Environmental and Exploration Geophysics I

tom.h.wilsontom.wilson@mail.wvu.edu

Department of Geology and GeographyWest Virginia University

Morgantown, WV

Magnetic Magnetic Methods (I)Methods (I)

http://www.geo.wvu.edu/~wilson/geo252/lect12/mag2.pdf

Anomaly associated with buried metallic materials

Bedrock configuration determined from gravity survey

Results obtained from inverse modeling

Computed magnetic field produced by bedrock

Where are the drums and how many are there?

Locating Trench Boundaries

Theoretical modelExamination of trench for internal magnetic anomalies. actual field data

Gilkeson et al., 1986

Trench boundaries - field data

Trench Boundaries - model dataGilkeson et al., 1986

Locating abandoned wells

From Martinek

Abandoned Wells

From Martinek

Abandoned Well - raised relief plot of measured magnetic field intensities

Falls Run Coal Mine Refuse Pile Magnetic Intensity

Wire Frame

Gochioco and Ruev, 2006

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Magnetic monopoles

1 212 2

12

1

4m

p pF

r p1

p2

r12Fm12 Magnetic Force Magnetic Permeability

p1 and p2 pole strengthsCoulomb’s Law

1 212 2

12

1

4m

p pF

r

2

1

4o o

ot

F pH

p r

Force

Magnetic Field Intensity often written

as H

pt is an isolated test pole

2

1" "

4E

Et

pFF

p r

The text uses F instead of H to represent magnetic field intensity, especially when referring to that of the Earth (FE).

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

monopole vs.

dipole

Toxic Waste

The earth’s main magnetic field

Steve Sheriff’s Environmental Geophysics Course

Proton Precession Magnetometers

Tom Boyd’s Introduction to Geophysical Exploration Course

Measuring the Earth’s magnetic field

Source of Protons and DC current source

Proton precession generates an alternating current in the surrounding coil

22

GFF

L

Mf

Proton precession frequency (f) is directly proportional to the main magnetic field intensity F. L is the angular momentum of the proton and G is the gyromagnetic ratio which is a constant for all protons (G = 0.267513/ sec). Hence -

fF 4874.23

Magnetic Elements

Magnetic north pole: point where field lines point vertically downward

Geomagnetic north pole: pole associated with the dipole approximation of the earth’s magnetic field.

The compass needle points to

the magnetic north pole.

Date

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Magnetic Elements for your location

Today’s Space Weather

Magnetic Field Variations

Long term drift in magnetic declination and inclination

Magnetic field variations generally of non-geologic origin

Magnetic fields like gravitational fields are not constant. Their variations are much more erratic and unpredictable

http://www.earthsci.unimelb.edu.au/ES304 /MODULES/ MAG/NOTES/tempcorrect.html

Diurnal variations

Today’s Space Weather

Real Time Magnetic field data

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 the anomalies we observed at the Falls Run site are of 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 at Falls Run would have been about 1/2 nT from one end of the site to the other.

International geomagnetic reference formula

The single most important correction to make is one that compensates for diurnal variations, micropulsations and magnetic storms. This is usually done by reoccupying a base station periodically throughout the duration of a survey to determine how total field intensity varies with time and to eliminate these variations in much the same way that tidal and instrument drift effects were eliminated from gravity observations.

Anomalies - Total Field and Residual

The regional field can be removed by surface fitting and line fitting procedures identical to those used in the analysis of gravity data.

Magnetic susceptibility is a key parameter, however, it is so highly variable for any given lithology that estimates of k obtained through inverse modeling do not necessarily indicate that an anomaly is due to any one specific rock type.

Opposites attract

S

N

S

N

SN

Magnetic fields are fundamentally associated with circulating electric currents; thus we can also formalize concepts like pole strength, dipole moment, etc. in terms of current flow relationships.

pl = n iA+

-

l

n turns

Cross sectional area A

pl is the dipole moment

Units of pole strength

niAp ampere meter

l

I=kF

EkFI

I is the intensity of magnetization and FE is the ambient (for example - Earth’s) magnetic field intensity. k is the magnetic susceptibility.

The intensity of magnetization is equivalent to the magnetic moment per unit volume or

V

MI

and also, EkFI . Thus

M plI

V V E

pkF

Aand yielding

Ep kAF

Magnetic dipole moment per unit volume

M plwhere

The cgs unit for pole strength is the ups

Ep kAF

Recall from our earlier discussions that magnetic field intensity

2 or

pH F

r

2p Fr

so that

Thus providing additional relationships that may prove useful in problem solving exercises.

2r

AkFF EFor example,

What does this tell us about units of these different quantities?

2 2 (or )

p upsH F

r cm

We refer to the magnetic field intensity as H or, more ambiguously, as F

Force

pole strength

dyneH

ups

1 an Oersted

dyne

ups

2thus 1 Oersted 1

ups

cm

2 2 yields Oersted-cmp Fr p

5Note also that 1 Oersted = 10

&

1 nT = 1

nT

Force varies inversely as the square of the distance between charges, masses or poles. It has the general form

221

r

mmF

drr

mmFdrV

221

Potential on the other hand refers to the energy available to do work and is the integral of the force times displacement.

What is this integral?

drr

mmFdrV

221

Remember the general power rule for integration

Crn

drr nn

1

1

1

Since n is -2, n+1 = -1 so that the potential V (per unit pole) is simply

r

m

r

mV

As we have done repeatedly with the force, we divide it by unit mass, charge or pole to obtain

2""

r

mF an acceleration, electric or magnetic field intensity.

Doing the same with the potential yields a potential per unit pole strength, or just

Most importantly, working with potentials offers us some simplification since the denominator is in r and not r2. It offers

useful simplification when characterizing the dipole field.

Basic Magnetic Unit and Vector Concepts

Problem - At a point 20 cm from the center of a thin magnetized rod 40 cm long and equidistant from its ends, the magnetic field is 500 nT. What is the pole strength in Oersted-cm2?

Sign conventions imply that the test pole is positive.

HR=2Hx=500nT

UNITS - nanoteslas, ups, Oersteds …..

105

HRX = 500nT

x

Given 2

what is H ?R xH H

Then, what is H+ or H-? Once we know this, we can then determine the pole strength.

H = p/r2

so p = Hr2

Bring questions to class Tuesday after Thanksgiving break –

November 28th

We will meet in the 310