Bulletin of the Seismological 5ociety of America, Yol. 52~ No, 4~ pp. 767-779 . October a 1962

A T R A N S I E N T T E C H N I Q U E FOR S E I S M O G R A P H C A L I B R A T I O N

]~¥ A. F. EsPiNOS•, G. I-I. SUTTON, AND H. J. MILLER, S.J.

ABSTRACT

A transient technique for seismograph calibration was developed and tested by a variety of methods. In the application of this technique a known transient in the form of an electrical signal is iniected, through (a) a Willmore-type calibration bridge or (b) an independent coil, into the seismometer and the corresponding output transient of the system is recorded. The ratio of the Fourier transform of this transient to that of the input pulse yields phase and rela- tive amplitude response of the seismograph as a function of period. Absolute amplitude re- sponse may be calculated if two easily determined constants of the seismometer are known. This technique makes practical the daily calibration of continuously-recording seismographs without disturbing the instruments more than a very few minutes. The transient technique was tested and proven satisfactory with results of more conventional steady-state methods, using both digital and analog analyses of the output transients.

A variety of output transients corresponding to various theoretical response curves has been calculated for two standard input transients. By comparison of the calculated output transients with experimental results it is possible to obtain the response of the instrument with consider- able precision quickly and without computation.

INTRODUCTION

This paper describes a method for calibrating a seismograph rapidly, accurately, economically, and frequently. The seismograph is considered a "black box," and a known transient is applied to the input of the box and the consequent output transient is recorded. The ratio of the Fourier transforms of the output and input transients yields both the phase and relative amplitude response of the system. For an electromagnetic seismograph the amplitude response in absolute units may also be obtained if two parameters of the seismograph system, the electrodynamic constant of the seismometer coil and the mass of the seismometer boom are known, providing the mass and seismometer coil are at the same distance from the hinge point. If this is not the case, the ratio between the distance from the hinge point to the center of mass and that from the hinge point to the coil is also needed. No additional knowledge such as the period, damping, and coupling of the component parts is required.

The principle of this method is not new and it has been used by others (for example: Sohon, 1932; Chakrabarty, 1949; Matumoto, 1958; Duclaux, 1960). However, some variations in the application of the method which make calibration possible on a routine daily basis are described here, and results of tests which give some estimates of the accuracy under various operational schemes are also described.

The calibration procedure described in this paper permits daily determination of the amplitude and phase characteristics of the seismograph with very little effort. I t is only necessary to compare the observed transient response with a preealculated set of transients for black boxes whose amplitude and phase responses are known. These pre-ealeulated transients may be prepared to show the effect of variation of individual instrument parameters on the system response so that the method is of value during instrument installation and adjustment as well as in record interpreta- tion.

767

768 :BULLETIN OF THE SEISMOLOGICAL SOCIETY OF AMERICA

The convenience and flexibility of the transient method contrasts with the difficulties of the usual situation wherein the instrument is calibrated infrequently, perhaps once a year, and it is assumed that no changes occur over this interval. The transient method is, of course, quite general and may be applied to any kind of seismograph or similar instrument, providing a suitable input pulse can be injected into the system. Transient techniques have the advantage over steady-state techniques in that the entire calibration may be obtained with only a brief dis- turbance of the record.

EXPERIMENTAL PROCEDURE

For the present study, two kinds of long-period seismographs were used. Both contain the same basic long-period seismometer, the Columbia or its near equivalent, the Press-Ewing, manufactured by the Sprengnether and the Lehner and Griffith companies, respectively. In one case, here called configuration A, the seismometer was coupled to a long-period recording galvanometer (Lehner and Griffith) through a passive resistive network. In the other case, configuration B, the seismometer was coupled to a Varian G-10 graphic recorder (manufactured by Varian Associates) through an active coupling network. With the latter arrangement, it was possible to provide an analog voltage at the output which could be automatically converted to digital form for certain of the tests described later.

In both cases a calibrating bridge (Willmore, 1959) was built into the circuit permanently. Although Willmore described its use only for a steady-state method of calibration, the bridge serves equally well for transient calibration, (Duclaux, 1960). The parameters of the bridge are included in the overall design of the system and, in fact, may be chosen to have a negligible effect on the response of the system. For the cases discussed here, a step or an impulse of current was applied to the seismometer coil. This causes a displacement of the boom which is equivalent to that resulting from a step or impulse in acceleration of the earth. If the transducer has appreciable inductance, the time variations of the impressed current will be somewhat modified, resulting in a reduction of the high frequency components of the input signal.

For comparison purposes, on one of the instruments the input transient was also applied to a second coil, independent of the signal detecting coil and the bridge (Murphy, 1954, has described the steady-state method using an extra coil). An auxiliary coil can also be used for the calibration of nonelectromagnetie seismo- graphs. Lifting a small weight from the mass is another method for obtaining an input transient equivalent to the injection of the electrical step function described

a b o v e . In order to test the transient technique for seismograph calibration and to

compare its precision with that of other methods, a series of experiments was per- formed. These experiments were: (a) transient (step and impulse I) calibration using a calibrating bridge, (b) transient calibration using an independent coil, (e) steady- state calibration using a calibrating bridge, and (d) steady-state calibration using an independent coil.

1 In practice this is a decaying exponential pulse, whose t ime constant is small compared to the periods of interest , obtained from the discharge of a eondensor.

A T R A N S I E N T T E C H N I Q U E F O R S E I S M O G R A P H C A L I B R A T I O N 769

In addition, a number of output transients and corresponding response curves were obtained for a variety of theoretical seismographs through the use of an analog computer. These curves are instructive and have many uses, particularly in relation to seismograph design. Certain of the transients were compared with experimental data to demonstrate and evaluate this method of obtaining response curves. The accuracy of the analog computer (a Pace TR-10 manufactured by Electronics Associates, Inc.) was shown to be more than adequate for this applica- tion by comparison with results obtained by digital methods.

A S

D

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BALANCE CONDITION

R/R I = R2/R 3

I_-/,--I,l~v~ R4

R 6

STEP FUNCTIONINPUT

IMPULSE FUNCTION INPUT

STEADY STATE FUNCTION INPUT

FIG. 1. Circuit diagram of seismograph calibration bridge and calibration function generators.

The purpose of the calibrating bridge is to permit the application of a forcing electrical signal to the seismometer coil without disturbing the recording element, but in x way such that this element is left free to respond to the motion of the seismometer boom resulting from the applied signal (Willmore, 1959). Figure 1 shows a circuit diagram of a seismometer coupled to a galvanometer through a resistive network which includes the calibrating bridge. If there is appreciable inductance in the seismometer coil, a reactive element is required for balance of the bridge (Willmore, 1959) but. inductance is negligibly small in the long-period instruments used in the tests described here and the bridge is entirely resistive.

In figure 1, resistors R and r include the internal resistances of the seismometer and galvanometer respectively, S is the shunt resistor. Resistors R1, R~, and R3 are elements added to complete the calibrating bridge. By choosing R~ much larger than R, and R1 much smaller than R, the circuit as seen by the seismometer and

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A T R A N S I E N T T E C H N I Q U E F O R ~ E I S N I O G R A P H C A L I B R A T I O N

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PERIOD (SECONDS)

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FIG. 3. Comparison of long-period seismograph response to acceleration as obtained by impulse, step and steady-state techniques for a one coil system with calibrating bridge. Solid curve is the same for the three cases (configuration B).

I i , l l l l l i I I 1 1 1 1 , w I i i t i l l - 4 . 0

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RESPONSE -- 1.0 -(RADIANS)

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PERIOD (SECONDS) FIG. 4. Displacement phase response corresponding to conditions of figure 3. Circles correspond

to steady-state, solid line to step and dashed line to impulse (configuration B).

772 B U L L E T I N O F THI~ S E I S M O L O G I C A L S O C I E T Y O F /kM]~R1CA

by the galvanometer is essentially the same as the simple " T " coupling network normally used. Thus, the response of the system is not appreciably modified by a temporary introduction of the bridge. Even this small difference between the op- erating and calibrating configurations may be eliminated by including the bridge

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FIe. 5. Comparison of long-period seismograph response to acceleration as obtained by im- pulse, step and steady-state techniques using an independent calibrating coil. Solid curveis the same as in figure 3 (configuration B).

as a permanent part of the circuit and including the bridge parameters in the overall

design of the seismograph. The symbol T is used here for free period, ~o for angular frequency, e for the damp-

ing coetficient and z for coupling coefficient (Sutton and Oliver, 1959). The sub- scripts 0 and g refer to the seismometer and galvanometer respectively. For con- tiguration A, T0 = 30 sees, T~ = 100 sees, e0 ~ 0.75 co0, eg = 0.8 ~og, z = 0, R = 465 ohms, R1 ~ 10 ohms, R2 = 100K ohms, and R3 consists of a 2K ohms fixed resistor in series with a resistance variable from 0 to 250 ohms.

A T R A N S I E N T T E C H N I Q U E F O R S E I S M O G R A P H C A L I B R A T I O N 773

For configurat ion B, To = 15 secs, e0 ~ 0.6 ~0, ¢ = 0, R = 217K ohms, R1 = 2K ohms, R2 = 10M ohms and R3 consists of a fixed 45K ohms resistor in series wi th a resistance variable f rom 0 to 71K ohms. This seismometer feeds into two cascaded single stage low-pass R C filters, each cornered at 45 seconds, then to a Hewle t t -Paekard lk~[odel 425A D.C. amplifier. The amplifier drives a digitizer and a Var ian recorder. The recording circuitry is equivalent to a recording ga lvanometer with Tg -- 45 sec, e~ = 1.1 ~g.

Seismographs with electronic amplification or more complicated circuitry t h a n

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STEP FUNCTION OF ACCELERATION

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m ANALOG COMPUTER OUTPUT ee DIGITAL COMPUTER OUTPUT

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TIME (SECONDS) FIG. 7. Comparison of transient response of theoretical seismograph (To = 30 sec, T~ = 100 see.)

to step function of acceleration obtained from digital and analog computers.

77~ BULLETIN OF THE SEISMOLOGICAL SOCIETY OF AMERICA

that shown in figure i (for example, circuits including a filter galvanometer, Pomeroy & Sutton, 1960) can be calibrated in a similar manner. In all cases, the circuit seen by the seismometer coil is put across the terminals B and C.'

Normally the bridge is balanced by clamping the seismometer boom and adjusting R~ for zero galvanometer deflection as a transient or steady-state signal is applied to the terminals A and D of figure 1. Of course, R1 or R3 can also be used as the variable arm of the bridge. Variation of R1 produces the smallest variation in the impressed coil current. During routine operation, the balance of the bridge m a y be checked by using a step function for calibration and observing any deviations from

I I FIG. 8. Typical output data from analog computer for impulse and step of acceleration and

steady-state displacement input for one set of instrument parameters: TJTo = 3, ~0.-- ~o0, eg = ~o~ , a = 0. Number shown for Lissajous figures equal ratio of driving period to To/z.

the normal equilibrium position of the trace after the transient response to the step has died out. Simple circuits for generating a step, impulse, or sinusoidal input (from a commercial ultra-low-frequency oscillator) are also indicated in figure 1. Values of the generating circuit parameters may be adjusted to give an output signal of convenient amplitude.

At Palisades, in routine operation the transient calibration technique is in use on several long-period seismographs and will soon be added to others. A step function is normally used, largely because it is easy to generate, and is applied at the end of one day's record and at the beginning of the next so as to minimize bat tery drain. Polari ty is fixed so tha t the greatest deflection is toward the center of the record in each case. Although the calibration signals could easily be applied automatically at a given time, it is preferable to retain remote manual control by an operator with access to a visible recording seismograph. This avoids superposition of the calibration pulse on the record of an earthquake. A typical record showing two calibration pulses is shown in figure 2.

A T R A N S I E N T T E C H N I Q U E F O R S E I S M O G R A P H C A L I B R A T I O N 775

When the seismometer has a second or auxiliary coil, of course, no bridge is required and it is only necessary to apply the desired input transient or steady-state signal to this coil and to observe the corresponding output. In order that the cir- cuitry used with the independent coil for injecting the desired input does not modify the system, the external resistance is 5 to 10 times greater than the critical damping resistance of the independent coil.

In order to measure the effectiveness of the transient method of calibration, a number of comparisons of the results obtained by this method with those obtained

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.I 1.0 I0.0 I00.0 Tground / T O

FIe. 9. Relative displacement response curves for four sets of instrument parameters.

by the steady-state method, were made. For these tests the transient output of the seismograph with electronic amplification was digitized by driving an encoder, associated electronics, and an IBM card punch. A Fourier transform of this transient was then obtained using an IBM 709 digital computer. If an impulse is used as the input, the Fourier transform of the output corresponds to the acceleration response of the instrument. Amplitudes must be multiplied by co 2 to get the dis- placement response and phases must be increased by ~r to get the corresponding phase response. If a step is used as the input, the Fourier transform corresponds to the integral of the acceleration response and the amplitudes must be multiplied by ~ to get the displacement response and phases must be increased by 37r/2 to get the corresponding phase response.

Figures 3 and 42 show a comparison of the magnification and phase response data

The phase response curves shown in the following papers are in error by ~ radians : Hagi- wara (1958) ; Brune, Nafe, and Oliver (1960) ; Pomeroy and Sutton (1960).

776 B U L L E T I N OF T H E S E I S M O L O G I C A L SOCIETY OF AMERICA

for a one coil seismograph with a calibrating bridge as determined by the impulse, step and steady-state techniques. Identical solid lines are drawn through the data of Figure 3 for ease of comparison. The three methods give results which are in good agreement throughout the period range of interest and the precision of the methods may be estimated from the scatter of the data. This precision is more than adequate for virtually all present applications to data from seismograms. Figures 5 and 6 show similar results obtained with an independent calibrating coil and the same conclusions apply. It is evident that in the short-period range the scatter is less for the impulse than for the step. This is expected since the ampli-

~ I E N T RESPONSES TO STEP OF ACCELERATION

To

A ~ S I E N T RESPONSES TO IMPULSE OF ACCELERATION

I I To 5

FIa. 10. Transient responses for four seismographs listed in figure 9.

tudes of the frequency components in a step function decrease with increasing frequency, while for an impulse the amplitudes are all equal (Goldman, 1948).

The seismograph equation was set up on a digital and on an analog computer. Figure 7 shows a comparison between the theoretical transient responses to a step function of acceleration obtained from the two computers. This test demonstrates that the precision of the analog computer is satisfactory for this application. Sueh analog computations are used extensively in subsequent work.

Figure 8 shows a typical output sheet from the analog computer for a theoretical seismograph with E0 = coo, eg = cog, ~ = 0, and T~/To = 3. The transient responses shown in the lower part of this figure are for an input step and impulse of accelera- tion into the system. I t is evident that the impulse response is the derivative of the step response. The Lissajous figures were obtained by applying the equivalent of steady-state displacements of various periods to the system. The output is plotted on the y axis and the input on the x axis. The steady-state amplitude and phase

A TRANSIENT TECHNIQUE FOR SEISMOGRAPH CALIBRATION 777

displacement response (magnification) of the seismograph are obtained from the Lissajous figures by measuring the distances A, B and C as shown in the lower right of this figure. The ratios A/B and C/B yield the amplitude and sine of the phase response corresponding to the period listed in the middle of the Lissajous figure (Number shown equals ratio of driving period to T0/2). With a set of data sheets such as these the magnification of a seismograph can be obtained by matching the experimental and theoretical transients and using the theoretical steady-state response given on the appropriate data sheet. When such sheets are prepared for superposition on a seismogram the transients are scaled to the time scale of the seismogram and a number of pulses of different amplitudes are plotted to facilitate comparison. The method of determining absolute gain is described in the appendix.

An estimate of the resolution which can be obtained by the transient comparison technique can be obtained from figures 9 and 10. Figure 9 shows a set of relative .displacement response curves, and figure 10 the corresponding output transients for input steps and impulses. It is clear that resolution at least as good as that required for normal seismogram analysis may be obtained. Since the process of taking in- formation from the seismogram in the transient calibration technique is much like that used in normal record interpretation, it is unlikely that more accurate calibra- tion will be required before better methods of handling seismic data are developed. A series of output pulses on a time scale of i minute = 15 mm with the correspond- ing response curves has been constructed for approximately 100 different eases for long-period seismographs and is available in the form of a set of transparencies for direct comparison with seismograms.

CONCLUSION

In conclusion, the transient technique for seismograph calibration is shown to be a simple and reliable method of calibrating the system, requiring only a short time disturbance of the record. The transient response of the system, when Fourier analyzed, yields the frequency response with a precision equivalent to that obtained by means of steady-state methods. This technique can also be used in adjusting a seismograph by matching the transient response to that of a desired system. The ,overall response of the system is obtained without the necessity of determining either the period, damping or coupling of the seismometer or of the galvanometer.

ACKNOWLEDGMENTS

The authors are grateful to Jack Oliver who gave continuous advice and encouragement and who suggested the idea of compiling a book of transients with their associated steady-state responses. Mark Landisman, Yasuo Sato, and Paul Pomeroy provided helpful discussions and :suggestions.

This work was partially supported by the VELA-UNIFORM Program under contracts AF 19(604)7376 and AF 19(604)8375 with Air Force Cambridge Research Laboratories.

Computing facilities were made available by the Watson Scientific Computing Laboratory, Columbia University.

APPENDIX

The absolute magnification, M, at a given frequency, f, can be obtained from comparison of the seismograph output transient with a set of standard transients

778 B U L L E T I N OF T H E S EIS M OLOGICAL SOCIETY OF A M E R I C A

resulting from a step input. This need be done at only one frequency to fix the scale of the relative magnification curve.

The following equation applies:

M = D f / Y F = - ( m / G ) ( D / / D t ' ) ( v t ' / v / ) D t / i t

where

m / G =

D s ' / D t' =

V t t / V f ! =

D t =

it =

D s = y ~ =

ratio of mass to electrodynamic constant of seismometer being cali- brated ratio of s teady-state trace ampli tude to max imum trace ampli tude of the transient for the s tandard ratio of ampli tude of transient input to ampli tude of s teady-state input for the s tandard max imum trace ampli tude of the calibration-transient of seismograph ampli tude of calibration-transient driving current to coil of seismometer s teady-state trace ampli tude of seismograph steady-state ground motion

The electrodynamic constant can be obtained using

G 2 = 2 ( h - h , , ) o J o m R

where h = E0/~0 is the seismometer damping factor when the seismometer coil sees a total resistance R, including the internal coil resistance, and h~ is the open circuit (mechanical) damping factor.

REFERENCES

Brune, J. N., J. E. Nafe, and J. E. Oliver 1960. "A Simplified Method for the Analysis and Synthesis of Dispersed Wave Trains",.

J . Geophys. Res . , 65: 287-304. Chakrabarty, S. K.

1949. "Response Characteristics of Electromagnetic Seismographs and Their Dependence on the Instrumental Constants," Bull. Seism. Soe. Am. , 39: 205-218.

Duclaux, Mme F. 1960. "Seismometrie Theorique, Memorial des Sciences Physiques," Fascicule L X I V ,

Gauthier-Villars, Paris, France, 38-44, 98-110. Goldman, S.

1948. Frequency Analysis Modulation and Noise, McGraw-Hill Book Co., New York, 53-140.

Hagiwara, T. 1958. "A Note on the Theory of the Electromagnetic Seismograph", Bull. Earthq. Res.

Inst., Tokyo Univ., 36: 139-164. Matumoto, T.

1958. "Calibration of an Electromagnetic Seismograph by Means of the Frequency Analy- sis," Bull. Earthq. Res. Inst., Tokyo Univ., 30: 55-64.

Murphy, L. M., R. M. Wilson, L. R. Burgess, and T. H. Yearce 1954. "Response Curves of an Electromagnetic Seismograph by Sine-Wave Simulator

Methods," Bull. Seism. Soc. Am. , 44: 7-20.

A TRANSIENT TECHNIQUE FOR SEISMOGRAPH CALIBRATION 779

Pomeroy, P. W. and G. H. Sutton 1960. "The Use of Galvanometers as Band-rejection Filters in Electromagnetic Seismo-

graphs," Bull. Seiem. Soc. Am., 50:135 151. Sohon, P. W.

1932. Seismometry. Introduction to Theoretical Seismology, Part II, Wiley, N. Y. Sutton, G. H., and J. Oliver

1959. "Seismographs of High Magnification at Long Periods," Annales de Geophysique, 15: 423-432.

Willmore, P. L. 1959. "The Application of the Maxwell Impedance Bridge to the Calibration of Electro-

magnetic Seismographs," Bull. Seism. Soc. Am., 49: 99-114.

LAMONT GEOLOGICAL OBSERVATORY COLUMBIA UNIVERSITY PALISADES~ ]NTEw YORK CONTRIBUTIO~ NO. 564.

Manuscript received on January 24, 1962.