Environmental and Exploration Geophysics I

Environmental and Exploration Geophysics I Magnetic Methods (V) 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

Problems we’ve been working on … Tom Wilson, Department of Geology and Geography

Questions? Tom Wilson, Department of Geology and Geography

Problems from chapter 7 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 7.1 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 for the potential. The negative sign is NOT needed when computing the gradient. Tom Wilson, Department of Geology and Geography

To answer this problem we must evaluate the horizontal gradient of the vertical component - or See Equation 7.20 Tom Wilson, Department of Geology and Geography

Evaluate the horizontal gradient Since  is co-latitude, the direction of increasing  is southward (in the northern hemisphere). As we travel from pole to equator ZE decreases, thus the gradient is negative. Tom Wilson, Department of Geology and Geography

Can you find it? 4. 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. What is z? What is I? Background noise at the site is roughly 5nT. 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

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

Considerable difference in magnitude of For the dipole For the horizontal cylinder Tom Wilson, Department of Geology and Geography

Detecting abandoned wells 4. 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

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

Half max relationships In general one will not make such extensive comparisons. You may use only one of the diagnostic positions, for example, the half-max (X1/2) 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. X1/2 = Z/2 X1/2 = 0.77Z X1/2 = Z X1/2 = Z/2 Breiner, 1973 Tom Wilson, Department of Geology and Geography

Just as an aside: 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 X1/2. But don’t forget that equivalent solutions with shallower origins do exist! Tom Wilson, Department of Geology and Geography

Question 4 Is the anomaly associated with a sphere? We’ll make quick work of it an use only three diagnostic positions (red above) Tom Wilson, Department of Geology and Geography

Question 4 or vertical cylinder? Again, we can get by with only three diagnostic positions (red above) 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

X3/4 X1/2 X1/4 0.9 1.55 2.45 diagnostic distance Sphere vs. Vertical Cylinder; z = __________ The depth 2.17 1.31 0.81 1.95 2.03 2.00 3.18 2 1.37 2.86 3.1 3.35 2.86 3.1 3.35 1.95 2.03 2.00 Tom Wilson, Department of Geology and Geography

gmax g3/4 g1/2 g1/4 5.01 5.0 5.07 Sphere or cylinder? 5.08 5 5.1 3.47 3.28 3.00 Tom Wilson, Department of Geology and Geography

What is R? Algebraic manipulation 5. 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

Carefully read over the Magnetics lab manual Follow the recommended reporting format. Specifically address points mentioned in the results section, above. Tom Wilson, Department of Geology and Geography

Specifically address points mentioned in the results section. Tom Wilson, Department of Geology and Geography

Magnetics Lab Questions?? Review from lab manual Where are the drums? Tom Wilson, Department of Geology and Geography

1. Illustrate configuration of bedrock derived from gravity inversion 2. Bedrock contribution to total magnetic anomaly from lab manual Tom Wilson, Department of Geology and Geography

anomaly 3. Discuss results of model computations to estimate drum location. Consider non-uniqueness and limitations of your result Tom Wilson, Department of Geology and Geography

Remember you want an object that is actually thick enough to contain whole (undeformed drums) Tom Wilson, Department of Geology and Geography

4. How many drums did you find? Area of one drum ~ 4 square feet Make sure the scale of your graph is 1:1 Tom Wilson, Department of Geology and Geography

5. How does the 1/r3 drop off influence the confidence in your result? …. 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

Questions about the Magnetics lab Again - follow the recommended reporting format. Specifically address listed points (1-5). Tom Wilson, Department of Geology and Geography

Sampling issues – for leisure consideration … Jump to last slide for reminders You are asked to run a magnetic survey to detect a buried drum. What spacing do you use between observation points? $$ Reliability Tom Wilson, Department of Geology and Geography

X1/2=Z/2 How often would you have to sample to detect this drum? Tom Wilson, Department of Geology and Geography

oops! …. 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 GEM2, 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. X1/2 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 X1/2 =Z/2 Tom Wilson, Department of Geology and Geography

Resolution issues 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

The end of the tunnel is in sight ! - Onward ... General Review this coming Thursday Turn in your magnetics lab report Thursday, December 10th. Exam, Friday December 17th; 3-5pm Questions? Tom Wilson, Department of Geology and Geography

Environmental and Exploration Geophysics I