Using analytic signal in determination of the magnetization to density ratio (MDR) of the geological bodies



Gravity and magnetic data are usually processed and interpreted separately, and fully integrated results basically are created in the mind of the interpreter. Data interpretation in such a manner requires an interpreter experienced both on topics concerning potential field theory and the geology of the study area. To simplify the joint interpretation of data, the automatic production of auxiliary interpreting products, in the form of maps or profiles, is useful to help a less experienced interpreter or when investigating regions with poorly known geology. Fortunately, a suitable theoretical background for the joint interpretation of gravity and magnetic anomalies is well established and can serve promptly in generating such products. Because of its mathematical expression, this theory commonly is referred to as the Poisson relation or the Poisson theorem, as in more recent publications. In summary, the Poisson theorem (term adopted here) establishes a linear relationship between the gravity and magnetic potentials and, by extension, between the corresponding anomalies measured in practice or derived from them by applying suitable data processing. For the joint interpretation of potential field data, the Poisson theorem has been used mainly to determine the magnetization–density ratio (MDR) (Garland, 1951; Chandler et al., 1981; Chandler and Malek, 1991) and, less often, the magnetization direction of single dense and magnetic structures (Ross and Lavin, 1966; Cordell and Taylor, 1971).
In this study we propose to combine a 3-D analytic signal method and Poisson theorem to calculate the MDR value. The amplitude of the simple analytic signal is defined as the square root of the squared sum of the vertical and two horizontal derivatives of the magnetic field (Roest et al. 1992). The outlines of the geological boundaries can be determined by tracing the maximum amplitudes of the analytic signal. The analytic signal exhibits maximum amplitudes over magnetization contrasts. Hence, the advantage is that in addition to the geological boundaries indicated by the maximum amplitudes of analytic signals, we can determine the MDR without considering the datum levels.
The final equation for estimation of MDR is:

Where |MAS0| represents the amplitude of simple zeroth-order analytic signal of magnetic anomaly and |GAS1| represents the amplitude of first-order analytic signal of gravity anomaly. In this equation G is gravitational constant.
On the basis of gravity and magnetic anomaly data, we have proposed a method by applying analytic signals to Poisson theorem to calculate the MDRs of geological structures. The advantage of using this method is that not only we can estimate the MDR distribution of the subsurface sources; we can also determine the geological boundary. The synthetic models and real data have shown that the proposed method is feasible. Also we applied the proposed method on real gravity and magnetic data from Gol-e-Gohar No.3 anomaly. Based on the estimated MDR values, the maximum of the MDR has located on southern part of study area which is in agreement with location of subsurface ore body. Furthermore, this method proves that there are two major rocks in the study area namely, Metamorphism and Igneous.