GG 450 Feb 21, 2008

Magnetic Interpretation

Homework return

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 susceptibility

sedimentary 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.

Magnetic Anomaly Map Bedrock Geology Map

Minnesota

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.

Today’s field

Field when seamountwas formed

Field when oceancrust 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:

€

V = −I

ρG

dU

dw; where V is the magnetic potential,

I is the magnetic intensity,

G is the gravity constant,

ρ is the density,

and dU

dw is the derivative of the gravity potential

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):

M a p

A

BC r o s s s e c t i o n

AB

N

He

o c e a n

s e d i m e n t

m a g n e t i z e d c r u s t

u p

The boundary will be a negative pole, thus lines of force will look like the following:

C r o s s s e c t i o n

AB

He

o c e a n

s e d i m e n t

m a g n e t i z e d c r u s t

u p

And the total field anomaly will be:

C r o s s s e c t i o n

AB

He

o c e a n

s e d i m e n t

m a g n e t i z e d c r u s t

u p

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 field2) 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 basementOre bodiesStructural trendsArcheological surveysDetection of voidsWell loggingMarine 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.