Tom Wilson, Department of Geology and Geography Environmental and Exploration Geophysics I tom.h.wilson Department of Geology and Geography West Virginia University Morgantown, WV Magnetic Methods (II)

Objectives for the day Tom Wilson, Department of Geology and Geography Magnetic materials Brief review magnetic field components Corrections? Do we need them? Sign conventions and units The potential field The dipole field The vertical gradient of the dipole field Problems to do from Chapter 7 Wrapping up the gravity lab

Magnetic materials & magnetic domains Tom Wilson, Department of Geology and Geography 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.

Tom Wilson, Department of Geology and Geography 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 Tom Wilson, Department of Geology and Geography

Tom Wilson, Department of Geology and Geography Long term drift in magnetic declination and inclination Magnetic field variations are generally of non-geologic origin

Declination Tom Wilson, Department of Geology and Geography

Changes per day are small, but change over the year quite significant Tom Wilson, Department of Geology and Geography Last Thursday Today Small change in field strengths of about ½ nT

Variations in the Earth’s Magnetic field Tom Wilson, Department of Geology and Geography

Magnetic reversals Tom Wilson, Department of Geology and Geography Reversals are quite infrequent occuring on average about once every 250,000 yrs.

Tom Wilson, Department of Geology and Geography Normal dipolar field Field Between Reversals

Tom Wilson, Department of Geology and Geography Solar activity and sunspot cycles Nov. 30 th 2010 Nov. 28 th 2011 Nov. 19 th 2013

Corrections Tom Wilson, Department of Geology and Geography Magnetic fields like gravitational fields are not constant. However, magnetic field variations are much more erratic and unpredictable /MODULES/ MAG/NOTES/tempcorrect.html Diurnal variations

Short term fluctuations Tom Wilson, Department of Geology and Geography

Short term micropulsations Tom Wilson, Department of Geology and Geography Today’s Space Weather Real Time Magnetic field data Real Time Magnetic field data

Tom Wilson, Department of Geology and Geography From the Advanced Composition Explorer Satellite

Tom Wilson, Department of Geology and Geography 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 ( nT/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

Tom Wilson, Department of Geology and Geography 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

Tom Wilson, Department of Geology and Geography 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 Tom Wilson, Department of Geology and Geography The Earth’s main field S N The induced magnetic field of a metallic drum The induced field opposes the main field

The dipole field and sign conventions Tom Wilson, Department of Geology and Geography SN

Dipole fields and current flow Tom Wilson, Department of Geology and Geography pl = n iA + - l n turns Cross sectional area A pl is the dipole moment 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 Tom Wilson, Department of Geology and Geography I=kF I is the intensity of magnetization and F E is the ambient (for example - Earth’s) magnetic field intensity. k is the magnetic susceptibility.

Tom Wilson, Department of Geology and Geography The intensity of magnetization is equivalent to the magnetic moment per unit volume or and also,. Thus and yielding Magnetic dipole moment per unit volume where The cgs unit for pole strength is the ups

Tom Wilson, Department of Geology and Geography Recall from our earlier discussions that magnetic field intensity so that Thus providing additional relationships that may prove useful in problem solving exercises. For example,

H (or F via Berger et al.) can be expressed in two forms Tom Wilson, Department of Geology and Geography We refer to the magnetic field intensity as H (or as in Burger et al., F)

Tom Wilson, Department of Geology and Geography From above, we obtain a basic definition of the potential (at right) for a unit positive test pole (m t ). The potential is the integral of the force (F) over a displacement path. Note that we consider the 1/4  term =1

Tom Wilson, Department of Geology and Geography Thus - H (i.e. F/p test, 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

Tom Wilson, Department of Geology and Geography 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.

Tom Wilson, Department of Geology and Geography 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.

Tom Wilson, Department of Geology and Geography r-r- r+r+ r Determine r+ and r-

Tom Wilson, Department of Geology and Geography 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 Working with the potentials of both poles..

Tom Wilson, Department of Geology and Geography Converting to common denominator yields From the previous discussion, the field intensity H is just where pl = M – the magnetic moment

Tom Wilson, Department of Geology and Geography H - monopole = H - dipole 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 Tom Wilson, Department of Geology and Geography We’ll discuss solutions to these problems on Thursday …

The general report format to be followed for the gravity lab Tom Wilson, Department of Geology and Geography 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.

Tom Wilson, Department of Geology and Geography 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.

Tom Wilson, Department of Geology and Geography 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 Tom Wilson, Department of Geology and Geography 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’) Tom Wilson, Department of Geology and Geography 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 Tom Wilson, Department of Geology and Geography 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.

Tom Wilson, Department of Geology and Geography Items on the list …. Magnetics papers are in the mail room Gravity lab is due this Thursday November 21 st (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 5 th and December 10 th. Final is from 3-5pm on December 13 th.

Regular section submissions Tom Wilson, Department of Geology and Geography All those in the regular section submit paper copies of your paper summaries and lab reports.

Writing Section reminders (electronic submissions only) Tom Wilson, Department of Geology and Geography The gravity lab is self reviewed and is due this Thursday, November 21 st. 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 Tom Wilson, Department of Geology and Geography