Chap. 9] 



SEISMIC METHODS 



583 



mograph it is an exponential. The effect of friction may be distinguished 

 from damping by measuring both ratios and differences of successive 

 amplitudes. In a damped curve the ratio is constant (corresponding to a 

 geometric progression), while in a friction curve the difference is constant 

 (representing an arithmetic progression). The vector figure of amplitude 

 progression is an Archimedian spiral for friction and a logarithmic spiral 

 for damping. 



As shown in Fig. 9-97, equiphase amplitudes lose the amount 4f within 

 one period so that az = ai — 4f. Since deflection is force divided by 

 spring constant, the loss of deflection f due to the frictional force is equal 

 to m'g^/c, with f as Coulomb's friction factor and m' the "equivalent" 

 mass of the seismograph. The period of a seismograph with friction is 

 the same as the period of a seismograph without friction. 



Fig. 9-97. Seismograph oscillations under influence of friction. 



4. Free oscillations with damping. The type of amplitude decay just 

 discussed may be said to be due to exterior friction. Conversely, interior 

 friction (as in liquids) produces damping in proportion to the first or 

 second power of the velocity of motion. In velocity damping, the closest 

 approach to a correct reproduction of actual ground motion is obtained. 

 Three types of damping are employed in seismic detectors: (1) air, (2) oil, 

 and (3) electromagnetic damping. 



Air damping is effective only if the mass of the seismograph is small 

 and the frequency low. Hence, it has found application in condenser- 

 microphone detectors and in some inductive geophones with very light 

 coils. Oil damping is most frequently employed. In mechanical seis- 



" These statements refer to seismic detectors. Air damping can be effective in 

 station seisihographs (Wiechert) when used at the end of levers which, however, are 

 usually xmdesirable on detectors. 



