606 



SEISMIC METHODS 



[Chap. 9 



response Wr of detector, amplifier, and galvanometer is (from eqs. [9-926], 

 [9-95], and [9-98a]) 



W, = V„(/„).V.co'(/d).^.V„(/„) = W,.W,.Wa.T.a,, 



K 



(9-99) 



where V,(/,)/X = W„ . 



The resultant dynamic magnification of the entire channel is therefore 

 proportional to the 'product of all dynamic magnifications and to a trans- 



50 



X 



2(h 



deA^aaeaefer dtfledioa 

 for twit Qrtaaf mfiai 



•\jW^)(1*n*) 



Tuning Fattor /^ 



to 



10 



3.0 



4JI 



5.0 



6.0 



7.0 



9.0 



10 



Fig. 9-110. Response of 0.7 critically damped seismograph and galvanometer, if the 

 natural undamped galvanometer frequency is ten times that of the seismograph. 



mission constant. Fig. 9-111 shows the characteristics of a peaked ampli- 

 fier superimposed on the detector-galvanometer curve of Fig. 9-1 10. The 

 over-all response is calculated for an amplifier peaked at three times the 

 natural frequency of the detector-, with an equivalent dampi ng rate o f 

 0.316, so that its damped frequency factor (/„) = l/aja\/(l — n„^ -|- Wn^ , 

 Therefore, with rio = co/coa , Wa = 3ajo , iia. = 0.316, and na = no/3, (/a) = 



1/wo 



Vsi — 14.4no -h n\ • When multiplied by the factor represented 

 in Fig. 9-110, this gives the theoretical curve shown in Fig. 9-111, which 

 is seen to agree well with the results of test block experiments. 



