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

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. 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 summary - F AT is an approximation of T, the scalar difference obtained from measurements of the total field (F ET ) made by the proton precession magnetometer. For the purposes of modeling we work backwards. Given a certain object, we compute the horizontal (H A ) and vertical (Z A ) components of the anomaly and combine them to obtain F AT - the anomaly we obtain from the proton precession magnetometer measurements.

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?

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

Total FieldVertical Gradient

Representing the earth’s horizontal field in dipole form as The vertical gradient is just the variation with change of radius or How would you evaluate the vertical gradient of the horizontal component of the earth’s magnetic field?

What is the horizontal gradient of the vertical component of the earth’s magnetic field (Z E ) ? Recall

Recall the horizontal gradient operator? Evaluate

An important point to carry away from the preceding discussion is the distinction between the horizontal and vertical gradient operators. Thus if you were asked “what is the horizontal gradient of the horizontal component?” you are required to evaluate 46

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

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

For any relative response function, for example, the buried vertical cylinder - Z A /Z max provides a quantitative description of the shape of the anomaly associated with the vertical cylinder, and that shape or the relative variations of anomaly magnitude as a function of the variable x/z (where z is the depth to the top of the buried cylinder in this case) will be the same for any buried vertical cylinder regardless of its size or depth. Thus, since the shape of the relative response does not vary, we have a means of estimating the depth to the top of the cylinder from measurements of distances (x) from the peak anomaly to points where the anomaly falls off to a certain fraction of its peak value.

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 3/4 ths, 2/3 rds, 1/2, 1/3 rd and 1/4 th of the maximum value of the anomaly are referred to as X 3/4, X 2/3, X 1/2, X 1/3 and X 1/4, respectively. X 2/3 X 1/2 X 1/3 X 1/4

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

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

X/Z Vertical Cylinder SphereHorizontal Cylinder X 3/ X 1/ X 1/ Depth Index Multipliers Vertical Cylinder SphereHorizontal Cylinder X 3/ X 1/ X 1/

Sphere, Vertical Cylinder; z = __________ Diagnostic positions Multipliers Sphere Z Sphere Multipliers Cylinder Z Cylinder X 3/4 = X 1/2 = X 1/4 = The depth

Diagnostic positions Multipliers Sphere Z Sphere Multipliers Cylinder Z Cylinder X 3/4 = X 1/2 = X 1/4 = Sphere or cylinder?

5. Given that derive an expression for the radius, where I = kH E. 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 H E =55000nT. Z max (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.

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. Breiner, 1973

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

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

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 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

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

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

A 50 foot long drum? Drums in the bedrock?