480 SEISMIC METHODS [Chap. 9 



scattering accentuates the low and attenuates the high frequencies with an 

 increase in distance. 



The effects of dispersion on the propagation of seismic waves have been 

 observed in station seismology. The phenomenon is similar to the dis- 

 persion of light by refraction. In optics the degree of dispersion depends 

 on the substance and varies inversely as wave length ; that is, the index of 

 refraction is greater for small than for large wave lengths. Since light 

 velocity is inversely proportional to the refractive index, the velocity in- 

 creases with wave length. In other words, both refractive index and dis- 

 persion are inversely proportional to wave length, period, and velocity. 

 This is noiTnal dispersion. If the velocity decreases with wave length, 

 abnormal dispersion occurs. 



In seismology the effect of dispersion on intensity or amplitude has been 

 observed for longitudinal and transverse waves. In a wave with com- 

 ponents having different periods, a maximum will occur at a given station 

 because of interference. If the velocity varies with period because of 

 dispersion, this maximum will travel to another station, not with the veloc- 

 ity of the individual waves, but with greater or less velocity, called the 

 group velocity, C. If no dispersion is present, C = v. If the velocity v 

 increases with the wave length (or period), there is normal dispersion, and 

 the group velocity C is less than v. For abnormal dispersion, if the veloc- 

 ity decreases with wave length, the group velocity is greater than the 

 individual wave velocity. Normal dispersion has been observed in the 

 first longitudinal impulses; the occurrence of the maximum in this wave 

 group has been found to be delayed with increasing epicentral distances. 

 The effect of dispersion is most pronounced in transverse surface waves; 

 further details are given on page 927. 



3. Absorption and dissipation. The decrease of seismic intensity with 

 distance, due to geometric spreading, scattering, and dispersion, is ac- 

 companied by losses due to energy absorption giving rise to damping. 

 Hence, at the distance r the intensity 



I, = Ioe-«' (9-36a) 



where o is an absorption coefficient or the reciprocal of the distance at 

 which lo is reduced to lo/e. Hence, 



a = ?:?log^, (9-366) 



r Ir 



where Ir/Io may be designated as acoustic transparency and lo/Ir as 

 acoustic opacity and is measured in decibels: db = 10 log Ir/Io . Con- 



" B. Gutenberg, Handb. der Geophys., IV(1), 27-28 (1929). 

 "« Ibid. 



