SEISMIC METHODS 661 



phase. Obviously, at large distances from the source, small portions of 

 the wave front will approximate a plane. (Compare wave front F of 

 Figure 408.) 



The normal to the wave front at any instant is called the zvave ray, 

 or the ray. Rays, for example, aa' and aa'a'' of Figure 408 are generally 

 used as a convenient tool for describing the paths of elastic waves. A ray, 

 such as aa'a". . . , has a number of important properties, chief of which 

 is that the travel time along such a path from the source to any point 

 on the path is the "least" time in which energy of the type considered 

 can travel from the source to the point.* 



Propagation of Seismic Waves 



In using the seismograph as a prospecting tool, it is customary to 

 generate a seismic signal by detonating a charge of dynamite in a shallow 

 borehole. The exploding dynamite constitutes a very intense point source 

 of energy. Accordingly, the compressive displacements of the earth in the 

 immediate vicinity of the charge exceed the range of linear elasticity of 

 earth materials. The region of proportionality between stress and strain 

 is exceeded. In many cases this results in fracturing and permanent set 

 which accounts for the large dissipation of energy into forms other than 

 elastic wave radiation. As the disturbance moves out from the explosion, 

 the amplitudes decrease because of geometrical spreading of the spherical 

 front, and finally come within the range of linear elasticity. From this 

 point on, efficient propagation of the elastic wave ensues and the general 

 theory of elastic wave propagation, which assumes proportionality between 

 stress and strain, is applicable. 



The wave form of the impulse at this point of linearity will vary con- 

 siderably with the physical characteristics of the material surrounding the 

 shot point. In some cases where ideal conditions exist this impulse may be 

 as short as 0.02 seconds, while in other cases it may be spread out into a 

 wave train a tenth of a second or more in length. Examples of this have 

 been discussed by J. Sharpe.f 



This impulse, which first arrives in the region of linear displacements, 

 is further modified by the transmission and reflection characteristics of 

 the earth strata. The original spectral distribution of energy in the linear 

 impulse is subject to considerable variation, depending on the particular 

 locality. In general, however, its energy is spread out over a relatively 

 wide band of frequencies, from a few cycles to many thousand cycles per 

 second. As the impulse travels through the earth, the higher frequencies 

 are lost more rapidly than the lower frequencies. There are several mech- 

 anisms responsible for this change in amplitude versus frequency: (1) 



* It should be pointed out, however, that the entire energy reaching a given point 

 need not travel along the wave ray. 



t J. Sharpe, Geophysics, Vol. 7, 1942, p. 311. 



