Geophysics - Determining Depth of Faulting from Magnetic Field Intensity Measurements

THE magnetic method of prospecting is well suited to determination of faulting in the basement rock. In addition to establishing the horizontal position of the fault, it often furnishes valuable information concerning the depth and amount of faulting. Consider a simple case of a vertical fault, represented in cross-section in Fig. 1. Let A A' represent the plane of observation (ordinarily the surface of the earth), and BB'B"B"' the upper surface of the basement. Assume that the sedimentary rocks are nonmagnetic, so that the magnetic susceptibility of the material above the basement is zero. Let k indicate the susceptibility of the basement rock, c the density contrast between it and the neighboring sedimentary rocks, and the amount of vertical displacement. Fig. 1 shows the material, indicated by cross- hatching, which gives rise to the magnetic anomaly. In most cases it can be assumed that is small compared to the thickness of the sedimentary rocks. The semi-infinite, rectangular slab of rock of susceptibility k, density contrast , and thickness t may then be replaced by a semi-infinite sheet CC' of mass t per unit area at depth 2 (the mean depth of the slab). Nettleton 1 states that this approximation results in an error of less than 2 pct for the computed gravitational field intensity when t is as great as 2/2 and decreases rapidly for smaller values of t. By a theorem of Poisson, the magnetic field intensity can be determined readily from the gravitational field. The theorem states that W = (I/) • (U/i) i1 [1] where W is the magnetic potential associated with the structure, I is the intensity of magnetization which is assumed to have the direction of the inducing field, ? is the constant of gravitation, the density contrast, U the gravitational potential associated with the structure, i the direction of the inducing magnetic field, and i1 a unit vector in that direction. The multiplication indicated in Eq. 1 is