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Temperature effects on long-period seismographs: an accurate method to determine the transfer function

INSTITUTE OF GEOPHYSICS SWISS FEDERAL INSTITUTE OF TECHNOLOGY, P.O.B. 266, CH-8049 ZURICH, SWITZERLAND

Abstract

A simple method for monitoring the transfer function of a long-period (LP) seismograph as a function of time is described. This method makes it possible, under certain restrictions, to estimate quite accurately (one order of magnitude better than the least-squares inversion of the calibration pulse) changes in the transfer function of a system using only the maximum amplitude information of the transient calibration pulses. The restrictions of this method are: (1) no change in the period of the horizontal seismometers (T_S) and galvanometers (T_G): (2) length of the spring of a vertical seismometer (boom position) is a function of temperature only; and (3) magnetic field is uniform in the range of expected boom (coil) excursions. In other words, the system parameters are affected only by temperature. Briefly, temperature affects mainly the resistance of the coils (copper) of seismometer (R_S) and galvanometer (R_G), which changes the current flowing in the circuit and hence the amplitude of the calibration pulse. The expected changes in the damping of the seismometer (h_S), galvanometer (h_G) and in the seismometer period (vertical component) have only negligible additional effect on the amplitude. Therefore, from the observed daily variation in the amplitude of the calibration pulses, it is simple to calculate changes in R_S and R_G and, hence, the in situ temperature as a function of time. The effect of temperature on the vertical seismometer boom position, and hence T_S, can be determined beforehand (or at any time) for each instrument. From this, T_S as a function of time can be inferred. Finally, from the calculated variations in R_S and R_G, variation in h_G can be determined; from variations in R_S, R_G and T_S, variation in h_S and then the coupling factor () can be determined. Analysis of the calibration data from a vertical component at Zurich for a 2-year period, 1972–73, is presented as an illustration of the method. The in situ seasonal temperature variation was inferred to be around ±4 C. In terms of the variation in the system phase response (delay), this amounts to about ±0.20 sec (at most) at a period of 100 sec, and less at shorter periods. This estimate is in good agreement with direct determination of the differences in phase delay for a similar system under controlled temperature conditions. It is also consistent with the fact that no systematic variation in phase response as a function of time was detected using the least-squares inversion of the calibration pulse (method not accurate enough). This indicates that the temperature effect on the phase response is fairly small and that under normal conditions modern LP instruments satisfy to a good approximation the requirements of this calibration method.