Final review sessions - II Environmental and Exploration Geophysics I Final review sessions - II 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

Exam review week – session II Magnetics lab due today - December 9th Afternoon of the 10th (at the latest!) Exam, Friday December 17th; 3-5pm Tom Wilson, Department of Geology and Geography

Last problem set handed back today What is the horizontal gradient of the Earth’s vertical magnetic field (ZE) in an area where the horizontal field (HE) equals 20,000 nT and the Earth’s radius is 6.3 x 108 cm. We know Tom Wilson, Department of Geology and Geography

Tom Wilson, Department of Geology and Geography Evaluate the horizontal gradient of the vertical component of the Earth’s magnetic field. or See discussions of Equation 7.20 -0.0063 nT/m Tom Wilson, Department of Geology and Geography

Can you find it? What is z? What is I? 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? Tom Wilson, Department of Geology and Geography

Tom Wilson, Department of Geology and Geography Problem 4 Vertically Polarized Horizontal Cylinder General form Evaluate and compare Zmax= 18nT (using z=1.75m) Zmax= 15.3nT (using z=1.75m) Tom Wilson, Department of Geology and Geography

Detecting abandoned wells The online group magnetic problems all have problems similar to problem 5 in the problem set returned today. 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. Tom Wilson, Department of Geology and Geography

Tom Wilson, Department of Geology and Geography 0.9 X3/4 1.55 X1/2 2.45 X1/4 Sphere vs. Vertical Cylinder; z = Diagnostic distance *DIM 2.86 1.95 3.1 2.03 3.35 2 Diagnostic positions Multipliers Sphere ZSphere Multipliers Cylinder ZCylinder X3/4 = X1/2 = X1/4 = 3.18 2 1.37 2.86 3.1 3.35 2.17 1.31 0.81 1.95 2.03 2.00 Tom Wilson, Department of Geology and Geography

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

Tom Wilson, Department of Geology and Geography By now - a familiar approach to solution? Diagnostic positions Multipliers Sphere ZSphere Multipliers Cylinder ZCylinder X3/4 = X1/2 = X1/4 = 4.6 7.7 12.4 3.18 2 1.37 14.6 15.4 17.0 2.17 1.31 0.81 9.98 10.1 10.0 Cylinder – 10 m deep Tom Wilson, Department of Geology and Geography

Tom Wilson, Department of Geology and Geography gmax g3/4 g1/2 g1/4 Sphere or cylinder? Diagnostic positions Multipliers Sphere ZSphere Multipliers Cylinder ZCylinder X3/4 = 1.6 meters 3.18 2.17 X1/2 = 2.5 meters 2 1.31 X1/4 = 3.7 meters 1.37 0.81 5.08 3.47 5.00 3.28 5.1 3 5.01 5.0 5.07 3.47 3.28 2.99 Tom Wilson, Department of Geology and Geography

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 Tom Wilson, Department of Geology and Geography

Tom Wilson, Department of Geology and Geography What is R? Algebraic manipulation 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. 0.3 meters Tom Wilson, Department of Geology and Geography

Tom Wilson, Department of Geology and Geography From the practice final … 4. You are given the main magnetic field intensity (FE), the declination (d) and the horizontal projection of FE: HE. 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. Tom Wilson, Department of Geology and Geography

Tom Wilson, Department of Geology and Geography Problem 6 – practice final > Tide & Drift. 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? Tom Wilson, Department of Geology and Geography

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

Tom Wilson, Department of Geology and Geography Repeat of a familiar analytical approach Diagnostic positions Multipliers Sphere ZSphere Multipliers Cylinder ZCylinder X3/4 = X1/2 = X1/4 = 8.8 16 26 3.18 2 1.37 2.17 1.31 0.81 Tom Wilson, Department of Geology and Geography

Tom Wilson, Department of Geology and Geography Some general questions …. 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 FE, HE, and d solve for YE, XE, ZE and i. Tom Wilson, Department of Geology and Geography

Exam, Friday December 17th; 3-5pm Questions? ... Turn in the Magnetics by Friday afternoon (December 10th) at the latest Exam, Friday December 17th; 3-5pm Tom Wilson, Department of Geology and Geography