Section A
Q1.
(a) What is the relationship between the angle of inclination of the remanent magnetisation and the magnetic latitude at the time of the magnetisation of the rock? Assuming that the angle of inclination is 60°, calculate the magnetic latitude.
(b) The P-wave from an earthquake arrives at a seismic station at 13 hours 19 minutes 58.9 seconds and the S-wave arrives at 13 hours 20 minutes 4.7 seconds. Assuming that the P-wave velocity is 5.6 km s^{-1} and that Poisson's ratio is 0.25, calculate the time at which the earthquake occurred.
(c) A cylindrical conductor of radius r0 has internal magnetic field intensity ec{H} = rac{103}{r} left[ rac{1}{2b2} sin br - rac{r}{4b} cos br ight] ec{b}_{phi} where b = rac{pi}{2r0}. Calculate the total current flowing in the conductor if radius r0 = 1 cm.
(d)
A gravity profile of 25 points indicates the presence of an ore body of horizontal cylindrical shape. Formulate a non-linear inverse problem to determine the depth (z), dimension (R) and density contrast (
hoc) for the ore body. Write the steps, along with necessary equations, to determine z, R and
hoc using Gauss-Newton method.
