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Environmental and Exploration Geophysics I tom.h.wilson Department of Geology and Geography West Virginia University Morgantown, WV Magnetic Methods (IV)
Could a total-field magnetic survey detect the illustrated burial chamber (spherical void) in a region where F E = 55,000nT and i = 70 o ? To do this we can compute F AT directly using equations 7-36 and 7-37.
We’ve got an F AT over 1.5 nT. A typical proton precession magnetometer reads differences of 1 nT. This is much too small of an anomaly to detect. Also, consider that our magnetometer usually sits atop a 2 meter rod. How will that change the maximum value of F AT.
At 5 meters the inverse cube relationship produces a pretty significant drop in the magnitude of F AT. At 0.35 nT this is much too small to be detected.
In class the other day, we recorded the following numbers at approximately 5 minute intervals. The smaller background variations have a standard deviation of about ±13nT.
Here we have much larger deviations of ±1283nT. Of course these measurements were made in the building so they are not representative of what might be happening at a field site, but you shouldn’t loose sight of the potential influence of background noise on conclusions drawn from the finest of models.
Is there a quicker way to estimate the possibility that we might observe this anomaly? We could use the simple geometrical object representations. Which object would you use to approximate this situation? The vertical field of a simple sphere or dipole Remember where this equation comes from?
The magnetic response of a sheet of dipoles is obtained by carrying out integrations over two sheets: one consisting of the negative poles and the other of the positive poles. where These individual integrations are very similar to the ones used to derive the Bouguer plate effects.
The effect of the bottom sheet will also equal The negative Sign comes from the convention that defines upward pointing vectors (from the positive pole) as negative. So the net result ….. is The process yields an intermediate more useful result.
The contribution from the top of the rod isand the contribution from the base of the rod is
The total field of this infinitely long intrusive (dike) will be or just In Problem 7.6 we are asked to determine the vertical field anomaly (Z A ) over the intrusive shown in the diagram (see text) at a point directly over the center of the intrusive. The intrusive has a very long strike-length. F E is vertical and equal to 55,000nT. Use equation 7-46 and compute Z A for two cases. Case 1: assume that the base of the intrusive is located at 12km beneath the surface. Case 2: assume the base is located at infinity. Compare the two results. (7.46)
In general for the top, Calculate bot in a similar fashion and take their difference at each point x along a profile.
Is there a quicker way to estimate the possibility that we might observe this anomaly? Again, those simple geometrical object representations might get us in the ballpark. Which object would you use to approximate this situation? The vertical field of a horizontal cylinder
The magnetic data graphed below represent vertical field measurements (Z A ) in an area where shallow crystalline basement is overlain by non-magnetic sediments. The basement gneisses are intruded by numerous thin kimberlite pipes. Both gneisses and kimberlite pipes are eroded to a common level surface. Determine the likely depth to basement. F E =58,000nT and i=80 o.
Do you remember what to do? What simple geometrical object should be used in this case and what property of the curve do you need to measure?
Determine the depth z to the center of the basalt flow. Also indicate whether you think the flow is faulted (two offset semi- infinite sheets) or just terminates (a semi- infinite sheet). What evidence do you have to support your answer? Refer to illustration on page 477 and associated discussion. This problem relies primarily on a qualitative understanding of equation 7-47.
Field of the semi-infinite plate X = 0 at the surface point directly over the edge of the plate. The field at a point X is derived from the two angles shown below - 1 and 2 - used in the text. 11 22 z t This is just a special case of the preceding example
The angle subtended by the top of the sheet at x is The angle subtended by the bottom of the sheet at x is
t X max =z z z = 1.75m t = 0.5m The edge of the fault is located at the inflection point.
Vertically Polarized Faulted Horizontal Slab or Semi Infinite sheet
Half-plate (the Slab, semi infinite plate, the half-sheet …) z t
Look carefully at the anomaly profile shown in Problem 7-8 and consider the overall shape of the anomaly and how it may allow you to discriminate between the faulted versus terminated flow interpretations.
The yellow curve at left is derived from the full computation (terms shown below) The blue curve is obtained from the SGO approximation
Peter’s half slope We’ll come back to this on Thursday
The final will be comprehensive, but the focus will be on material covered since the last exam. Come prepared to ask questions