Download GG 450 Lecture 13 Feb 8, 2006

GG 450
Feb 21, 2008
Magnetic
Interpretation
Homework
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Homework Due
Gravity Lab Presentations
~ 10 minutes each
COMMON APPLICATIONS OF MAGNETICS:
SEDIMENTARY BASINS: As magnetite is more
common in igneous and metamorphic rocks, the
depth of sedimentary basins is often easily
observed in magnetic anomalies.
VOIDS: In high susceptibility rocks, voids are
often detectable as "negative susceptibility"
anomalies:
Magnetic anomalies are associated with magnetic
minerals - primarily magnetite. As magnetite is
common in sedimentary rocks, anomalies vary laterally
with magnetite concentration.
Magnetite is even more common in metamorphic and
igneous rocks, thus larger anomalies are observed in
these rocks.
rock type
sedimentary
susceptibility
0.00005 cgs emu
metamorphic
0.0003
felsic igneous
0.0005
basic igneous
0.006
ultramafic
0.012
iron
1-10
MAGNETIC TRENDS: Probably the most important use of
magnetics in exploration and regional geophysics is to
establish trends of buried structures (Burger, Fig. 17-3).
This also includes seafloor magnetic anomalies. The
orientation of the earth's magnetic field at the time of
seamount formation can be determined from ship magnetic
data - important to take data on N-S lines.
Minnesota
Magnetic Anomaly Map
Bedrock Geology Map
Magnetic anomalies often delineate structural trends invisible
from the surface.
SEAMOUNT MAGNETISM:
Will Sager successfully used
magnetic data to obtain the
elements of the earth’s
magnetic field at the time
seamounts were formed. This
allows him to determine a
paleolatitude, whether normal
or reversed, to help constrain
the age of the seamount.
TodayХs field
Field when seamount
was formed
Field when ocean
crust was formed
If the two paleo-inclinations can be determined, then an
estimate of the seamount age can be obtained.
Comments on gravity lab reports
• Field data: Include a copy of your field data in
your report as an appendix, as well as any
necessary information needed to reoccupy your
gravity stations.
• Location Map: Being able to reoccupy stations
is very important. Include at least one map that
shows local landmarks that would assist in
relocation.
• You cannot define a 10km wide anomaly with
a 3 km long profile.
• If you re-sample a contour map along a
profile, you should use a similar density of
points as were present in your original data.
• Modeling:
• Elevation in gravity is critical. If you are unsure of the
location (and thus the elevation), you should not use
that data point. But – ignoring data because you don’t
know the elevation, is not good.
• Use fewer data points in your model than you have
data points. Since a model should SIMPLIFY, your
model should use LESS information than you have in
your data.
• If you use historical data and analyses, you need to
make it very clear how they were used.
• Geological reasonableness is important. How well
your model fits the data is FAR less important than the
reasonableness of the model.
Interpretation:
• Your models may be consistent with your data, and
with previous studies, but you can’t say much more
than that. What would you need to constrain your
models further?
- other types of data
- drilling
- better estimates of rock densities,
elevations
- 3-D modeling
ANALYSIS TOOLS:
Poisson’s Relation: In special situations, the magnetic
potential is related to the gravity potential by the formula:
I dU
V 
; where V is the magnetic potential,
G dw
I is the magnetic intensity,
G is the gravity constant,
 is the density,
and
dU
is the derivative of the gravity potential
dw
in the direction of magnetization.
Poisson’s relation states that a uniformly magnetized body
will generate a magnetic anomaly that has the shape of the
the derivative of the gravity anomaly (when the earth’s field
is vertical).
More importantly, if we can calculate the GRAVITY potential,
we can EASILY obtain the MAGNETIC potential, and thus
the magnetic anomaly, for a body with uniform
magnetization.
Recall that the
acceleration of gravity is
perpendicular to
equipotential surfaces.
The magnetic potential is
proportional to the change
in gravity potential in the
direction of the earth’s
magnetic field.
Take the SPHERE, for example. In gravity, we noted
that the potential of a sphere is exactly the same as if
all the mass were concentrated at the center of the
sphere. This makes calculating the MAGNETIC
potential very easy.
In fact, in ANY forward modeling problem, where we
calculate the gravity potential on the way to obtaining a
gravity anomaly, it is a QUICK step to compute the
magnetic anomaly also.
This is the way that GMSys calculates the gravity and
magnetic anomalies.
This does NOT imply that gravity anomalies will look like
magnetic anomalies, since the DERIVATIVE in Poisson’s
relation is in the direction of magnetization (the direction of
the earth’s field for induced anomalies). At the magnetic
poles, the magnetic anomaly will have the shape of the
vertical derivative of the gravity anomaly, but elsewhere
they will look different.
UPWARD AND DOWNWARD CONTINUATION: Useful in
gravity and magnetics, the idea is to apply a "filter" that will
make the data look as though it was taken at a different
elevation - higher or lower. Downward continuation can be
used to determine the maximum possible depth of the
source of an anomaly.
Probably the best known use for magnetic surveying is in marine
magnetics and the identification of the magnetic stripes on the ocean
floor. Let’s look how they might form:
First, making observations at the magnetic equator:
Anomaly boundary between a positive anomaly (earth’s field same as
today when formed) to the north and a negative anomaly to the south
(earth’s field reversed when formed):
Map
Cross sect ion
B
B
A
up
ocean
N
sediment
magnet ized crust
A
He
The boundary will be a negative pole, thus lines of force will look
like the following:
Cro ss sect ion
He
B
A
up
ocean
sediment
magnet ized c rust
And the total field anomaly will be:
Cro ss sect ion
He
B
A
up
ocean
sediment
magnet ized crust
+
REDUCTION TO THE POLE: Because
magnetic anomalies depend not only on
the shape and orientation of the
magnetic body in question, but on the
magnetic latitude of the region, it is
often desirable to apply a function that
will change the anomalies so that they
appear as though they were observed at
the magnetic pole. In this way, skewed
anomalies from symmetric bodies,
become symmetric themselves.
+
+
+
+
-
INVERSE MODELING: Prior information is used to
constrain parameters that are used to construct a
model directly from the data.
In both forward and inverse modeling, care must be
taken not to place great confidence in the validity of
the models. Good models provide insight that
should be consistent with reality, but, particularly in
potential field geophysics, non-uniqueness tells us
that there are other models just as good.
Monte Carlo methods: These methods of modeling
use random values of parameters within acceptable
limits to generate very large numbers of possible
models. These models are compared with
observations, and those models that provide
synthetic observations that are within the possible
errors of the observations are considered
reasonable.
These methods, when applied carefully, provide
realistic bounds on possible structures that could
yield the observations, with the advantage of not
being biased by prior prejudices.
For example, you might take take a grid model and
allow the susceptibilities to vary randomly within
limits in the grid. For each selection of
susceptibilities, the resulting model results are
compared with your field data. If the errors are
within some fixed limits, the model is deemed
acceptable, and another model is tried. VERY
many models are run (tens of thousands) and the
resulting set of acceptable models is studied.
MAGNETIC SURVEY INTERPRETATION
Magnetic anomalies are often very complex and difficult to interpret
for the following reasons:
1) While we are usually after the shape and depth of an anomalous
body, we also need to be concerned with
the direction of the earth’s field
the strength of the earth’s field
the orientation of the body with respect to the earth’s field
2) There are no unique answers:
There are an infinite number of models that will satisfy the
magnetic field, BUT the characteristics of the anomaly and constraints
from other information can remove an infinite number of possibilities.
3) While we often assume that an anomaly is generated by induced
magnetism, remanant magnetism can also contribute.
4) We also often assume that the susceptibility in a body is uniform,
but that is also likely to be a poor assumption. Pockets of high
susceptibility can greatly distort an anomaly.
USES:
Depth to basement
Ore bodies
Structural trends
Archeological surveys
Detection of voids
Well logging
Marine magnetics
Roman
encampment,
England
unexploded ordnance
Determining depth to bodies:
For relatively simple bodies, determine the distance between the
half-maximum anomaly points (Zamax), then:
Sphere and horizontal cylinder:
depth to center ~ Zamax/2
Semi-infinite sheet:
depth ~ 1/2 distance between maximum and
minimum of anomaly
Zamax
Zamax/2
While these relationships are useful for rough approximations,
modern analysis is done using computer modeling, such as with
GmSys, and with 3-D software that allows estimates of structure
using fixed constraints – such as a single layer below the surface
with constant depth and varying susceptibility, or fixed
susceptibility and varying depth.
With software such as GmSys it is easy to generate models of
various geometries at the magnetic latitude of interest and then vary
the depth for comparison with data.