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

On tap for the day • Brief review of the gravity lab • Go over the magnetics problems • Use of simple geometrical objects for magnetic anomaly analysis • In class problem • Some additional problems for discussion • Magnetics lab with lab worksheet Tom Wilson, Department of Geology and Geography

The anomaly should be negative since the density contrast is negative. The residual has to be shifted into the negative so it is consistent with defined density contrasts +2 0… -2 -4. 0+ Tom Wilson, Department of Geology and Geography

The anomaly over short valleys is less than that over infinitely long ones Valleys extend in and out to infinity Valleys extend in and out 1000 ft Decreasing valley extent to ± 100 Valley has to be even deeper to get feet reduces the anomaly much a good match between calculations further and observations (640 to 672) Tom Wilson, Department of Geology and Geography

Near the deepest point in the model valley, the anomaly reads -1. 18 mg If we adjust the anomalies to accurately reflect the influence of the negative density contrast we get a negative anomaly equal to …… Tom Wilson, Department of Geology and Geography

Problem 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. 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. Between now and next Tuesday complete the questions below. We will get you started today. Tom Wilson, Department of Geology and Geography

The relationship between the potential and field intensity requires use of the minus sign. However, no minus sign is required when computing the derivative or gradient Tom Wilson, Department of Geology and Geography

Again – just take the simple derivative to get the gradient (no negative sign) To answer this problem we must evaluate the horizontal gradient of the vertical component or Can you do it? Relationship is defined in the text Tom Wilson, Department of Geology and Geography

A simple question (reference formula 7. 2) Problem 7. 2. The magnetic field intensity of a dipole is given as Offer a mathematical argument to show that the field intensity near one end of a long magnetic dipole (for example that produced by well casing) is nearly equal to that of an isolated magnetic pole. r- and r+ refer to the distances from the point of observation to the negative and positive poles of the dipole, respectively. p denotes the pole strength. Hint: one of the poles will be at a much greater distance from the surface than the other. Tom Wilson, Department of Geology and Geography

A typical use for back of the envelope computations … Can you find it? 7. 3 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. Background noise at the site is roughly 5 n. T. Tom Wilson, Department of Geology and Geography

Is the wall detectable? Vertically Polarized Horizontal Cylinder Maximum field strength Remember this kind of formulization used in gravity General form Tom Wilson, Department of Geology and Geography Normalized shape term

Vertically Polarized Horizontal Cylinder Maximum field strength recall k=0 1. 5 m k=0. 001 k = 0. 001, FE= 55, 000 n. T 0. 5 m 1. 0 m What is R? Approximate cross sectional area of rectangular wall in circular form and solve for R: i. e. Cross sectional area of wall = 1 m x 0. 5 m Lastly – what is z? Tom Wilson, Department of Geology and Geography

Abandoned well or underground storage tank 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 your understanding of the local issues suggests two possibilities: the anomalies are due to 1) a concentrated, roughly equidemensionally shaped object (a sphere); or 2) a long vertically oriented cylinder. Tom Wilson, Department of Geology and Geography

The well: Vertically Polarized Vertical Cylinder Look familiar? Tom Wilson, Department of Geology and Geography

Equidimensional object? Vertical Magnetic Anomaly Vertically Polarized Sphere (see section 7. 5. 4) As a function of x/z … The notation can be confusing at times. In the above, consider H = FE= intensity of earth’s magnetic field at the survey location. Tom Wilson, Department of Geology and Geography

Sphere or vertical cylinder ZA is magnetic field intensity at some particular point of interest, for example at a point where Z is ½ the maximum value Zmax or ¼ or ¾. Tom Wilson, Department of Geology and Geography

Some review – how do we get diagnostic positions? At what point (x/z) does the anomaly fall to ½ its maximum value? Let so Remember doing this with the gravity anomaly associated with a spherically distributed density distribution? Tom Wilson, Department of Geology and Geography

The anomaly over a magnetized vertical cylinder has the same shape as gravity anomaly over a sphere and we could solve for z as x 1/2 is referred to as a diagnostic position. It’s the distance (from the anomaly peak) to the point on the surface where the anomaly drops to ½ of its maximum value. 1. 305 is referred to as the depth index multiplier. Tom Wilson, Department of Geology and Geography

We could solve this equation for any diagnostic position For example – the point where the anomaly falls to 1/4 th of it’s maximum value: then The diagnostic position is x¼ (the distance from the peak to the point where the anomaly drops to 1/4 th its maximum value); the depth index multiplier is 0. 81. Tom Wilson, Department of Geology and Geography

Each diagnostic position gives you an estimate of z (depth to object). See class handout Tom Wilson, Department of Geology and Geography Diagnostic positions Multipliers Cylinder X 3/4 = 1. 2 m 2. 17 *X 3/4= z X 1/2 = 1. 9 m 1. 31 *X 1/2 = z X 1/4 = 2. 8 m 0. 81 *X 1/4 = z

This also gives you a way to test whether the anomaly is produced by a sphere (isolated dipole) or vertical cylinder (isolated pole). Diagnostic positions X 3/4 = 1. 2 m X 1/2 = 1. 9 m X 1/4 = 2. 8 m Tom Wilson, Department of Geology and Geography Multipliers Sphere 3. 18 2 1. 37 ZSphere Multipliers ZCylinder Vert Cylinder 2. 17 1. 31 0. 81 Take a few minutes and evaluate

Well casing or UST Diagnostic positions Multipliers Sphere ZSphere Multipliers Vertical Cylinder X 3/4 = 3. 18 2. 17 X 1/2 = 2 1. 31 X 1/4 = 1. 37 0. 81 ZCylinder … is determined by finding which of the two possible objects under consideration give the most consistent estimates of z. Accuracy in your diagnostic positions make a big difference! Tom Wilson, Department of Geology and Geography

Another twist on the abandoned well problem 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

Manipulate to solve for R… You have k = 0. 1 and HE =55000 n. T, Zmax = 62. 2 n. T. what else do you need and how do you get it? Tom Wilson, Department of Geology and Geography

Some questions and activities to help you summarize the magnetics lab activity See class handout 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

Pancake solution Tom Wilson, Department of Geology and Geography

anomaly Tom Wilson, Department of Geology and Geography

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 The x and y scaling has to be 1: 1!

The magnetic field varies as 1/r 3 Anomaly at 500, 1000, 2000 m What happens when you double, … quadruple the distance? Tom Wilson, Department of Geology and Geography Dipole anomalies fade out quickly with increases in depth

Some questions and activities to help you summarize the magnetics lab activity Bring in for discussion on Thursday. . See class handout Tom Wilson, Department of Geology and Geography

Choice of sample interval is an important survey design issue In general, your sample interval should 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

Z/2 = /2 X 1 Sampling 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

A practical survey design issue You are asked to run a magnetic survey to detect a buried drum. What spacing do you use between observation points? If the depth to the center of the drum is expected to be about 3 meters then we’d want to have a minimum sample interval of 1. 5 meters. This choice is based on the half-max relationship for the buried dipole Tom Wilson, Department of Geology and Geography

Detailed list of diagnostic positions - dipole i. e. buried magnetic dipole You can usually make quick work of it an use only three diagnostic positions (red above) Tom Wilson, Department of Geology and Geography

Vertical cylinder Again, we can get by with only three diagnostic positions (red above) Tom Wilson, Department of Geology and Geography

Summary example … 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 Diagnostic positions Multipliers Sphere ZSphere Multipliers Cylinder 0. 9 = 1. 55 3. 18 2 1. 37 2. 86 3. 1 3. 35 2. 17 1. 31 0. 81 X 3/4 = X 1/2 X 1/4 = 2. 45 Tom Wilson, Department of Geology and Geography ZCylinder 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 X 1/2 = 2. 5 meters 2 X 1/4 = 3. 7 meters 1. 37 Tom Wilson, Department of Geology and Geography ZSphere 5. 01 5. 08 5. 0 5 5. 07 5. 1 Multipliers Cylinder 2. 17 1. 31 0. 81 ZCylinder 3. 47 3. 28 3. 00

Spend the remainder of the class looking over the lab review sheet And avoid the flattened drum cluster Tom Wilson, Department of Geology and Geography

Reminders • • Magnetic papers are in the mail room • • • Magnetic paper summaries are also due on December 5 th • Final is from 3 -5 pm on December 13 th. Work on problems 7 -1 through 7 -3. They will be due this Thursday, December 5 th and returned for review on December 10 th Magnetics lab summary and news article are due on the 10 th We will have two final exam review sessions: December 5 th and December 10 th, this Thursday and next Tuesday Tom Wilson, Department of Geology and Geography

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

Writing Section reminders (electronic submissions only) • Self-reviewed magnetic methods paper summary (only one) is due on December 5 th. • The self-reviewed magnetics article is due on December 10 th. All those in the writing section submit their papers and lab electronically. Don’t forget to turn on track changes while doing your selfreviews. Only submit the self-reviewed file. Tom Wilson, Department of Geology and Geography