GE391 Introduction to Geophysics

Homework

Due 10/22/2009

Prof. Alan L. Kafka

Prof. John E. Ebel

1)  For a dipole field, the inclination angle I is related to the magnetic latitude q by the equation

tan(I) = 2 cot (q)

Given this equation, what is the inclination angle at (a) London, England (51¡N, 0¡E), (b) Canberra, Australia (35¡S, 149¡E), (c) Spitzbergen (78¡N, 16¡E), and (d) Rio de Janeiro, Brazil (23¡S, 43¡W).  Assume that the magnetic poles are aligned with the geographic poles.

Also, what magnetic latitude are you at if your inclination angle is (e) 76¡ and (f) -36¡?  In each case, what magnetic longitude are you at?

2) For some rock sequences, such as the late Precambrian Keweenawan of the Lake Superior province, the magnetic reversal pattern is asymmetric, in that normal and reversed intensity vectors are not antiparallel.  In the case mentioned, the normal intensity vector is inclined downward at 39¡ to the horizontal, the reversed upward at 69¡, in the same vertical plane.  Discuss the following as possible causes of this behavior: (a) the addition of a secondary component, to normal and reversed rocks equally, following an original symmetric reversal; (b) plate motion between the times of formation of normal and reversed rocks; (c) a non-geocentric dipole as the source of the earthÕs field.  If you have available both paleolatitudes and paleointensities for normal and reversed samples, to what extent could you distinguish between these causes?

3)  Across a mid-ocean ridge, the distance between total field anomaly pairs representing the Gilbert magnetic reversal epoch is 187 km.  How fast has the ridge been spreading since that time?  You will need to use the web or a book from the library to find the time of the Gilbert magnetic reversal.

4)  The formula for the strength B of a dipole magnetic field

B=(m0 m / 4 p a3)(1 + 3 sin2fm)1/2

where m0 is the magnetic permeability of free space, m is the dipole moment of the dipole magnetic field, a is the radius from the center of the dipole where the field is being measured, and fm is the magnetic colatitude (90¡ - the latitude).  Assume that the EarthÕs magnetic field is a dipole.  What is the maximum intensity of the field at the core-mantle boundary?  At what distance above the EarthÕs surface is the magnitude of the magnetic field one-half of its value at the surface of the Earth?  The moment of the dipole field of the Earth is m = 7.94 x 1022 A-m2, and the surface magnetic field at the magnetic equator is B=.307 Gauss.