MINIMUM-PHASE SEISMOGRAPHS AND THE DETERMINATION OF THEIR PHASE RESPONSES

On the basis of minimum-phase criteria analysis has been made for some kinds of seismographs which are now in common use at Chinese seismological stations. The result shows that such seismographs are minimum-phase systems. The phase responses may be calculated from their amplitude responses.According to The Operating Code for eismological Observation promulgated by State Seismological Bureau the amplitude desponse of the type DD-1, DK-1, and SK seismographs have been calibrated and their phase responses were calculated from these amplitude responses by the Hilbert transformation. The calculated phase responses were compared with that measured by a phasometer. The maximum error was found to be less than 5 for type DD-1 and DK-1 seismographs in the period range from 0.0125 s to 12.5 s and 0.05 s to 100 s, respectively. For type SK seismograph in the period range of 0.01s to 100s the maximum error is less than 1.5.This technique may be used to calibrate the seismograph phase response at the permanent stations. It is more accurate than the FFT method and the analytical method by means of approximate expression of a transfer function.The key to the use of this technique lies in the correct judgement of the slopes of the higher and lower frequency parts of the amplitude response curve. The error depends on the calibration accuracy of the amplitude response. By interpolation the tail and the truncation error may be neglected.