A RAPID METHOD FOR CALIBRATING WILLMORE SEISMOGRAPHS

Size: px

Start display at page:

Download "A RAPID METHOD FOR CALIBRATING WILLMORE SEISMOGRAPHS"

Osborn Lambert
5 years ago
Views:

1 Bulletin of the Seismological Society of America. Vol. 54~ No. 5~ Part A, pp October~ 1964 A RAPID METHOD FOR CALIBRATING WILLMORE SEISMOGRAPHS BY K. G. BARn ABSTRACT A method is described for calibrating Willmore seismographs. It could be applied to any other electromagnetic seismograph having a galvanometer period substantially shorter than the seismometer period. The method is rapid and involves very little equipment. An overall accuracy of 20% in the velocity sensitivity is easily attainable. The calibration of an electromagnetic seismograph involves determining its magnification or velocity sensitivity as a function of period. This can be done by injecting a sinusoidal e.m.f, into the seismograph circuit and measuring its response as a function of the signal period (Willmore 1959) or by applying a step or impulse signal and Fourier analyzing the response (Espinoza et al 1962). The first method requires a signal generator that can produce very low frequency signals, and the second requires an analogue or digital computer. Both are suitable for observatory use, but are unsuitable for field use. The method to be described uses equipment that can be built into ~ box measuring 6" x 6" x 4", and enables the calibration curve to be rapidly constructed. The velocity sensitivity of any electromagnetic seismograph can be written (Willmore 1960) where S~ = AF(Xg, T/T,)F(X~, TITs) (1) 1 -- BF(Xg, T/Tg)F(M, T/T~) F(X, x) = jx (2) x 2-1 -{- 2j~c ag ~s 1 A = 41dM X 10-7 X~ X ~ X (3) B - 4R~ R~ z2 - - (4) Here Xg and X~ are the galvo and seismometer in circuit damping coefficients, G and ~ are the galvo and seismometer open circuit damping coefficients, Tg and T~ are the galvo and seismometer free periods in seconds, a~ and as are the galvo and seismometer current sensitivities in cms/amp, Rg and R~ are the galvo and seismometer circuit resistances in ohms, M is the seismometer mass in grams, Z is the transfer resistance of the network in ohms, ] Sv [is the velocity sensitivity in secs, arg Sv is the angle by which the ground velocity leads the seismograph trace. 1473

2 1474 BULLETIN OF THE SEISMOLOGICAL SOCIETY OF -&MERIC-& The seismometer current sensitivity can be found from the relation between the seismometer damping coefficient and the seismometer circuit resistance. 41raMa, 2 X 10 -r X, = ~, + (5) TsaR, The term involving B represents the galvanometer reaction. The measurements to be described permit this term to be calculated, but the calculations are greatly simplified if it can be ignored. In the case of a Willmore seismograph the attenuator is adjusted so that Xg and X~ are both approximately 0.5, and the internal damping can be neglected. The nominal galvanometer and seismometer periods are 0.25 sec. and 1.0 secs. In Fig. 1 F(0.5, x) and the product F(0.5, T/.25) X F(0.5, T/1.0) +J / F(0.5, 0.~5 ) F (0.5, i.~) ~_- i4. 0 = 2.0_~ x=l.5 ~ FCO.5,x) x=o'2d x=o 5 T=0'25 1 -J " x=0.67 FIG. 1 are plotted on a polar diagram, using the property that the locus of F(X, x) is a circle of radius ¼X and centre ({k, 0). It is clear from the diagram that the quantity 1 I 1 -- BF(0.5, T/0.25) F(0.5,T/1.0) is a maximum at T = 0.5 sec., where its value is B The maximum sensitivity used in the network operated by the Seismic Research Unit employs the network shown in Fig. 2, for which Rg = 405~; R, = 599~; Z = 1760~ giving B =.078. In this case the factor will not differ from unity by more than 2.4% and we can write I & l = n I F(x~, T/T~) I[ F(X,, T/T~)I (a)

3 CALIBRATING WILLMORE SEISMOGRAPHS 1475 To calculate the velocity sensitivity we need to know the seismometer mass, the transfer resistance of the network, and the current sensitivities, free periods and damping coefficients of the seismometer and galvanometer. The seismometer mass and all of the circuit resistances can be assumed to stay constant, and need only be measured once. In any repeated calibration we need only determine a~t~x~agtg and X,. This can be done rapidly using the test circuit shown in fig. 3. To measure the galvanometer parameters, the seismometer is unplugged, the switches $1 and S~ are in positions A. The recorder is set running, and a current step applied to the galvanometer circuit by closing $2. This is done for three different galvanometer circuit resistances selected by $4. The circuit resistances are all less than the critical damping resistance of the galvanometer so that the damping coefficient and period for each value of the circuit resistance can easily be measured on the record. 220C1 t, o: FIG C~ 2.2MCt,/x/x, SEISMOMETER l 1.2K K 180~ FIG. 3 The free period of the galvanometer is found by plotting the period of the oscillations against (1 - Xg2) -1/2 and taking the slope. The damping coefficient is found by plotting Xg against 1/Ro and extrapolating to the value of 1/R~ in the operating circuit. If the galvanometer reaction is required ag is also determined from this graph. The current sensitivity is found by measuring the shift in the rest position of the galvanometer, and calculating the galvanometer current from the battery voltage and the circuit resistances. The seismometer parameters are found by plugging in the seismometer, opening the switch $2 and switching S, to position B. When $1 is switched to B, a current is passed through the seismometer coil which deflects the mass. $1 is then returned to position A and the oscillations of the seismometer mass recorded by the galvanometer. In this circuit the galvanometer is critically damped and coupled very loosely to the seismometer. The fact that the galvanometer period is only a quarter of the seismometer period ensures that the galvanometer transients can be ignored after the first swing of the mass. The periods and damping coefficients are measured

4 1476 BULLETIN OF THE SEISMOLOGICAL SOCIETY OF AMERICA F(X, x) I / \ k= ~= 3.5 f,~ X= 0.7 ~ /j \,.2 / \.I I FIG. 4 \ x \ lsv I in sec 104 [F(~.g, TITs) 1 /-IFO,~, T/T~) I > )~i I03 O.Ih 102 I I0 period in sec. FIG. 5

5 CALIBRATING WILLMORE SEISMOGRAPHS 1477 for each value of the circuit resistance, and the free period, the damping coefficient in the operating circuit, and, if necessary ~8, determined as before. The current sensitivity of the seismometer is determined from the slope of the plot of k8 against 1/R., which from equation (5) is 4~3M~ 2 X 10-7 ohms. T~ ~ The velocity sensitivity curve of the seismograph can be rapidly constructed if galvanometer reaction can be ignored. A set of templates of IF(k, x) / are required, cut on the same log log scale as the final sensitivity curves, as in fig. 4. Near to one of the free periods, the velocity sensitivity is inversely proportional to the damping of the component concerned, so a template for each multiple of 0.05 is sufficient to ensure that the error in velocity sensitivity nowhere exceeds 10%. Six templates are adequate to cover the range of damping coefficients encountered with Willmore seismographs. Each template is ruled with a line corresponding to the free period (x = 1) and a line corresponding to [ F()~, x) I = 0.1. Figure 5 shows how the final velocity sensitivity curve is constructed. A horizontal line I S~ I = 0.1A is drawn on the graph, and each template is positioned as shown in figure (5), and its outline drawn on the graph. The sum of the two curves is constructed with the line I Sv I = A as zero using the edge of a piece of paper, and the resulting curve is the velocity sensitivity curve. Seven of the seismograph stations maintained by the Research Unit have been calibrated in this way every few months since Their velocity sensitivities have varied by less than 10% during this time. ~EFERENCES Willmore The application of the Maxwell impedance bridge to the calibration of electromagnetic seismographs. B.S.S.A. Vol. 49, pp , Jan. Espinoza, Sutton & Miller A transient technique for seismograph calibration. B.S.S.A. Vol. 52, No. 4, pp , Oct. Willmore The detection of earth movements. Methods & Techniques in Geophysics Vol. 1. UNIVERSITY OF THE WEST INDIES ST. AUGUSTINE, TRINIDAD Manuscript received March 2, 1964.

SHIVAJI UNIVERSITY, KOLHAPUR

SHIVAJI UNIVERSITY, KOLHAPUR s Seat GROUP III 1. Transistor Series Voltage Regulator With a given rectifier, prepare a regulated power supply, using transistor. Vary output currents changing load resistance. Hence measure output voltages