SEISMIC METHODS 663 



frequency cut-off to lower frequency as the depth increases, but the low 

 frequency cut-off is believed to be substantially independent of depth, 

 since it is controlled by a reflection coefficient rather than by distance of 

 travel. In prospecting to depths of the order of 10,000 feet or less, the 

 highest amplitude frequencies generally lie between 25 to 80 cycles per 

 second. The wavelengths of the seismic waves can be computed readily 

 from /A = V, where / is frequency, A is wavelength, and v is velocity. 

 The velocity will run from as low as 2000 feet per second or less in the 

 surface zones to as high as 15,000 or 20,000 feet per second in deep or 

 hard formations. Velocities around 8,000 or 10,000 feet per second are 

 quite common, and frequencies of 40 or 50 c.p.s. correspond to wavelengths 

 of the order of 200 feet. 



In the conventional application of the seismograph it is customary to 

 use filters in the recording channels which eliminate some of the frequencies 

 in the complex wave arriving at the surface of the earth. This practice is 

 necessary in the visual analysis of records to discriminate against a variety 

 of unwanted signals which would otherwise make it difficult or impossible 

 to recognize reflection signals. It also means that the reflections as viewed 

 on the seismograms tend to have dominant frequencies in the pass band 

 of the filter and do not always show as marked a decrease in frequency 

 with depth as would be expected. 



Many attempts have been made to measure the dispersion of seismic 

 waves : i.e., variation of velocity with frequency. At present there is no 

 evidence that any appreciable dispersion exists except in the immediate 

 vicinity of the explosive charge where there is non-linearity between stress 

 and strain. The absence of dispersion is very important to seismic pros- 

 pecting, since it enables the earth to propagate a pulse without any undue 

 change in its length. In a dispersive medium, the various frequencies com- 

 posing a pulse separate from one another and lengthen the pulse to such 

 an extent that a definite arrival time cannot be determined. 



Later in the chapter, in connection with Figure 512, experimental data 

 are given relative to wave attenuation and frequency effects. 



Refraction and Reflection of Seismic Waves 



The terms refraction and reflection were used in connection with optical 

 theory long before much was known about seismic waves. However, it has 

 been found that the fundamental principles controlling the wave propa- 

 gation of both light and seismic waves are very similar. For a review of 

 these principles, the reader is referred to any standard treatise on geo- 

 metrical optics. 



The simplest meaning of the term refracted waves is that such waves 

 have undergone a change in the direction of propagation. This change in 

 direction occurs when waves cross a boundary at an angle less than 90 

 degrees separating media of different elastic properties. When an elastic 



