A Study on Estimating the Relief of Magnetic Basement

Abstract A new method of estimating the relief of the magnetic basement is designed. In the method, the pseudo-gravimetric anomaly, which is vertical derivative of the pole-reduced magnetic potential, is calculated. The pseudo-gravimetric anomaly is downward continued up to the predetermined mean depth of the basement, and then converted to the equivalent distribution of surface densities. The variation of surface densities at the mean depth gives the relief of the magnetic basement. A model study for a two dimensional case is also given. Introduction The problem of magnetic interpretation to geophysicists may be said to consist in finding the distribution of magnetized material whose magnetic field is given on a plane surface. Therefore, we are confronted with the inverse problem of potential field theory, i.e., of determining the source from its potential. An approach to solve the problem is to select the dimensions and magnetic properties of a subsurface model so that its magnetic effect agrees as closely as possible with the observed anomalous pattern. This procedure is relatively simple. But it becomes more complicated if more than one simply shaped body is evidently responsible for the measured anomalies which anybody trying this has experienced for himself. Hahn (1965) has introduced a method of estimating the relief of a layer with homogeneous magnetization and a surface relief capable of producing the measured anomalies. The magnetized bodies within his task of geological investigation are assumed to be crystalline rocks showing a sufficiently high degree of metamorphism, and/or intermediary to basic igneous rocks. The complex of these rocks may be represented by some sort of a layer with a more or less constant magnetization and a surface relief which is responsible for the magnetic anomalies. His method gives the relief by using the concept of "relief wave" assuming the direction of the magnetization is same as that of the earth's field. In this paper, we would like to introduce another approach to find the relief of such a layer, without assuming the direction of the magnetization. This does not mean that the present method gives the solution without knowing the direction but it rather means that we can find the solution, at least theoretically, if the direction of the magnetization, which may be different from the present earth's field, is known. Our method uses "pseudo-gravity" the concept of which can be found in some literatures (Baranov, 1957). The pseudo-gravimetric anomalies, which are slight modification of Bhattacharyya's pole-reduced magnetic potential, are downward continued up to the predetermined mean depth of the basement. These are converted to an equivalent stratum, i.e., an equivalent distribution of surface densites. The variation of surface densities at the mean depth gives the relief of the magnetic basement.