Environmental and Exploration Geophysics I

Tom Wilson, Department of Geology and Geography

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

Department of Geology and GeographyWest Virginia University

Morgantown, WV

Magnetic Methods Magnetic Methods (II)(II)

Objectives for the day

Magnetic materialsBrief review magnetic field componentsCorrections? Do we need them?Sign conventions and unitsThe potential fieldThe dipole fieldThe vertical gradient of the dipole fieldProblems to do from Chapter 7Wrapping up the gravity 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.

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.

The vector components of the Earth’s magnetic field

http://en.wikipedia.org/wiki/File:XYZ-DIS_magnetic_field_coordinates.svg

Long term drift in magnetic declination and inclination

Magnetic field variations are generally of non-geologic origin

Declination - 2010

http://en.wikipedia.org/wiki/File:World_Magnetic_Declination_2010.pdf

Changes per day are small, but change over the year quite significant

Last Thursday

Small change in field strengths of about ½ nT

Variations in the Earth’s Magnetic field

http://en.wikipedia.org/wiki/File:Magnetic_North_Pole_Positions.svg

Magnetic reversals

Reversals are quite infrequent occuring on

average about once every 250,000 yrs.

http://www.pbs.org/wgbh/nova/magnetic/timeline.html

http://www.es.ucsc.edu/~glatz/geodynamo.html

Normal dipolar field

Field Between Reversals

Solar activity and sunspot cycles

Nov. 30th 2010 Nov. 28th 2011Nov. 19th 2013

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

Short term micropulsations

Today’s Space Weather

http://www.swpc.noaa.gov/today.htmlReal Time Magnetic field data

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

http://www.swpc.noaa.gov/ace/ace_rtsw_data.htmlFrom the Advanced Composition Explorer Satellite

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 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

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.

Reoccupy a base station at frequent intervals

Other corrections? Total Field versus Residual

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

The induced magnetic field of a metallic drum

The induced field opposes the main field

The dipole field and sign conventions

Dipole fields and current flow

pl = n iA+

n turns

Cross sectional area A

pl is the dipole moment

Units of pole strength

niAp ampere meter

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.

The response of magnetic materials to changes in the ambient magnetic field

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

and also, EkFI . Thus

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

so that

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

AkFFH EFor example,

H (or F via Berger et al.) can be expressed in two forms

2 2 (or )

p upsH F

We refer to the magnetic field intensity as H (or as in Burger et al., F)

pole strength

1 an Oersted

2thus 1 Oersted 1

2 2 yields Oersted-cmp Fr p

5Note also that 1 Oersted = 10

1 nT = 1

objectpV

From above, we obtain a basic definition of the potential (at right) for a unit positive test pole (mt).

p pV Fdr dr

The potential is the integral of the force (F) over a displacement path.

Note that we consider the 1/4 term =1

Thus - H (i.e. F/ptest, the field intensity) can be easily derived from the potential simply by taking the 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.

If r is much much greater than l (distance between the

poles) then the angle between r+ and r- approaches 0

and r, r+ and r- can be considered parallel so that the

differences in lengths r+ and r- from r equal to plus or

minus the projections of l/2 into r.

Determine r+ and r-

dipole

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

Working with the potentials of both poles ..

cos cos2 2dipole

l lr r

Converting to common denominator yields

cosdipole

From the previous discussion , the field intensity H is just

dVFFdrV , since

where pl = M – the magnetic moment

pdV d p p

dr dr r r

H - monopole =

cosddV d pl

dr dr r

H - dipole

2 cospl

This yields the field intensity in the radial direction - i.e. in the direction toward the center of the dipole (along r). However, we can also evaluate the horizontal and vertical components of the total field directly from the potential.

Look over problems 7.1, 2 and 3

We’ll discuss solutions to these problems on Thursday …

The general report format to be followedfor the gravity lab

Abstract: a brief description of what you did and the results you obtained (~200 words).Background: Provide some background on the data we’re analyzing. All of this would come from Stewart’s paper. Explain his approach and answer question 1 below in this section to illustrate his approach.Results: Describe how you tested the model proposed by Stewart along XX’. Include answers to questions 2 through 4 below in this discussion.Conclusions: Summarize the highlights of results obtained in the forgoing modeling process.

1. The residual gravity plotted in Figure 5 of Stewart's paper (also see illustrations in this lab exercise) has both positive and negative values. Assume that an anomaly extends from +2milligals to -2 milligals. Use the plate approximation (i.e. Stewart’s formula) and estimate the depth to bedrock? What do you need to do to get a useful result? Residuals of any kind usually fluctuate about zero mean value. What would you guess Stewart must have done to the residual values before he computed bedrock depth?

In your write-up answer the following questions and refer to them by number for identification.

Remember that Stewart’s use of the plate formula t=130g assumes g is always negative as it should be since the density contrasts his two-layer model are negative and yield negative anomalies. So to use that formula you would have to shift anomalies such as those shown at right into the negative.

2. At the beginning of the lab you made a copy of GMSYS window showing some disagreement between the observations (dots) and calculations (solid line) across Stewart's model (section XX' Figure 7). As we did in class and in the lab manual, note a couple areas along the profile where this disagreement is most pronounced, label these areas in your figure for reference. In your lab report discussion offer an explanation for the cause(s) of these differences? Assume that the differences are of geological origin and not related to errors in the data.

In your write-up answer the following questions and refer to them by number for identification.

See lab manual

Where do you see obvious disagreement and what did you have to do to get rid of it? Recall first gravity lab.

Just remember – valleys don’t have infinite extent – infinite plates do

3. With a combination of inversion and manual adjustments of points defining the till/bedrock interface, you were able to eliminate the significant differences between observed and calculated gravity. Your model is incorrect though since the valleys do not extend to infinity in and out of the cross section. Use the 2 ¾ modeling option to reduce the extents of the valleys in and out of the section to 800 feet. Make the changes to the Y+ and Y- blocks and then apply. Take a screen capture to illustrate the reduction in g associated with the glacial valleys. Make a screen capture of this display showing the new calculation line and the dashed gray values associated with the infinite valleys. Include this figure in your report and discuss your results.

Valleys are not infinite plates and Stewart’s cross section (as taken from his paper) did not quite explain the variations in gravity anomaly

observed along the section line (XX’)

4. Use Stewart's formula t = 130g and estimate the depth to bedrock at the x location of ~7920 feet along the profile. Does it provide a reliable estimate of bedrock depth in this area? Explain in your discussion.

5. Lastly, describe the model you obtained and comment on how it varies from the starting model taken from Stewart.

Use the preceding questions to guide your discussion & number them in your lab report discussion

These questions provide discussion points in your lab report. Use figures you've generated in GMSYS to illustrate points you want to make. All figures should be numbered, labeled and captioned.

Items on the list ….

• Magnetics papers are in the mail room

• Gravity lab is due this Thursday November 21st (writing section submission is self-reviewed showing track changes).

• Keep reading Chapter 7.

• Magnetic problems due next Thursday

• We will have two final exam review sessions: December 5th and December 10th.

• Final is from 3-5pm on December 13th.

Regular section submissions

All those in the regular section submit paper copies of your paper summaries

and lab reports.

Writing Section reminders(electronic submissions only)

• The gravity lab is self reviewed and is due this Thursday, November 21st.

All those in the writing section submit their papers and lab electronically. Don’t forget to turn on track changes while doing your self-review. Only submit the self-reviewed file.

What’s coming up?Some due date reminders

Environmental and Exploration Geophysics I

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