Chap. 9] SEISMIC METHODS 593 



mograph furnishes either the ground displacement or the acceleration, 

 depending on frequency adjustment, the effect of the transducer in an 

 electrical seismograph is superimposed on its mechanical action, and the 

 (mechanical) frequency response is modified. It is least changed by a 

 capacitive transducer. In piezoelectric and similar transducers, the con- 

 version of mechanical into electrical energy takes place in proportion to 

 the acceleration, and in electromagnetic transducers in proportion to the 

 velocity of the ground motion. The voltage output of the latter is there- 

 fore proportional to the ground frequency, provided the seismograph is 

 adjusted to a low natural frequency. When the natural frequency is so 

 adjusted that the seismograph acts as an accelerometer, its voltage output 

 is proportional to the third power of frequency. Only the theory of the 

 electromagnetic detector is discussed below; little is known at present 

 about the theory of the capacitive and pressure transducers. The theory 

 is applicable to both inductive and reluctance transducers. The overall 

 dynamic response of a seismic channel is dependent on the characteristics 

 of the detector, the amplifier, and the galvanometer, which will be dis- 

 cussed separately. 



1 . Theory of the electromagnetic detector!"^ Assume the transducer in an 

 electrical detector to consist of a circular coil attached to the seismograph 

 mass and to move in the field of an electromagnet. If the amplitude of 

 the mass is a, the induced e.m.f. is 



E= -H.Z^, (9-91a) 



at 



where Hg is the field of the magnet, I the length of wire, and E electro- 

 motive force. For an undamped seismograph a = VXw^sin oit/ (wo — w^), 

 and therefore 



^= -^^2Xcosin(a,«±90''). 

 at coq — w^ 



Hence, the e.m.f, generated is 



E = -5i^ ^x sin (cof ± 90^). (9-916) 



Wq — (a^ 

 For a seismometer adjusted to a low natural frequency, 



E = HJVwZ sin (coi ± 90°), (9-9 Ic) 



" See also F. Sohon, Introduction to Theoretical Seismology, Vol. II; F. Wenner, 

 Bureau of Standards Res. Paper No. 66, (1929); H. Benioff, Seis. Soc. Amer. Bull., 

 22, 155-169 (1932); and other references given in Heiland, op. cit., 452-454 (1934). 



