SOME FEATURES OF A DIGITAL-TO-ANALOG CONVERTER USED FOR PROCESSING SEISMIC INFORMATION

V. B. TEREKHIN, Yu. M. ACHKASOV, A. V. BARABASH

(Presented by the Sector for Automation of Oil and Gas Prospecting and Production Processes, Research Institute of AEM)

Seismic exploration is the leading method for prospecting oil and gas fields. However, the geological effectiveness of seismic exploration remains insufficient, which is the result of the imperfection of methods for analyzing seismograms. In the course of its development, the seismic method has always encountered difficulties, the chief of which are disturbances. These include:

a) disturbances excited by seismic sources of vibrations;
b) vibrations from nonseismic sources;
c) vibrations added during the reception, recording, and processing of seismic data.

The task is to isolate the useful signal against the background of the above-listed disturbances, that is, to increase the signal-to-noise ratio. This can be accomplished in two ways:

1. Conduct field work so as to excite a minimum of disturbances or eliminate disturbances during recording.
2. Process seismic signals so as to weaken or eliminate the disturbances contained in them.

In this respect, the second method of combating disturbances gives the best result. It includes the conversion of analog signals into digital form, accumulation, summation, filtering, and only after this reconversion into analog form for visual observation. Filtering a digital signal in an electronic digital computer is many times easier than filtering an analog signal.

The principal advantages of digital processing of seismic signals are the use of new mathematical programs, for example:

1. Velocity filtering.
2. Wiener filtering.
3. Horizontal stacking.
4. Suppression of satellite waves.
5. Inverse filtering (deconvolution).
6. Multichannel digital filtering.

Although the suitability of these methods has not yet been fully clarified, there is no doubt that new filtering operators will be found that are more effective than those currently available. Therefore, all other conditions being equal, digital processing of seismic information is much more advantageous than analog processing. It follows from the foregoing that one of the main units of the apparatus used in processing geophysical information in digital form is the “analog–code” and “code–analog” converters, which are subject to requirements corresponding to the nature and pecu-

features of geophysical information. Let us indicate the two most important of them:

1. The converters must be fast-acting, since the volume of geophysical information is large.

2. The conversion accuracy must be such that the signal is not distorted after conversion.

“Code—analog” converters may be divided into the following groups:

a) accumulating converters;

b) devices with intermediate conversion into time intervals;

c) devices with “Analog—code” converters in the feedback circuit (a digital tracking system);

d) bit-by-bit summation converters.

The principle of operation of accumulating converters consists in the fact that each pulse corresponds to a change in the analog quantity by one unit of voltage. However, their use is possible only in the case when the numerical quantity contains no jumps exceeding one. If this condition is violated, a systematic error inevitably appears.

In devices with intermediate conversion, the digital code is first converted into a time interval, and only then into an analog quantity. Their principal shortcoming is their high inertia.

Digital tracking systems have become widespread only for converting numerical codes into mechanical displacement. With the aid of such systems it is possible to convert a numerical code into an electrical quantity, but this is not expedient for two reasons: a) in a tracking system of this type there is an “Analog—code” converter, whose complexity is approximately equal to that of the “Code—analog” converter; b) sufficiently fast-acting, noise-immune converters of codes into electrical quantities are available, such as, for example, bit-by-bit summation converters operating in parallel.

In the present paper, certain features of a converter are proposed for consideration, the functional diagram and operating principle of which are described in [1].

As was indicated above, the basic requirement for converters is their high conversion accuracy. Converter errors may be of three types:

1. An error depending on the accuracy of operation of the converting device (instrumental error) [1].

2. An error arising as a result of the conversion principle itself, in particular from the discreteness of the input data (discreteness error). It depends on the conversion time \(T_{\mathrm{pr}}\), or, what is the same thing, on the sampling frequency \(f_{\mathrm{d}}\).

\[ T_{\mathrm{pr}}=\sum_{0}^{k} t_{\mathrm{el}}+t_{\mathrm{zad}}+t_{\mathrm{kl}}, \]

\(\kappa\) — the number of series-connected elements in the converter circuit with the same switching time;

\(t_{\mathrm{el}} = 0.6\ \mu\text{sec}\), for example, for element B—1 of the “Ural-10” complex;

\(t_{\mathrm{zad}}\) — delay time in the passage of a pulse through an element;

\(t_{\mathrm{zad}} = 0.2\ \mu\text{sec}\);

\(t_{\mathrm{kl}}\) — switching time of the electronic key;

\(t_{\mathrm{kl}} = 0.5\ \mu\text{sec} \div 0.8\ \mu\text{sec}\) (obtained experimentally for keys on P16B and MP11A transistors)

The total conversion time is \(5\ \mu\text{sec}\). Consequently, the maximum sampling frequency is

\[ f_{\mathrm{d}}=\frac{1}{T_{\mathrm{pr}}}=200\ \text{kHz}. \]

Decodi-

converters yield not the true value of the analog quantity, but an approximate one (Fig. 1). The latter depends on the quantization level of the seismograms in the digital computer.

Let us estimate the relative error of the analog signal as a result of discretization.

Let \(F(t)\) be a continuous function, \(f = 10^2\) Hz, \(T/2 = 5\) ms, \(f_{\mathrm{d}} = 500\) Hz, discretized at a frequency

\[ S_{\text{cont}}=\int_{0}^{T/2} F(t)\,dt \]

—the area enclosed between this function and the abscissa axis.

\(f(t_0 t_1 t_2 \ldots t_n)\) is the step function obtained as a result of the conversion.

\[ S_{\text{st}}=\sum_{0}^{n}\frac{b-a}{n}(y_0+y_1+y_2+\ldots+y_n) \]

—the area bounded by the step function and the abscissa axis.

\(n\) is the number of conversions in a half-period of the analog signal;

Fig. 1. 1 — analog signal before discretization;
2 — step signal after conversion.

\(b-a\) is the segment of the abscissa axis on which this function is considered. This sum \(S_{\text{st}}\) is an integral sum for \(F(t)\) on the interval \(T/2\) and approximately expresses the integral computed by the rectangle formula.

\[ \int_{0}^{T/2} F(t)\,dt=\frac{b-a}{n}(y_0+y_1+y_2+\ldots+y_n) \tag{1} \]

The relative discretization error obtained when computing the step function by the rectangle formula is equal to:

\[ \Delta=\frac{b-a}{n}=\frac{T/2}{n}. \tag{2} \]

For \(T/2 = 5\) ms, \(n = 250\) Hz, the error is \(\Delta = 2 \cdot 10^{-5}\). It follows from formula (2): the higher the frequency of the analog signal (the smaller \(T/2\)), the smaller the error for \(n=\mathrm{const}\).

The factor determining the speed of the converter is the magnitude of the dynamic error, by which is meant the degree of aging of information due to the time required for the conversion process. However, no special requirements are imposed on the dynamic error, since quantitatively it represents the difference between the true value of the quantity being converted at any moment of the conversion process and the value obtained by the conver-

…of the input and output quantities at the same instant of time:

\[ \rho_{\text{dyn}} = f_{\text{src}}(t_1) - f_{\text{out}}(t_1). \]

The dynamic error can be determined experimentally during operation of the “code–analog” converter in the process of processing geophysical information.

The developed and described converter is used in the seismic-section plotter (SSR), operating in conjunction with a BESM-4 electronic digital computer. The operation of the converter with the electronic digital computer is explained by the timing diagram in Fig. 2.

Fig. 2. Timing diagram of the operation of the “code–analog” converter with an electronic digital computer.

The logical control system of the SSR generates the signal “Number-code request” (Fig. 2, а) and its inversion (Fig. 2, б). The “Request” signal is fed into the converter to the circuit that generates the “synchronizing pulse” signal. From the negative edge of the inverted “Request” signal, the “Reset” signal is generated, which is fed to the electronic digital computer to bring the computing machine into readiness (Fig. 2, в). The code in the output register of the electronic digital computer

appears on the positive edge of the signal as an inversion of the “Call” (Fig. 2, ж). The “Call” signal in the converter is fed to the input of the delay element (monostable multivibrator), after which a “sync pulse” signal is formed for reading the code in the converter (Fig. 2, г, д, е).

The “Code–analog” converter has successfully passed laboratory tests and interfacing with the electronic digital computer, and is now in operation for the processing of seismic information.

REFERENCES

1. V. B. Terekhin, A. V. Barabash. Digital-to-analog converter for the output of seismic information from an electronic digital computer. Proceedings of the VI Scientific and Technical Conference on Automation. Tomsk State University Publishing House, 1969.

2. A. A. Bogdanov, A. S. Petrov. Digital recording and processing of seismic information, “Nedra,” Moscow, 1968.

3. A. B. Zavolokin. “Code–analog” converters, 1966.

4. B. N. Khlistunov. Fundamentals of digital electrical measuring technology. “Energiya,” 1966.

5. E. K. Krug, G. M. Aleksandridi. Digital regulators. “Energiya,” 1966.