuming a ; or,
having some information on
the possible size of the
object, we could solve for .
Note that these constants
(e.g. 0.02793) assume that
depths and radii are in the
specified units (feet or
meters), and that density is
always in gm/cm3.
We can undertake similar development for the
Horizontal Cylinder (see section 6.5.3 in our text)
gcyl


2 G  R 2  1 

 x 2  1
Z
 z 2 
g cyl
and


1

 g max  2
x


1
2
 z

Tom Wilson, Department of Geology and Geography
g max
gcyl
g max
2 G  R 2

Z


1

 2
x


1
2
 z

Diagnostic positions and multipliers for the
horizontal cylinder
Diagnostic Position
3/4 max
2/3 max
1/2 max
1/3 max
1/4 max
G 2R 2 
g max 
Z
R2
 0.0419  for meters
Z
R2
 0.01277  for feet
Z
1/ 2
 g max Z 
 (feet)
R  
0
.
01277




g max Z
 
(feet)
0.01277R 2
Tom Wilson, Department of Geology and Geography
Depth Index Multiplier
1/0.58 = 1.72
1/0.71 = 1.41
1/1= 1
1/1.42 = 0.7
1/1.74 = 0.57
Again, note that these
constants (i.e. 0.02793)
assume that depths and radii
are in the specified units
(feet or meters), and that
density is always in gm/cm3.
Return to problem 6.5
We worked through most of this the other
day: some assuming a horizontal cylinder and
some assuming the sphere.
Pb. 6.5 What is the radius of the smallest equidimensional void (such
as a chamber in a cave - think of it more simply as an isolated spherical
void) that can be detected by a gravity survey for which the Bouguer
gravity values have an accuracy of 0.05 mG? Assume the voids are in
limestone and are air-filled (i.e. density contrast = 2.7gm/cm3) and that
void centers are never closer to the surface than 100 meters.
Tom Wilson, Department of Geology and Geography
Solve for R:
sphere (left), cylinder (right)
 g Z2 

R   max
 4  G 
 3

1
3
 g max Z 
R

2





1
2
We assumed that since the instrument reads
with an accuracy of 0.05 mGals the gravity
anomaly would have to be larger than 0.05 mGals;
so we picked a gmax of 0.1mGals.
Tom Wilson, Department of Geology and Geography
Solve for R:
sphere (left), cylinder (right)
 g Z2 

R   max
 4  G 
 3

1
3
For the sphere (a
large chamber within
the cave system),
R~ 23.7 meters
Tom Wilson, Department of Geology and Geography
 g max Z 
R

2





1
2
For the horizontal
cylinder (a long
cave passageway),
R~ 9.4 meters (a
very large
passageway!)
In a problem similar to problem 6.9 (Burger et al.) you’re
given three anomalies. These anomalies are assumed to be
associated with three buried spheres.
Determine their depths using the half-maximum technique.
Carefully consider where the anomaly drops to one-half
of its maximum value. Assume a minimum value of 0.
0.5
Bouguer Anomaly (mGals)
0.45
0.4
0.35
A.
0.3
C.
B.
0.25
0.2
0.15
0.1
0.05
0
-1500
-1000
-500
0
500
Distance from peak (m)
Tom Wilson, Department of Geology and Geography
1000
1500
Magnetic Methods
Tom Wilson, Department of Geology and Geography
Magnetic polarity reversals on the sea floor provide
Tom Wilson, Department of Geology and Geography
Charged particles from the sun stream into the earth’s magnetic
field and crash into the gasses of the atmosphere
Tom Wilson, Department of Geology and Geography
Protons and electrons in the solar wind crash into
earth’s magnetosphere.
Tom Wilson, Department of Geology and Geography
We are also interested in local induced magnetic fields
Gochioco and Ruev, 2006
Tom Wilson, Department of Geology and Geography
Data
Acquisition
Tom Wilson, Department of Geology and Geography
Measuring the Earth’s magnetic field
Proton Precession Magnetometers
water kerosene &
alcohol
Steve Sheriff’s Environmental Geophysics Course
Tom Boyd’s Introduction to Geophysical Exploration Course
Tom Wilson, Department of Geology and Geography
Magnetic Fields – Basic Relationships
Source of Protons and
DC current source
Proton precession generates
an alternating current in the
surrounding coil
Tom Wilson, Department of Geology and Geography
M
GF
f 
F
2L
2
Proton precession frequency (f) is directly
proportional to the main magnetic field intensity F and
magnetic dipole moment of the proton (M). L is the
angular momentum of the proton and G is the
gyromagnetic ratio which is a constant for all protons
(G = M/L = 0.267513/  sec). Hence -
F  23.4874 f
Tom Wilson, Department of Geology and Geography
Locating Trench
Boundaries
Theoretical model
Tom Wilson, Department of Geology and Geography
Examination of trench for
internal magnetic anomalies.
actual field data
Gilkeson et al.,
1986
Trench boundaries - field data
Trench Boundaries - model data
Tom Wilson, Department of Geology and Geography
Gilkeson et al.,
1986
Abandoned Wells
From Martinek
Tom Wilson, Department of Geology and Geography
Locating abandoned wells
Tom Wilson, Department of Geology and Geography
Abandoned Well - raised relief plot of
measured magnetic field intensities
Tom Wilson, Department of Geology and Geography
From Martinek
Magnetic Fields – Basic Relationships
Magnetic monopoles
Fm12
r12
Fm12 Magnetic Force
 Magnetic
Permeability
p1 and p2 pole
strengths
Tom Wilson, Department of Geology and Geography
p1
1 p1 p2

4 r122
Coulomb’s Law
p2
Magnetic Fields – Basic Relationships
Fm12
1 p1 p2

4 r122
Fo
1 po
Ho 

pt 4 r 2
Force
Magnetic Field
Intensity often
written as H
pt is an isolated test
pole
F
1 pE
" FE" 

pt 4 r 2
The text uses F instead of H to represent magnetic
field intensity, especially when referring to that of the
Earth (FE).
Tom Wilson, Department of Geology and Geography
Magnetic Fields – Basic Relationships
The fundamental magnetic element is a dipole or combination
of one positive and one negative magnetic monopole. The
characteristics of the magnetic field are derived from the
combined effects of non-existent monopoles.
Dipole
Field
Tom Wilson, Department of Geology and Geography
Magnetic Fields – Basic Relationships
monopole
vs.
Toxic Waste
dipole
Tom Wilson, Department of Geology and Geography
The earth’s main magnetic field
Tom Wilson, Department of Geology and Geography
Magnetic Elements
Tom Wilson, Department of Geology and Geography
Location of north magnetic pole
http://www.compassdude.com/compass-declination.shtml
Tom Wilson, Department of Geology and Geography
Magnetic Elements
Tom Wilson, Department of Geology and Geography
Magnetic Elements
Tom Wilson, Department of Geology and Geography
Magnetic Elements
Tom Wilson, Department of Geology and Geography
Magnetic north pole: point where
field lines point vertically
downward
The compass
needle points to
the magnetic
north pole.
Tom Wilson, Department of Geology and Geography
Geomagnetic north pole: pole associated with the
dipole approximation of the earth’s magnetic
field.
Magnetic Intensity
61000
F (nanoteslas or gammas)
60000
59000
58000
57000
56000
55000
54000
53000
1900
1920
1940
1960
Date
Tom Wilson, Department of Geology and Geography
1980
2000
Magnetic Inclination
Tom Wilson, Department of Geology and Geography
Magnetic Inclination
Inclination (degrees)
72
71
70
69
68
1900 1920 1940 1960 1980 2000
Date
Tom Wilson, Department of Geology and Geography
Magnetic Declination
Tom Wilson, Department of Geology and Geography
Magnetic Declination
declination (degrees west)
W -9
-8
-7
-6
-5
-4
-3
-2
1900 1920 1940 1960 1980 2000
Date
Tom Wilson, Department of Geology and Geography
Magnetic Elements for your location
http://www.ngdc.noaa.gov/geomagmodels/struts/calcPointIGRF
Tom Wilson, Department of Geology and Geography
Magnetic Elements
http://www.ngdc.noaa.gov/geomag/magfield.shtml
Today’s Space Weather
http://www.swpc.noaa.gov/today.html
Tom Wilson, Department of Geology and Geography
Introduction to the magnetics computer lab
Anomaly associated
with buried metallic
materials
Computed magnetic
field produced by
bedrock
Results obtained
from inverse
modeling
Bedrock configuration
determined from gravity
survey
Tom Wilson, Department of Geology and Geography
Where are the drums and
how many are there?
Tom Wilson, Department of Geology and Geography
Enjoy the Break!
• Hand in the gravity lab today
• hand in the in-class problems for credit.
• Magnetic papers are in the mail room.
• Magnetic paper summaries will be due
Tuesday, December 6th.
• Continue reading Chapter 7 –
•Look over the magnetics lab. We’ll launch
into this effort on Tuesday, Novemner 29th.
Tom Wilson, Department of Geology and Geography