1. Tom Wilson, Department of Geology and Geography Environmental and Exploration Geophysics I tom.h.wilson tom.wilson@mail.wvu.edu Department of Geology and Geography West Virginia University Morgantown, WV Final review sessions - II

2. Tom Wilson, Department of Geology and Geography Exam review week – session II Magnetics lab, Magnetics paper summaries are due today - December 10 th Exam, Thursday December 17 th ; 3-5pm

3. Tom Wilson, Department of Geology and Geography 7.1 field (Z E ) in an area where the horizontal field (H E ) equals 20,000 nT and the Earth’s radius is 6.3 x 10 8 cm. We know

4. Tom Wilson, Department of Geology and Geography In the problem you are asked to evaluate the horizontal gradient of the vertical component of the Earth’s magnetic field. So … or See discussions of Equation 7.20 -0.0063 nT/m

5. Tom Wilson, Department of Geology and Geography 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. Given background noise level of  5nT. What is z? What is I?

6. Tom Wilson, Department of Geology and Geography Vertically Polarized Horizontal Cylinder General form Evaluate and compare

7. Tom Wilson, Department of Geology and Geography The anomaly associated with vertical well casing has a shape like that produced by an isolated pole. So its shape is identical to that of the gravity anomaly associated with a sphere or a point mass. If the magnetic object is more localized and equidimensional in shape it will drop off more suddenly with distance from the anomaly peak. The online group magnetic problems all have problems similar to problem 5 in the problem set returned today.

8. Tom Wilson, Department of Geology and Geography Sphere vs. Vertical Cylinder; z = Diagnostic distance *DIM Diagnostic positions Multipliers Sphere Z Sphere Multipliers Cylinder Z Cylinder X 3/4 = X 1/2 = X 1/4 = 2.86 3.1 3.35 1.95 2.03 2.00 2.17 1.31 0.81 3.18 2 1.37 0.9 X 3/4 1.55 X 1/2 2.45 X 1/4

9. Tom Wilson, Department of Geology and Geography Figure 1: This profile line crosses through the maximum value of a circular shaped anomaly encountered in a 2D grid of magnetic data. Problem 3 practice test: Silo liner or storage tank?

10. Tom Wilson, Department of Geology and Geography By now - a familiar approach to solution? Diagnostic positions Multipliers Sphere Z Sphere Multipliers Cylinder Z Cylinder X 3/4 = X 1/2 = X 1/4 = 2.17 1.31 0.81 3.18 2 1.37 4.6 7.7 12.4 Cylinder – 10 m deep

11. Tom Wilson, Department of Geology and Geography Diagnostic positionsMultipliers Sphere Z Sphere Multipliers Cylinder Z Cylinder X 3/4 = 1.6 meters3.182.17 X 1/2 = 2.5 meters21.31 X 1/4 = 3.7 meters1.370.81 Sphere or cylinder? 5.01 5.0 5.07 3.47 2.99 3.28 g max g 3/4 g 1/2 g 1/4

12. Tom Wilson, Department of Geology and Geography If you look through the magnetic group problems you should find the following: Anomaly 1: Sphere with depth to center of 4 meters Anomaly 2: Cylinder with depth to top of 4 meters Anomaly 3: Cylinder with depth to top of 10 km

13. Tom Wilson, Department of Geology and Geography 6. 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. Algebraic manipulation

14. Tom Wilson, Department of Geology and Geography 4. You are given the main magnetic field intensity (F E ), the declination (d) and the horizontal projection of F E : H E. What is the vertical component of the earth’s magnetic field? What is the inclination of the main magnetic field? 5. You are standing 10 feet from a point directly over the end of abandoned casing string. The top of the abandoned well casing lies 10 feet beneath the surface. The effective pole strength for the casing string is 5 ups. What is the vertical component of the anomalous field at the observation point? State your answer in nanoTeslas. From the practice final …

15. Tom Wilson, Department of Geology and Geography At 8 am you start your gravity survey at Base Station 5 in your survey area. You set out to establish another base station (Base Station 6) about an hours drive from Base 5. At 8am the acceleration due to gravity at Base Station 5 is 5.3 milliGals relative to the main base station in your survey area. You make it to the new base station and take a measurement 53 minutes after making the Base 5 observation. Your reading at Base Station 6 is 4.3 milliGals. You return to Base 5 but stop for gas along the way. You finally re-measure the Base 5 acceleration at 10 am (120 minutes after your initial measurement). The reading at Base Station 5 dropped 2 milliGals during that 120 minute period. What is the acceleration at Base Station 6 relative to the main base? Problem 6 – practice final > Tide & Drift.

16. Tom Wilson, Department of Geology and Geography Problem 7. Another problem that can be addressed using simple geometrical analysis

17. Tom Wilson, Department of Geology and Geography Diagnostic positions Multipliers Sphere Z Sphere Multipliers Cylinder Z Cylinder X 3/4 = X 1/2 = X 1/4 = 2.17 1.31 0.81 3.18 2 1.37 Repeat of a familiar analytical approach 8.8 16 26

18. Tom Wilson, Department of Geology and Geography 8. What is the theoretical gravity. 9. Write out the equation that defines the theoretical gravity 10. What is the terrain corrected Bouguer anomaly? 11. Given F E, H E, and d solve for Y E, X E, Z E and i. Some general questions ….

19. Tom Wilson, Department of Geology and Geography Exam review week – session II Magnetics lab, Magnetics paper summaries are due today - December 10 th Exam, Thursday December 17 th ; 3-5pm