Early geophysical papers of the Society of Exploration Geophysicists . earlygeophysical00soci Year: 1947 H. A. WILSON A = I, o> = t/6, h = t/18 A = 1, a) = t/6, m = t/6 j4 = 1, a; = t/6, h = t/2. We see that with critically damped seismographs the shape of the curves ob- tained depends less on the period of the seismograph than with undamped seismographs. When the period of the seismograph is much smaller than that of the wave the deflections are very small. Fig. 13. •.-x Fig. 14. It appears that the only case in which the deflection of the seismograph is approximately equal and opposit
Early geophysical papers of the Society of Exploration Geophysicists . earlygeophysical00soci Year: 1947 H. A. WILSON A = I, o> = t/6, h = t/18 A = 1, a) = t/6, m = t/6 j4 = 1, a; = t/6, h = t/2. We see that with critically damped seismographs the shape of the curves ob- tained depends less on the period of the seismograph than with undamped seismographs. When the period of the seismograph is much smaller than that of the wave the deflections are very small. Fig. 13. •.-x Fig. 14. It appears that the only case in which the deflection of the seismograph is approximately equal and opposite to that of the ground during the passage of one or more waves is that of an undamped seismograph with period much larger than that of the waves. In this case, however, a single wave sets up an oscillation which continues indefinitely. The principal conclusion which can be drawn from the above results is that seismographs do not register the actual motion of the ground so that arguments based on wave forms or the apparent arrival of waves later than the first wave must be used with great caution. Critically damped seismographs are obviously better when it is desired to observe the arrival of several waves separated by appreciable intervals. The inverse problem of calculating the motion of the ground from the recorded deflections of the seismograph will now be considered. The equation — x = y-\-2ky-{-p2y on integrating gives — x = y + 2ky -f- p2J03dt + C. We may suppose that y = 0 at t = 0 so that — x0 = yo-\-C. But at / = 0 — x so that a2 = 0 when / = 00. 236
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