ON THE QUESTION OF DETERMINING THE DIRECTION OF MAGNETIZATION OF IRREGULARLY SHAPED BODIES FROM ANOMALIES

Z. A. Myshko

(Presented by Professor D. S. Mikov)

In interpreting magnetic anomalies it is necessary to know the direction of magnetization of the disturbing bodies. The latter is usually determined either by studying oriented samples, or directly from the anomalies of the vertical and horizontal components, for example, by the integral method.

Ore bodies of complex shape are magnetized nonuniformly by the Earth's magnetic field. In order to determine the magnitude of the change in the direction of magnetization as a function of the shape of the bodies, we considered the following theoretical example.

A two-dimensional object with the cross section shown in Fig. 1, with an excess magnetic susceptibility of 0.2 CGS, is magnetized by the Earth's field \(T_0 = 0.5\) oersted, inclined in the plane of the body’s cross section at an angle \(i = 40^\circ\). This object may be regarded as consisting of three bodies with cross sections according to Fig. 1.

To calculate the intensity and direction of magnetization of each body, the field \(T_0\) was projected onto the axes of these bodies, and then, taking into account the corresponding demagnetizing coefficients along the axes of the bodies, the following magnetization intensities and angles were calculated for each body:

\[ \begin{aligned} \text{For body 1} \quad & I_1 = 0.055 \ \text{CGS} \qquad \gamma_1 = 67^\circ 20' \\ \text{For body 2} \quad & I_2 = 0.037 \ \text{CGS} \qquad \gamma_2 = 50^\circ 00' \\ \text{For body 3} \quad & I_3 = 0.047 \ \text{CGS} \qquad \gamma_3 = 34^\circ 10' \end{aligned} \]

Thus, under one and the same field \(T\), different parts of an object of complex shape are magnetized differently and in different directions. The anomaly created by such an object will be equal to the sum of the anomalies from three separate bodies with different magnetization intensities and directions.

Using D. S. Mikov’s point palette, in accordance with the data obtained, we calculated the anomalies \(Z_1, Z_2, Z_3\) and \(H_1, H_2, H_3\) from each body, and as a result of their summation obtained the anomalies \(Z\) and \(H\) for the entire object.

Fig. 1. Graphs of \(Z\) over an object of considerable extent and complex cross-section under different magnetizations

When carrying out a magnetic survey over such objects, their total magnetic field \(Z\) and \(H\) will be measured. This raises the question: what magnetization should be adopted for interpreting the anomaly from such an object?

1. If the magnetization is considered vertical, then our body will create an anomaly \(Z_b\) of an entirely different form than the total \(Z\).

2. If the upper part of the disturbing object (body 1) is exposed by pits and its samples are studied—that is, the magnitude and direction of the magnetization \(I_1\) and \(\gamma_1\) are determined—then the anomaly \(Z'_1\), calculated for the entire object from these data (Fig. 1), will also differ sharply from the total \(Z\).

3. It is not difficult to see that if, during drilling, body 3 were exposed and, from samples, \(I_3\) and \(\gamma_3\) were determined, then the anomaly \(Z_3\), created by the whole object with such magnetization, would likewise differ greatly from the observed \(Z\).

Consequently, if any of the above-considered directions of magnetization is assumed, the interpretation on the section will yield an entirely different, nonexistent body.

For the interpretation to have the correct outcome, it is necessary to know the average value of the magnetization angle of this object, which requires sampling throughout the entire body; this can be done only after detailed exploration of the body.

By the integral method and by the ratio of areas according to the method of D. S. Mikov, using the total curves \(Z\) and \(H\), we determined the direction of magnetization:

\[ \gamma = \operatorname{arctg} \frac{ \displaystyle \int_{-\infty}^{+\infty} xZ \cdot dx }{ \displaystyle \int_{-\infty}^{+\infty} xH \cdot dx } = 45^\circ 20' \quad \text{and} \quad \gamma' = \arcsin \left( -\frac{Z_{-}}{Z_{+}} - 1 \right) = 50^\circ . \]

The anomaly \(Z_h\), calculated for the whole body with allowance for this direction of magnetization, proved to be the closest to the total \(Z\). This fact indicates that, despite the inhomogeneity of the magnetization of the object caused by its complex shape, in interpreting anomalies it is always more correct to use the average total direction of magnetization, calculated, for example, by the integral method from the measured anomalies \(Z\) and \(H\).

If this is not done, an incorrect idea of the shape of the disturbing object may be obtained when interpreting the anomalies.

REFERENCES

1. D. S. Mikov. Methods for Interpreting Magnetic Anomalies. Tomsk State University Press, 1962.