A Network of Magnetic Measurements for the Search for Gold-Ore Veins of Darasun

L. Ya. Erofeev

(Presented by Professor D. S. Mikov)

In studying prospective areas, especially near known ore fields, great importance is attached to the search for quartz and quartz-sulfide veins. Determining their location by geophysical methods significantly reduces the volume of costly mining work and substantially accelerates the development of new areas. Studies in recent years in the field of methods for investigating vein-type gold-ore deposits have established that, in a number of cases, ore veins in the magnetic field are accompanied by relatively reduced, linearly elongated anomalies. In itself, this circumstance in principle makes it possible to apply magnetic surveying for these purposes.

However, in practical form, the search for anomalies accompanying vein formations is associated with certain difficulties, which, for example, for the Darasun gold-ore deposit, amount to the following. First, alongside negative anomalies (relative to the enclosing rocks) caused by veins, there are a large number of anomalies of another nature at the deposit, which in a single section have a form and intensity commensurate with the sought anomalies. Second, the sought anomalies have variable parameters.

Without carrying out special investigations, it may be noted that, under the conditions of this deposit, the identification of anomalies caused by veins on a single profile is impossible without bringing in additional information, regardless of the measurement interval along the profile. Consequently, in the given situation the question can concern only the identification of these anomalies by a series of profiles, using the effect of signal accumulation. For this, at the Darasun gold-ore deposit there are favorable conditions—the correlation of the sought anomalies along the axis of their strike substantially exceeds that of most other changes in the intensity of the vertical component of the magnetic field.

Thus, the solution of the problem of choosing the optimal survey network under these conditions reduces to the following. It is necessary to determine how the points should be arranged on the profile and what distances should be taken between measurement profiles so that the sought signal is distinguished in the best possible way in the given field.

Let us proceed to determine the magnitude of the measurement interval along the profile. Taking into account the known property of discrete observations, one may approach the solution of the posed problem from several positions. For example, one may investigate the process of change in the amplitude of an anomaly.

when the measurement spacing is changed. In this case the distance between measurement points can be determined if one specifies the “noise” level and the accuracy of reconstructing the anomaly amplitude, by expanding a signal of specified shape in a series of Chebyshev polynomials.

One can also investigate the behavior, when the measurement spacing is changed, not of the anomaly amplitude alone but of the gradient, which will make it possible to analyze the pattern of noise and signal more distinctly. However, all this is suitable in those cases where the anomalies sought differ substantially, in amplitude or linear dimensions, from all other variations of the field intensity within which the search is being carried out. At the Darasun gold-ore deposit the search conditions are more complex. In this case it is desirable to use not some single parameter, or group of parameters, reflecting individual features of the anomaly, but such a set of them as would unambiguously represent the anomaly and the process of its change, which could be investigated as the survey spacing is changed. In this case it becomes possible to study the character of the change in the noise in the same respect, thereby increasing the number of elements of comparison and hence the possibility of distinguishing the signal.

Comparison of anomalies of specified shape with a field strongly complicated by noise can be successfully carried out by means of the “inverse probability” method known in information theory. This method makes it possible to compare a signal with noise by such a number of parameters as unambiguously represent the signal. The measure of agreement between the specified shape and intensity of the signal and the process under study is the so-called likelihood coefficient:

\[ K=\exp\left[-\frac{1}{2\sigma^{2}}\sum_{i=1}^{m} a^{2}(x_i)\right]\cdot \exp\left[\frac{1}{\sigma^{2}}\sum_{i=1}^{m} f_i a(x_i)\right]. \]

Here \(\sigma^{2}\) is the variance of the noise;

\[ f_i \]

is the value of the intensity at the \(i\)-th point of the profile;

\[ a(x_i) \]

is the ordinate of the expected-signal point at the \(i\)-th point.

When the number of points on the profile (the measurement spacing) is changed, both the sought shapes of anomalies and all other variations of intensity on the profile under study will be deformed. The deformation of the various variations will be different. Obviously, in this case it is possible to specify such a distance between observation points at which the signal, by this method, will be distinguished in the given distribution in the best way, i.e., the error of its detection will be minimal.

In the process of detecting a signal by the inverse-probability method, two kinds of errors may arise. An error of the first kind consists in accepting the decision that an anomaly is present when in fact it is not. An error of the second kind consists in considering that the sought anomaly is absent when in fact it is present.

The total error is determined by the relation:

\[ Q=P_0\cdot\alpha+P_1\cdot\beta, \]

where \(P_0, P_1\) are the a priori probabilities of the presence and absence of an anomaly, taken to be equal to 0.5;

\[ \alpha \ \text{and}\ \beta \]

are, respectively, the probabilities of errors of the first and second kind.

The method that ensures a minimum of this total error is known as the “ideal observer.”

The detection characteristic for this criterion, in the case of application of the inverse-probability method, can be represented by the dependence of the total error on the anomaly-to-noise ratio:

\[ \rho=\frac{E_0}{\sigma^{2}}, \]

where

\[ E_0=\sum_{i=1}^{m} a^2(x_i) \]

is the energy of the anomaly. Then, as shown in [3], the minimum error is

\[ Q_{\min}=\frac{1-\Phi\left(\sqrt{\frac{\rho}{2}}\right)}{2}, \]

where

\[ \Phi_t=\frac{2}{\sqrt{2\pi}}\int_0^z \exp\left(-\frac{t^2}{2}\right)\,dt \]

is taken from tables of an integral of this form.

On this basis, the dependence was obtained of the number of measurement points by which the anomaly must be represented on the ratio of the mean value of the anomaly amplitude to the standard deviation of the noise, \(\overline{a}/\sigma\), for fixed values of the reliability of signal detection (Fig. 1).

Using this dependence, one can choose the survey spacing. To do this, it is necessary to specify the degree of reliability and determine the ratio \(\overline{a}/\sigma\).

The choice of the first parameter is dictated mainly by economic considerations. To determine \(\overline{a}\) and \(\sigma\), one must know the laws of variation of the field intensity over the area under study. The mean value of the intensity of the sought anomalies \(\overline{a}\) can be determined from survey data that were specially obtained at the Darasun deposit. As a result, it was established that the mean ordinate of the most probable form of an anomaly caused by the Darasun veins is equal to 250–400 gamma, and their width is 60–80 m [1].

Fig. 1. Characteristic of anomaly detection by the Kotelnikov criterion (A. A. Nikitin et al.).

In studying the structure of the magnetic field of Darasun, it was also established that in the magnetic field of the deposit four types of magnetic-field disturbances are encountered most often. The mean values of the amplitudes of these anomalies are 500, 350, 370, and 250 gamma. Anomalies

have an average width of 150, 37, 18, and 9 m, respectively. Thus, the anomaly-to-noise ratio within this deposit will be close to unity, i.e.

\[ \frac{a}{\delta} \approx 1. \]

Knowing this, let us determine the number of points \(m\) falling on the anomaly, having first specified the degree of reliability with which it is to be identified. Let us take a reliability of 90%; then \(m=7\), and the spacing is 8–12 m. It is now necessary to establish which, in fact, variations in intensity will be significantly distorted at this spacing of measurements.

To do this, we calculate the intervals of “absence of correlation” for those variations in intensity that are most often encountered in the deposit. The boundaries of this interval \(l_1\) and \(l_2\) are determined by the formula

\[ l_{1,2}=\frac{k}{4}\cdot \lambda \pm \left(\frac{\lambda}{4}-\tau_{\mathrm{n}}\right), \]

where \(k\) is an odd positive number;
\(\lambda\) is the wavelength;
\(\tau_{\mathrm{n}}\) is the distance at which the normalized autocorrelation radius is less than 0.3.

The intervals of absence of correlation for the anomalies cited above will be: for the first, 65–115 m; 245–295 m...; for the second, 14–26 m; 54–66 m...; for the third, 6–12 m; 19–21 m...; for the fourth, 3–5 m; 11–13 m... . Thus, at the selected spacing the most probable anomaly caused by ore veins can be identified with 90% reliability against the background of variations in intensity localized at the third and fourth anomalies. As for the variations in intensity localized at the first two anomalies, it must be stated that these variations are practically impossible to distinguish from the sought anomalies on the basis of measurements on a single profile at any spacing.

We shall choose the distance between profiles on the basis of the following considerations. The ore veins at the Darasun deposit are accompanied by negative, linearly elongated anomalies. All other variations in the intensity of the vertical component of the magnetic field, to a first approximation, in comparison with the anomalies caused by veins, dikes, and fault disturbances, have an isometric form. Consequently, for effective application of the method of accumulation of survey profiles, it is desirable to arrange the profiles relative to one another so that the increments of intensity attributed to “noise” undergo a significant change, while the sought anomaly remains relatively constant.

The form of the disturbance in the magnetic field over quartz veins remains relatively constant, on average, over a distance of several tens of meters [2]. The most intense “noise,” comparable in magnitude with this interval, is localized at the third maximum in the spectrum of variations in the intensity of the magnetic field of Darasun. It is quite obvious that the profiles must be arranged so that these variations in intensity on adjacent profiles occur in antiphase. For this, the sampling interval must be taken equal to half the wavelength of these “noises,” i.e., on the order of 15–20 m. In this case the distribution of high-frequency variations in intensity localized at the fourth maximum in the spectrum of the deposit will be close to the normal distribution law, which will favorably affect the identification of the sought anomalies.

The variations in intensity attributed to large-scale “noise,” i.e., those localized at the first two anomalies, will not undergo significant change and, obviously, will correlate fairly well from profile to profile.

Under the conditions of Darasun, these “noises” may be considerably attenu-

can be identified without substantial loss of useful information if the area under study is covered not continuously by profiles spaced 15–20 m apart, but by series of profiles—which is important from an economic standpoint—taking the distance between the series in such a way that these “interferences” appear in each series in opposite phase. This distance between series of profiles must be chosen so that the distance between the midlines of adjacent series of profiles is half the wavelength of the “interferences,” i.e., on the order of 40–60 m.

In this connection, the question arises of choosing the number of profiles in one series. Under these conditions, it is most rational to take three profiles in one series. In that case, the distance between the outer profiles of a series will be equal to the period of oscillation of the intensity of the principal interferences, which will favorably affect the identification of the anomalies sought.

When the pattern of the magnetic field is very complex, and such a thinning of the survey profiles is impossible, this circumstance must be taken into account in interpreting the material obtained. In areas where vein formations are accompanied by anomalies of field intensity that are stable in form and magnitude, the survey may be carried out not by series of profiles, but by single profiles spaced 40–60 m apart.

These recommendations on the choice of a magnetic-survey network under the conditions of Darasun were used in studying the peripheral areas of this deposit. The survey was carried out over an area of about 15 sq. km. The results of checking the anomalies revealed by mining operations, as well as analysis of the field observed in the direction of thinning of the survey network, convincingly demonstrated the validity of the recommendations made for choosing the network of magnetic measurements.

REFERENCES

1. L. Ya. Erofeev. Structure of the magnetic field of the Darasun gold-ore deposit (Transbaikalia). This collection.

2. L. Ya. Erofeev. Forms of magnetic anomalies over the ore veins of the Darasun gold-ore deposit and their nature. This collection.

3. A. A. Nikitin, A. G. Tarkhov, I. N. Mikhailov. On evaluating the reliability of identifying weak geophysical anomalies by the method of inverse probabilities. Razvedochnaya geofizika, No. 15, 1966.