FORMATION OF SEISMIC INFORMATION RECORDING IN PHOTORECORDERS OPERATING IN CONJUNCTION WITH AN ELECTRONIC DIGITAL COMPUTER

Yu. M. Achkasov, V. A. Beinarovich, L. G. Vatskaya

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

Exploration for mineral resources, including oil and gas, is an important task of the national economy. In order to further expand exploration work and improve its geological effectiveness, it is necessary, among the most important problems, to develop new, more accurate methods and equipment for seismic prospecting, and also to develop automated equipment and methods for processing seismic information that make it possible to reduce the time required to issue results and to increase their accuracy.

Especially promising is the recently emerging use, for purposes of seismic prospecting, of electronic digital technology [1], which makes it possible to substantially increase the accuracy of seismic-information processing and to automate the processes of obtaining results. At present it is expedient to carry out the processing of geophysical information on general-purpose electronic digital computers (BESM-4, Minsk-22, etc.). The results of seismic prospecting are usually presented in the form of graphic images of depth sections of the earth’s crust, with the boundaries between layers of different physical density indicated. Seismic information obtained from an electronic digital computer after processing consists of nonsinusoidal seismic oscillations with frequencies on the order of 5–100 cps and a dynamic range of 42 dB. Each seismic signal (trace) is a lattice function with a constant time-quantization interval (2 msec) and ordinates expressed as numbers in binary code. The photorecorder is assigned functions associated with obtaining images of sections on photographic material by the methods of variable amplitude (Fig. 1, a), variable density (Fig. 1, b), variable width (Fig. 1, c), and a combined method—variable density and variable width (Fig. 1, d).

The photorecorder developed at the Research Institute of Atomic Energy contains a digital-to-analog converter (DAC), a filtering unit, an amplifier with automatic gain control, a playback unit with writing and indicator cathode-ray tubes, a logical control system, and an optomechanical section. Recording of seismic information is carried out trace by trace on photographic material fastened to a rotating drum, onto which the “writing stroke” from the writing cathode-ray tube is projected. This tube, together with the optical system, is located on a carriage that moves uniformly along the drum, parallel to its generatrix. The section is recorded in the form of a group of traces arranged in parallel (Fig. 1). In this case, scanning of the beam along the trace is accomplished by rotation of the drum, while the shift between individual traces is accomplished by—

Fig. 1. Methods of recording seismic information.

by means of carriage displacement (recording in a spiral, with a break at the point where the photographic material is fastened). The control system ensures strict in-phase positioning of the recorded traces along the drum sweep.

The formation of the various recording methods is carried out in the reproduction unit, whose functional diagram is shown in Fig. 2. Seismic information is fed to the input of the reproduction unit in the form of a nonsinusoidal voltage \(U_1\). Depending on the desired method of recording the section, set by the SZP switch, the formation of the “writing stroke” by the principal devices is carried out as follows.

a) Recording by the variable-amplitude method (Fig. 1, a).

The seismic signal is fed to a two-stage linear amplifier, comprising the cathode-follower stage KP, the amplifier stage U1, and a four-position divider ShP, which provides a fourfold change in amplitude scale when the trace-recording pitch is changed (the distance between traces is 1, 2, 3, and 4 mm). The signal is then fed to the push-pull amplifier PPU and from its output to the vertical deflection plates of the cathode-ray tubes: the recording tube PELT and the indicator tube IELT.

b) Recording by the variable-density method (Fig. 1, b).

The seismic signal is fed to the cathode follower KP, then to the modulation amplifier UM, and further to the modulators of the cathode-ray tubes PELT and IELT, producing brightness modulation. At the same time, a sawtooth signal from the sweep generator GZ, calibrated in amplitude for

Labels in Fig. 2 include: U1, KP, 1ShP, GZ, 1SZP, 2SZP, 3SZP, U1, PPU, PELT, IELT, UM, GVR, 2PU, BP.

Fig. 2. Functional diagram of the playback unit.

obtaining the length of the “writing stroke” on the PELT, is applied to the vertical beam-deflection channel (U1, PPU), ensuring, depending on the position of the ShP switch, a constant trace-recording width of 1, 2, 3, or 4 mm on the photographic drum. The frequency of the GZ signal exceeds the maximum frequency of the seismic signal by several tens of times, which ensures uniform exposure of all sections of the trace across the width on the photographic drum.

c) Recording by the variable-width method (Fig. 1, c).

The seismic signal is fed to the vertical beam-deflection channel (as in recording by the variable-amplitude method). At the same time, a sawtooth sweep signal from GZ is applied to the input of U1. As a result of the summation, a sweep-voltage signal with two-sided modulation by the seismic signal is obtained on the vertical deflection plates of the ELT. One half of the modulated signal is clipped, and the remaining part of the “writing stroke” is projected onto the photographic drum, which provides trace recording as the drum rotates by the variable-width method. The amplitude of the envelope (the seismic signal) is regulated by the recording-width switch ShP.

d) Recording by the combined method (Fig. 1, d).

This is provided by switching on the units according to method “c” and by additionally connecting the seismic signal for brightness modulation (to the input of UM).

In all recording modes, the vertical beam-deflection signal is simultaneously fed to the recording CRT, located on the movable carriage in the light-tight compartment of the photographic drum, and to the indicator CRT, mounted fixedly on the control panel. The indicator CRT serves for image adjustment and recording control. In the adjustment mode, instead of a seismic signal, a test signal with calibrated amplitude and a frequency of 50 Hz is applied to the input of the playback unit. In all operating modes, a sawtooth voltage from the time-sweep generator GVR, with adjustable frequency, is applied to the horizontal-deflection plates of the indicator CRT from the paraphase amplifier 2PU. This makes it possible to observe on the CRT screen several periods of the 50-Hz test signal in the adjustment mode, or a “floating” image of the seismic signal in the recording mode. The BP unit supplies power to all stages. All playback devices are made entirely with electron-vacuum devices. Compared with the semiconductor version, this made it possible to obtain increased stability of operation of the playback unit with stabilization only of the anode voltage, and also to ensure interchangeability of the devices.

The basic requirement imposed on the playback unit is linearity in converting the seismic signal into an image. The linearity of the conversion is determined by the degree of frequency (linear) distortion and by the nonlinear-distortion coefficient of the amplification path.

Frequency distortions are associated with nonuniformity of the frequency response of the playback unit. To reduce them, the frequency passband of the playback unit was chosen to be 10,000 times greater than the frequency band of the seismic signals; in the playback unit a minimum number of coupling capacitors is used, and no interstage or matching transformers are employed. In this case, the roll-off of the frequency response at high frequencies is determined only by the wiring capacitances and by the interelectrode capacitances of the amplifier tubes. The gain in this case begins to decrease only at a signal frequency of the order of several hundred kilohertz, which is practically of no importance, since the maximum frequency of the seismic signal is approximately 100 Hz. The greatest difficulties arise in amplifying seismic signals with the lowest frequency (of the order of 5 Hz). Here the reactance of the coupling capacitors begins to make itself felt.

The magnitude of the gain coefficient of the playback path is determined by the product of the gain magnitudes of the cascaded stages. The magnitude of the gain coefficient of a single stage is determined by the following expression [2]:

\[ |K(\omega)| = \frac{S} {\sqrt{(G_i+G_a+G_g)^2+ \left[ \frac{G_g}{\omega C_g}(G_i+G_a)-\omega C_0 \right]^2}} \tag{1} \]

where \(\omega\) is the angular frequency of the signal;
\(S\) is the transconductance of the tube characteristic;

\[ G_i=\frac{1}{R_i} \]

is the conductance of the tube;

\[ G_a=\frac{1}{R_a} \]

is the conductance of the anode load;

\[ G_g=\frac{1}{R_g} \]

is the conductance of the grid circuit;

\(C_g\) is the capacitance of the coupling capacitor;

\(C_0\) is the capacitance shunting the anode load (wiring capacitance and interelectrode capacitance of the tube).

Analysis of expression (1) shows that at medium frequencies the gain reaches a maximum

\[ \left|K(\omega_{\mathrm{avg}})\right| \approx \frac{S}{G_i+G_a+G_g}, \tag{2} \]

whereas at lower frequencies it decreases

\[ \left|K(\omega_{\min})\right| \approx \frac{S_{\min} C_g}{(G_i+G_a)G_g}. \tag{3} \]

From expressions (2) and (3), the relative value of the gain of one stage as the frequency is lowered is

\[ \Delta=\frac{\left|K(\omega_{\min})\right|}{\left|K(\omega_{\mathrm{avg}})\right|} \approx \frac{\omega_{\min} C_g}{G_g} \left(1+\frac{G_g}{G_i+G_a}\right), \tag{4} \]

whence one can obtain an expression for choosing the capacitance

\[ C_g \approx \frac{G_g\cdot \Delta} {\omega_{\min}\left(1+\dfrac{G_g}{G_i+G_a}\right)}. \tag{5} \]

Taking into account that the conductance of the grid-leak resistance \(G_g\) is usually much less than the total conductance of the tube \(G_i\) and of the anode load \(G_a\), the second term in the denominator of expression (5) may be neglected, and the simplest approximate relation obtained:

\[ C_g R_g \geq \frac{\Delta}{\omega_{\min}}, \tag{6} \]

which makes it possible to choose the stage parameters for prescribed values of \(\Delta\) and \(\omega_{\min}\). Thus, when four identical stages are used in the playback channel (recording modes \(a\) and \(g\)), with an allowable decrease in the total gain at the lowest frequency of \(5\ \mathrm{Hz}\) by 5%, we obtain

\[ C_g R_g \geq \frac{\sqrt[4]{0.95}}{2\pi\cdot 5}=0.0314\ \mathrm{F}\times\Omega . \]

The coefficient of nonlinear distortion is caused by the inevitable curvature of the tube characteristics, which in the general case leads to a change in the amplitude of the fundamental frequency of the signal and to the appearance of higher harmonics that distort the shape of the amplified signal. The analytical expression for the coefficient of nonlinear distortion is determined by [1]:

\[ K_f=\frac{\sqrt{A_2^2+A_3^2+\cdots}}{A_1}, \tag{7} \]

where \(A_1, A_2\), etc., are the amplitudes of the first, second, and subsequent harmonics of the output signal.

These amplitudes can be determined by representing the tube characteristic by means of a Taylor series and finding the currents for the individual harmonics. In practice, however, a graphical calculation method is used, which, by choosing the initial operating point in the middle of the linear portion of the tube characteristic and limiting the maximum possible signal amplitude, makes it possible to ensure a specified minimum value of the coefficient of nonlinear distortion [3]. Limitation of the amplitude at the level of the maximum permissible value is provided by the automatic gain-control (AGC) system of the preamplifier, from which the seismic signal is fed to the playback unit that forms the seismogram record.

REFERENCES

1. Collection. Digital recording and processing of seismic exploration information. Series: Petroleum Geology and Geophysics. VNIIŒNG, Moscow, 1968.
2. I. S. Gonorovskii. Fundamentals of Radio Engineering. Svyazizdat, 1957.
3. G. V. Voishvillo. Low-Frequency Amplifiers Using Electron Tubes. Svyazizdat, 1959.