Magnetic Methods (III)

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

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

Tom Wilson, Department of Geology and Geography
Magnetic Field Variations – annual drift of the magnetic pole Tom Wilson, Department of Geology and Geography

Diurnal variations in the Earth’s Magnetic field
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 Diurnal variations /MODULES/ MAG/NOTES/tempcorrect.html Tom Wilson, Department of Geology and Geography

Solar activity and sunspot cycles Nov. 30th 2010 sunspot 1130 Tom Wilson, Department of Geology and Geography

Micropulsations The magnetosphere extends about 6-7 solar diameters in the direction of the sun, possible 1000 times the earth’s radius in the tail. Most of the solar wind particles are heated and slowed at the bow shock and detour around the earth Today’s Space Weather 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

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

Corrections? 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 ( nT/m). The effect over 80 m of elevation would about 1/2 nT. International geomagnetic reference formula Tom Wilson, Department of Geology and Geography

Correcting for Diurnal Variations
Reoccupy the base 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. Tom Wilson, Department of Geology and Geography

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. 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. Tom Wilson, Department of Geology and Geography

+ - The induced magnetic field of a metallic drum N - + F E S The Earth’s main field Tom Wilson, Department of Geology and Geography

Vector Awareness N S Tom Wilson, Department of Geology and Geography

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. + - l n turns Cross sectional area A pl = n iA pl is the dipole moment Tom Wilson, Department of Geology and Geography

I=kF Hysterisis Loops I is the intensity of magnetization and FE is the ambient (for example - Earth’s) magnetic field intensity. k is the magnetic susceptibility. Tom Wilson, Department of Geology and Geography

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

What does this tell us about units of these different quantities?
Summary What does this tell us about units of these different quantities? We refer to the magnetic field intensity as H (or as in Burger et al., F) Tom Wilson, Department of Geology and Geography

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

The reciprocal relationship between potential and field intensity
Thus - H (i.e. F/ptest, the field intensity) can be easily derived from the potential simply by taking the derivative of the potential Tom Wilson, Department of Geology and Geography

The Dipole Field 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. In spite of this special situation, the magnetic field of an object is defined by the simple dipole field or combinations of dipole fields. 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

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

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

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

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

Toward dipole center (i.e. center of Earth’s dipole field
Vd represents the potential of the dipole. Tom Wilson, Department of Geology and Geography

arc - length relationship
HE is represented by the negative derivative of the potential along the earth’s surface or in the S direction. Tom Wilson, Department of Geology and Geography

Evaluating the derivative along the surface
Tom Wilson, Department of Geology and Geography

-dV/dS Tom Wilson, Department of Geology and Geography

Where M = pl and Let’s tie these results back into some observations made earlier in the semester with regard to terrain conductivity data. 32 Tom Wilson, Department of Geology and Geography

The field along the dipole equator
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. Tom Wilson, Department of Geology and Geography

The field at the pole At the poles,  is 0, so that What is ZE at the equator?  is 90 Tom Wilson, Department of Geology and Geography

Field at pole is twice that at the equator
ZE at the poles …. 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. Tom Wilson, Department of Geology and Geography

Consider one of the Lab Questions
…. compare the field of the magnetic dipole field to that of the gravitational monopole field Gravity:500, 1000, 2000m A more rapid decay Increase r by a factor of 4 reduces g by a factor of 16 Tom Wilson, Department of Geology and Geography

A 4 fold increase in distance
For the dipole field, an increase in depth (r) from 4 meters to 16 meters produces a 64 fold decrease in anomaly magnitude Thus the 7.2 nT anomaly (below left) produced by an object at 4 meter depths disappears into the background noise at 16 meters. 0.113 nT 7.2 nT Tom Wilson, Department of Geology and Geography

Some in-class problems for the last week of class
On Tuesday during the last week of class, we’ll work through some problems that will help you review materials we’ve covered on magnetic fields. Some of the problems are not too much different from those we worked for gravitational fields and so will help initiate some review of gravity methods. The first problem relates to our discussions of the dipole field and their derivatives. 7.1 What is the horizontal gradient in nT/m of the Earth’s vertical field (ZE) in an area where the horizontal field (HE) equals 20,000 nT and the Earth’s radius is 6.3 x 108 cm. Tom Wilson, Department of Geology and Geography

Problem 1 Recall that horizontal gradients refer to the derivative evaluated along the surface or horizontal direction and we use the form of the derivative discussed earlier. Tom Wilson, Department of Geology and Geography

To answer this problem we must evaluate the horizontal gradient of the vertical component - or Take a minute and give it a try. Tom Wilson, Department of Geology and Geography

Can you find it? 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. Tom Wilson, Department of Geology and Geography

Magnetic effects of simple geometric shapes
Read over pages 454 to 482 to get a general sense of how simple geometric objects can be used in the interpretation and modeling of magnetic fields. The following problems illustrate some uses of these ideas. Tom Wilson, Department of Geology and Geography

Problem 7.3 Vertically Polarized Horizontal Cylinder Maximum field strength General form Normalized shape term Remember this kind of formulization used in gravity Tom Wilson, Department of Geology and Geography

Detecting abandoned wells
Non text question: In your survey area you encounter two magnetic anomalies, both of which form nearly circular patterns in map view. These anomalies could be produced by a variety of objects, but you decide to test two extremes: the anomalies are due to 1) a concentrated, roughly equidemensional shaped object (a sphere); or 2) to a long vertically oriented cylinder. Tom Wilson, Department of Geology and Geography

Non-text question Vertical Magnetic Anomaly Vertically Polarized Sphere The notation can be confusing at times. In the above, consider H = FE= intensity of earth’s magnetic field at the survey location. As a function of x/z … Tom Wilson, Department of Geology and Geography

Non-text question Vertically Polarized Vertical Cylinder Look familiar? Tom Wilson, Department of Geology and Geography

Non-text question Given that derive an expression for the radius, where I = kHE. Compute the depth to the top of the casing for the anomaly shown below, and then estimate the radius of the casing assuming k = 0.1 and HE =55000nT. Zmax (62.2nT from graph below) is the maximum vertical component of the anomalous field produced by the vertical casing. Tom Wilson, Department of Geology and Geography

Where we started ... Since the bedrock is magnetic, we have no way of differentiating between anomalies produced by bedrock and those ? produced by buried storage drums. Tom Wilson, Department of Geology and Geography

Why gravity? Acquisition of gravity data allows us to estimate variations in bedrock depth across the profile. With this knowledge, we can directly calculate the contribution of bedrock to the magnetic field observed across the profile. Tom Wilson, Department of Geology and Geography

Introduction to the magnetics computer lab Anomaly associated with buried metallic materials Bedrock configuration determined from gravity survey Results obtained from inverse modeling Computed magnetic field produced by bedrock Tom Wilson, Department of Geology and Geography

Beware of the flattened drum solution
non-uniqueness Magnetics lab, part 2: A perfect fit – but is it correct? Beware of the flattened drum solution Tom Wilson, Department of Geology and Geography

Let’s continue with the second part of the magnetics lab Where are the drums and how many are there? Tom Wilson, Department of Geology and Geography

The road ahead Questions? Next week will be spent in review
Problems discussed in class today will be due next week. We will be going over them as in-class problems, but you will be graded on them as usual. Magnetics paper summaries are due this Thursday December 2nd Magnetics lab is due next Thursday, December 9th Exam, Friday December 17th; 3-5pm Questions? Tom Wilson, Department of Geology and Geography

Magnetic Methods (III)

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