Environmental and Exploration Geophysics I Magnetic Methods IV

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

Vertically polarized sphere or dipole Vertically polarized vertical cylinder Vertically polarized horizontal cylinder Tom Wilson, Department of Geology and Geography

Vertically polarized sphere or dipole Vertically polarized vertical cylinder Vertically polarized horizontal cylinder Tom Wilson, Department of Geology and Geography

We measure the distances (x) to the various diagnostic positions and then convert those x’s to z’s using the depth index multipliers which are just the reciprocal of the x/z values at which the anomaly drops to various fractions of the total anomaly magnitude. Tom Wilson, Department of Geology and Geography

is a function of the unit-less variable x/z Dipole/sphere Vertical cylinder Horizontal cylinder The vertical field is often used to make a quick estimate of the magnitude of an object. This is fairly accurate as long as i is 60 or greater Tom Wilson, Department of Geology and Geography

For these three magnetic objects, the anomalies associated with the sphere and horizontal cylinder both drop off to 1/2 their maximum value at X = ½ the depth Z X/Z Vertical Cylinder Sphere Horizontal Cylinder X 3/4 0. 46 0. 315 0. 31 X 1/2 0. 766 0. 5 0. 495 X 1/4 1. 23 0. 73 0. 68 Depth Index Multipliers Vertical Cylinder Sphere Horizontal Cylinder X 3/4 2. 17 3. 18 3. 23 X 1/2 1. 305 2 2. 02 X 1/4 0. 81 1. 37 1. 47 The vertical cylinder behaves like a magnetic monopole. Tom Wilson, Department of Geology and Geography

The map view clearly indicates that consideration of two possible origins may be appropriate - sphere or vertical cylinder. Tom Wilson, Department of Geology and Geography

In general one will not make such extensive comparisons. You may use only one of the diagnostic positions, for example, the half-max (X 1/2) distance for an anomaly to quickly estimate depth if the object were a sphere or buried vertical cylinder…. Burger limits his discussion to half-maximum relationships. X 1/2 = Z/2 X 1/2 = 0. 77 Z X 1/2 = Z/2 Breiner, 1973 Tom Wilson, Department of Geology and Geography

Remember how the proton precession magnetometer works. Protons precess about the earth’s total field with a frequency directly proportional to the earth’s field strength The proton precession magnetometer measures the scalar magnitude of the earth’s main field. Tom Wilson, Department of Geology and Geography

The gradient is just the rate of change in some direction - i. e. it’s just a derivative. How would you evaluate the vertical gradient of the vertical component of the earth’s magnetic field? Tom Wilson, Department of Geology and Geography

The vertical gradient is just the variation of ZE with change in radius or distance from the center of the dipole. Tom Wilson, Department of Geology and Geography

Vertical Gradient Tom Wilson, Department of Geology and Geography

Total Field Vertical Gradient http: //rubble. phys. ualberta. ca/~doug/G 221/Mag. Lecs/magrem. html Tom Wilson, Department of Geology and Geography

Visit http: //www. gemsys. ca/papers/site_characterization_using_gsm-19 gw. htm Tom Wilson, Department of Geology and Geography

Can you evaluate the vertical gradient of the horizontal component of the earth’s magnetic field? Representing the earth’s horizontal field in dipole form as The vertical gradient is just the variation with change of radius or Tom Wilson, Department of Geology and Geography

You are asked to run a magnetic survey to detect a buried drum. What spacing do you use between observation points? Tom Wilson, Department of Geology and Geography

Z/2 = /2 X 1 How often would you have to sample to detect this drum? Tom Wilson, Department of Geology and Geography

…. how about this one? The anomaly of the drum drops to ½ at a distance = ½ the depth. Tom Wilson, Department of Geology and Geography

Sampling does depend on available equipment! As with the GEM 2, newer generation magnetometers can sample at a walking pace. Tom Wilson, Department of Geology and Geography

Remember, the field of a buried drum can be approximated by the field of a dipole or buried sphere. X 1/2 for the sphere (the dipole) equals one-half the depth z to the center of the dipole. The half-width of the anomaly over any given drum will be approximately equal to its depth Or X 1/2 =Z/2 Tom Wilson, Department of Geology and Geography

Tom Wilson, Department of Geology and Geography

The sample rate you use will depend on the minimum depth of the objects you wish to find. Your sample interval should probably be no greater than X 1/2. But don’t forget that equivalent solutions with shallower origins do exist! Tom Wilson, Department of Geology and Geography

Follow the recommended reporting format. Specifically address points mentioned in the results section, above. Tom Wilson, Department of Geology and Geography

Tom Wilson, Department of Geology and Geography

e r a ere s? h W drum the Tom Wilson, Department of Geology and Geography

Tom Wilson, Department of Geology and Geography

Tom Wilson, Department of Geology and Geography

Tom Wilson, Department of Geology and Geography

From the bedrock Tom Wilson, Department of Geology and Geography

anomaly Tom Wilson, Department of Geology and Geography

Tom Wilson, Department of Geology and Geography

4. How many drums? Area of one drum ~ 4 square feet What’s wrong with the format of this plot? Tom Wilson, Department of Geology and Geography

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

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 n. T anomaly (below left) produced by an object at 4 meter depths disappears into the background noise at 16 meters. 7. 2 n. T Tom Wilson, Department of Geology and Geography 0. 113 n. T

Again - follow the recommended reporting format. Specifically address listed points. Tom Wilson, Department of Geology and Geography

The first problem relates to our discussions of the dipole field and their derivatives. 7. 1. What is the horizontal gradient in n. T/m of the Earth’s vertical field (ZE) in an area where the horizontal field (HE) equals 20, 000 n. T and the Earth’s radius is 6. 3 x 108 cm. Tom Wilson, Department of Geology and Geography

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. Hint: See Equation 7. 20 Tom Wilson, Department of Geology and Geography

4. A buried stone wall constructed from volcanic rocks has a susceptibility contrast of 0. 001 cgs emu with its enclosing sediments. The main field intensity at the site is 55, 000 n. T. 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. What is z? What is I? Background noise at the site is roughly 5 n. T. Tom Wilson, Department of Geology and Geography

Vertically Polarized Horizontal Cylinder General form Normalized shape term Tom Wilson, Department of Geology and Geography

5. 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

Tom Wilson, Department of Geology and Geography

Tom Wilson, Department of Geology and Geography

Determine depths (z) assuming a sphere or a cylinder and see which assumption yields consistent estimates. It’s all about using diagnostic positions and the depth index multipliers for each geometry. Tom Wilson, Department of Geology and Geography

X 3/4 X 1/2 X 1/4 distance Sphere vs. Vertical Cylinder; z = diagnostic _____ The depth Diagnost ic positions Multiplier s Sphere X 1/2 = 0. 9 1. 55 X 1/4 = 2. 45 X 3/4 = Tom Wilson, Department of Geology and Geography ZSp here 3. 18 2 1. 37 Multiplie rs Cylinder ZCylin der 2. 86 3. 1 3. 35 2. 17 1. 31 0. 81 1. 95 2. 03 2. 00

gmax g 3/4 g 1/2 g 1/4 Sphere or cylinder? Diagnostic positions Multipliers Sphere X 3/4 = 1. 6 meters 3. 18 5. 01 2. 17 3. 47 X 1/2 = 2. 5 meters 2 5. 0 1. 31 3. 28 X 1/4 = 3. 7 meters 1. 37 5. 07 0. 81 2. 99 Tom Wilson, Department of Geology and Geography ZSphere Multipliers Cylinder ZCylinder

Algebraic manipulation 6. Given that derive an expression for the radius, where I = k. HE. 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 =55000 n. T. Zmax (62. 2 n. T from graph below) is the maximum vertical component of the anomalous field produced by the vertical casing. Tom Wilson, Department of Geology and Geography

Feel free to discuss these problems in groups, but realize that you will have to work through problems independently on the final. Tom Wilson, Department of Geology and Geography

Problems 1 & 2 are due today, December 3 rd Next week will be spent in review Problems 3 -6 are due next Tuesday, Dec 8 th Magnetics lab, Magnetics paper summaries are due Thursday December 10 th Exam, Thursday December 17 th; 3 -5 pm Tom Wilson, Department of Geology and Geography