Magnetic Methods- continued Environmental and Exploration Geophysics I Magnetic Methods- continued tom.h.wilson tom.wilson@mail.wvu.edu Department of Geology and Geography West Virginia University Morgantown, WV

Total Field Anomalies - What are they? Recall that the proton precession magnetometer makes measurements of the total field, not the vector components of the field. Recall also that the total field can be derived from other magnetic elements. The formula below represents the anomalous total field in terms of the horizontal and vertical components of the anomalous field.

Remember how the proton precession magnetometer works 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.

In this diagram FET is is the vector sum of the earth’s main field and the anomalous field associated with a buried dipole field. The proton precession magnetometer measures the magnitude of FET.

Magnetic Elements for your location F is known

In summary - FAT is an approximation of T, the scalar difference obtained from measurements of the total field (FET) made by the proton precession magnetometer. For the purposes of modeling we work backwards. Given a certain object, we compute the horizontal (HA) and vertical (ZA) components of the anomaly and combine them to obtain FAT – an approximation of the anomaly we obtain from the proton precession magnetometer measurements – the total field anomaly.

Gradients vertical component horizontal component 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? vertical component horizontal component

The vertical gradient is just the variation of ZE with change in radius or distance from the center of the dipole.

Total Field Vertical Gradient http://rubble.phys.ualberta.ca/~doug/G221/MagLecs/magrem.html

How would 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

Relative Response functions vertical polarization Vertically polarized sphere or dipole Vertically polarized vertical cylinder Vertically polarized horizontal cylinder

vertical polarization Zmax vertical polarization Vertically polarized sphere or dipole Vertically polarized vertical cylinder Vertically polarized horizontal cylinder

These distances are referred to as diagnostic positions These distances are referred to as diagnostic positions. Thus in the plot below the points along the x axis where the anomaly falls off to 3/4ths, 2/3rds, 1/2, 1/3rd and 1/4th of the maximum value of the anomaly are referred to as X3/4, X2/3, X1/2, X1/3 and X1/4, respectively. X1/3 X2/3 X1/2 X1/4

Those measurements provide us with the above table Those measurements provide us with the above table. In this case we have distances in multiples of x/z.

In working with an actual anomaly, we can measure the actual distances to points where a given anomaly drops to various fractions of the maximum anomaly value and then compute the depth z.

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.

Is a function of the unitless variable x/z 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

Depth Index Multipliers X/Z Vertical Cylinder Sphere Horizontal Cylinder X3/4 0.46 0.315 0.31 X1/2 0.766 0.5 0.495 X1/4 1.23 0.73 0.68 Depth Index Multipliers Vertical Cylinder Sphere Horizontal Cylinder X3/4 2.17 3.18 3.23 X1/2 1.305 2 2.02 X1/4 0.81 1.37 1.47

Sphere, Vertical Cylinder; z = __________ The depth 2.86 1.95 3.1 2.03 3.35 2 Diagnostic positions Multipliers Sphere ZSphere Multipliers Cylinder ZCylinder X3/4 =0.9 3.18 2.17 X1/2 =1.55 2 1.31 X1/4 =2.45 1.37 0.81

Sphere or cylinder? Diagnostic positions Multipliers Sphere ZSphere Multipliers Cylinder ZCylinder X3/4 = 1.6 3.18 2.17 X1/2 = 2.5 2 1.31 X1/4 = 3.7 1.37 0.81 5.08 3.47 5.00 3.28 5.1 3

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.

The map view clearly indicates that consideration of two possible origins may be appropriate - sphere or vertical cylinder.

Burger limits his discussion to half-maximum 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. Breiner, 1973

Sampling $$ Reliability You are asked to run a magnetic survey to detect a buried drum. What spacing do you use between observation points? $$ Reliability

How often would you have to sample to detect this drum?

oops! …. how about this one? The anomaly of the drum drops to ½ at a distance = ½ the depth.

Remember, the field of a buried drum can be approximated by the field of a dipole or buried sphere. X1/2 for the sphere 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

Resolution issues

The sample rate you use will depend on the minimum depth of the objects you wish to find.

Anomaly shapes - sign conventions

Sign Conventions Vectors that point down are positive. Vectors that point south are negative.

Original data The analytic signal

Nonuniqueness

A 50 foot long drum? Drums in the bedrock?

First round review Sample Test Questions