594 



SEISMIC METHODS 



[Chap. 9 



that is, the voltage output increases hnearly with frequency, 

 mometer adjusted to a high natural frequency, 



For a seis- 



in; = -UJ -,'<JX sin («« ± 90' 



Wo 



(9-91d) 



that is, the e.m.f. increases in proportion to the third power of frequency 

 (ground acceleration times frequency). Eq. (9-916) indicates that the 

 voltage is 90° out of phase compared with the mechanical phase of the 

 seismograph. Fig. 9-102 shows that for a seismograph of low^ natural 

 frequency the voltage output increases linearly with frequency in the 

 range where the dynamic mechanical magnification is equal to the static 



Fig. 9-102. Frequency response of electromagnetic seismograph (after Reutlinger). 

 (o) Mechanical response; (6) galvanometer response. 



magnification. The curve h represents the deflection of a galvanometer 

 coupled directly to the seismometer. The deviation from a straight line 

 is caused by the dynamic response of the galvanometer, which decreases 

 with increasing frequency. 



For a damped seismograph one obtains by differentiation of the steady 

 state term in eq. (9-89d), and substitution in (9-91a) 



E = -HJVX 



V(03l - C02)2 + 462 C02 



• CO -sin (co^-^ (p ± 90**). 



(9-92a) 



With T as a transmission constant equal to — HJC (where C is a factor 

 introduced by short circuiting the detector through the primary of an 

 impedance matching transformer), the peak e.m.f. = Em is 



Em = 



Vw'TZ 



VCcOo' -[O,')' + 462<0^ 



(9-926) 



