Environmental and Exploration Geophysics Ipages.geo.wvu.edu/~wilson/geol454/lect13/mag2.pdf ·...

Tom Wilson, Department of Geology and Geography

Environmental and Exploration Geophysics I

tom.h.wilson

[email protected]

Department of Geology and Geography

West Virginia University

Morgantown, WV

Magnetic Methods (II)


Reminders

• Gravity lab due today

• Writing section – Essay II final draft due Friday, 18th by noon

• Keep reading Chapter 7 on Magnetics.

• Problems 7.1, 2 and 3 due this Thursday

• We’ll get started on the magnetics lab today - due date Dec 1st.

• Additional problems 4 and 5 will be distributed this Thursday.

They will be due Dec. 1st.

Wrap up magnetic methods Dec 1st. We may have time for some exam review on the 1st. Dec. 6th class will be devoted to review.

The final is scheduled Wednesday, December 14th from 11am-1pm in rm 325 Brooks.

Problem 6.9


What is gmax on the

red curve?

gmax= 0.45mGals

What is X1/2?

Ideas to familiarize yourself with in reading Chapter 7


• Magnetic materials

• Corrections

• Sign conventions and units

• The potential field

• The dipole field

• Vertical and horizontal gradients of the

dipole field

• Problems to do from Chapter 7

• Intro to magnetics lab

Magnetic materials & magnetic domains


Ferromagnetic materials (iron,

nickel and cobalt) have very

high susceptibility.

Anti-ferromagnetic materials

have very low susceptibilities

(ex. hematite).

Ferrimagnetic minerals such

as magnetite, ilmenite and

pyrrhotite are the common and

produce a lot of the naturally

occurring magnetic anomalies.

Corrections


Magnetic fields like gravitational fields are not constant.

However, magnetic field variations are much more erratic and unpredictable

http://www.earthsci.unimelb.edu.au/ES304

/MODULES/ MAG/NOTES/tempcorrect.html

Diurnal variations

Short term fluctuations


http://en.wikipedia.org/wiki/File:Animati3.gif

//upload.wikimedia.org/wikipedia/commons/f/f2/Animati3.gif

//upload.wikimedia.org/wikipedia/commons/f/f2/Animati3.gif

Short term micropulsations


Today’s Space Weather

http://www.swpc.noaa.gov/today.html

Real Time Magnetic field data

http://www.swpc.noaa.gov/ace/ace_rtsw_data.html

http://www.sec.noaa.gov/today.html

http://www.swpc.noaa.gov/ace/ace_rtsw_data.html


In general there are few corrections to apply to magnetic data. The

largest non-geological variations in the earth’s magnetic field are those

associated with diurnal variations, micropulsations and magnetic

storms.

The vertical gradient of the vertical component of the earth’s magnetic

field at this latitude is approximately 0.025nT/m. This translates into

1nT per 40 meters. The magnetometer we have been using in the field

reads to a sensitivity of 1nT and anomalies of interest to us may be on

the order of 200 nT or more. Hence, elevation corrections are generally

not needed.

Variations of total field intensity as a function of latitude are also

relatively small (0.00578nT/m). The effect over 80 m NS distance

would about 1/2 nT, and over a kilometer, about 5.8 nT (increase to the

north. International geomagnetic reference formula

http://www.ngdc.noaa.gov/IAGA/vmod/igrf.html

http://www.ngdc.noaa.gov/IAGA/vmod/igrf.html

Another correction important in the regional

survey removal of the regional field


The regional field can be removed by

surface fitting and line fitting

procedures identical to those used in

the analysis of gravity data.

The efforts that Stewart undertook to eliminate the regional field from his data

may be very appropriate to magnetic field data analysis and modeling

Some basic relationships


The Earth’s main fieldS

N

The induced magnetic

field of a metallic drum

The induced field

opposes the main field

The dipole field and sign conventions

upward pointing field lines are negative


SN


objectpV

r

From above, we obtain a

basic definition of the

potential (at right) for a unit

positive test pole (pt).

1 2

2

p pV Fdr dr

r

The potential is the integral of the

force (F) over a displacement path.

Note that we consider

the 1/4 term =1


2

dV pH

dr r

Thus - H (i.e. F/ptest, the field

intensity) can be easily derived from

the potential simply by taking the

negative derivative of the potential

The reciprocal relationship between

potential and field intensity


Consider the case where the distance to the center of the dipole is much

greater than the length of the dipole. This allows us to treat the problem

of computing the potential of the dipole at an arbitrary point as one of

scalar summation since the directions to each pole fall nearly along

parallel lines.


cos cos2 2

dipole

p pV

l lr r

Converting to common denominator yields

2

cosdipole

plV

r

From the previous discussion , the field intensity H is just

dr

dV

dr

dVFFdrV , since

where pl = M – the

magnetic moment

Vertical derivative


2

cosddV d pl

dr dr r

ZE - dipole =

3

2 cospl

r

This yields the field intensity in the radial direction - i.e. in the direction

toward the center of the dipole (along r). This is just the vertical

component of the total field. We can also do this to obtain the horizontal

component of the Earth’s magnetic field intensity.

Horizontal field intensity


1d ddV dV

dS r d

Think about where this operator comes from

r

d dS

Main field components vary with colatitude


2

cosdE

dV d plZ

dr dr r

Vd represents the

potential of the dipole.

FE or H

Toward dipole

center (i.e. center of

Earth’s dipole field


2

cosd pl

rd r


3

sin

r

MH

ds

dVE

Where M = pl

and

3

cos2

r

M

dr

dVZE

Let’s tie these results back into some

observations made earlier in the semester

with regard to terrain conductivity data.


3

sin

r

MHE

Given

What is HE at the equator? … first what’s ?

is the angle formed by the line connecting the

observation point with the dipole axis. So , in

this case, is a colatitude or 90o minus the

latitude. Latitude at the equator is 0 so is 90o

and sin (90) is 1.

3r

MHE


0EH

At the poles, is 0, so that

What is ZE at the equator?

3

cos2

r

MZE

is 90

0EZ


ZE at the poles ….

3

cos2

r

MZE

3

2

r

MZE

The variation of the field intensity at the poles and

along the equator of the dipole may remind you of

the different penetration depths obtained by the

terrain conductivity meters when operated in the

vertical and horizontal dipole modes.

Problem 7.1


What is the horizontal gradient of the Earth’s magnetic

field (ZE) …

The horizontal gradient is just the horizontal

derivative, used to calculate the horizontal field,

accept, there is no negative sign

Horizontal gradient is E EdZ dZ

dS rd

Horizontal component of the Earth’s magnetic field HE is

dV dV

dS rd

Problem 7.1


3

sin Thus

r

MHE

3

cos2

r

M

dr

dVZE

2

cosE

dV dV d plH

ds rd rd r

1 d

r d

The relationship between the potential and

field intensity requires use of the minus sign.

However, no minus sign is required when computing

the derivative or gradient

Again – just take the simple derivative to get

the gradient (no negative sign)


To answer this problem we must evaluate the

horizontal gradient of the vertical component -

1E

dZ

r dor

3

1 2 cosd M

r d r

Take a minute and give it a try.

Problem 7.2


dipole

p pV

r r

Recognizing that pole strength of the

negative pole is the negative of the positive

pole and that both have the same absolute

value, we rewrite the above as

dipole

p pV

r r

Return to the simpler formulation of

the potential as the sum of potentials

from two poles

surface

r-

r+

A simple geometrical approximation for “back of the

envelope” computations … Can you detect the wall?


7.3 A buried stone wall constructed from volcanic rocks has

a susceptibility contrast of 0.001cgs emu with its enclosing

sediments. The main field intensity at the site is 55,000nT.

Determine the wall's detectability with a typical proton

precession magnetometer. Assume the magnetic field

produced by the wall can be approximated by a vertically

polarized horizontal cylinder. Refer to figure below, and see

following formula for Zmax.

Background noise at

the site is roughly 5nT.

Magnetic effects of simple geometric shapes


In-depth discussions of simple geometrical objects are

presented on pages 456 to 482.

For our purposes, however, we will avoid the heavy math

and consider the general usage of half-max relationships in

a manner similar to that developed for the analysis of

gravitational fields produced by simple geometrical

objects using diagnostic positions and depth index

multipliers.

The following problems illustrate some uses of these

ideas.

Archaeological application


Vertically Polarized Horizontal Cylinder

2

max 2

2 R IZ

z

Maximum field strength

2

2

2

2

2

2

2

1

12

zx

zx

z

IRZ

2

2

2

2

2

max 1

1)(

zx

zx

Z

xZ

General form Normalized shape term

Remember this kind of formulization used in gravity

The wall in problem 7.3 is better approximated

by the horizontal cylinder


2

max 2

2 R IZ

z

Maximum field strength

EI kF

k = 0.001, FE= 55,000 nT

Approximate cross sectional area of rectangular

wall in circular form and solve for R: i.e. wallAR

Cross sectional area of wall = 1m x 0.5m

Lastly – what is z?

What is R?k=0.001 0.5m

1.0m

1.5mk=0

recall

Problem 7.3 in-class group problem/discussion


Bring up GM-SYS – Magnetics lab part 1


Anomaly associated

with buried metallic

materials

Bedrock configuration

determined from gravity

survey

Results obtained

from inverse

modeling

Computed magnetic

field produced by

bedrock


Reminders

• Gravity lab due today

• Writing section – Essay II final draft due Friday, 18th by noon

• Keep reading Chapter 7 on Magnetics.

• Problems 7.1, 2 and 3 due this Thursday

• We’ll get started on the magnetics lab today - due date Dec 1st.

• Additional problems 4 and 5 will be distributed this Thursday.

They will be due Dec. 1st.

Wrap up magnetic methods Dec 1st. We may have time for some exam review on the 1st. Dec. 6th class will be devoted to review.

The final is scheduled Wednesday, December 14th from 11am-1pm in rm 325 Brooks.

Environmental and Exploration Geophysics Ipages.geo.wvu.edu/~wilson/geol454/lect13/mag2.pdf ·...

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