958 MISCELLANEOUS GEOPHYSICAL METHODS [Chap. 12 



acoustic waves in the ground is therefore comparable with the ranges of 

 audio-frequency and supersonic waves in air. 



Another cause of attenuation is loss of amplitude due to internal fric- 

 tion. In a viscous medium, the distance traveled by an elastic wave until 

 its amplitude is diminished to 1/e of the initial amplitude is the reciprocal 

 of the absorption coefficient, or SyhX^/Sir^U, where 11 is the static vis- 

 cosity coeflBcient, v the velocity, 5 the density, and X the wave length. 

 The range is thus inversely proportional to the square of the frequency. 

 With increasing distance, the higher frequencies drop out and the lower- 

 frequency components of the initial impulse remain. The range increases 

 further in direct proportion to the radiation impedance (product of veloc- 

 ity and density). Hence, the wave^ travel farther in firm and consolidated 

 than in loose and unconsolidated rocks (see page 478). Leigh ton^^^ has 

 given the following values for distances at which the poimding of a sledge 

 hammer could be detected with a 1000-cycle geophone through various 

 formations: 3000 feet through hard rock, 2000 feet through coal, 400 feet 

 through clay, and 550 feet through the mine cover. For vertical propaga- 

 tion down to 400 feet, Howell, Kean, and Thompson obtained half-value 

 distances of 900-cycle waves ranging from 78 to 640 feet. It follows 

 from the above that geoacoustic methods are well suited for the location 

 of highly absorptive formations underground, such as clay seams, faults, 

 and shear zones. 



2. Geoacoustic sound transmitters. More than twenty years ago Fes- 

 senden suggested the use of submarine transmitters in wells as a source of 

 elastic waves for the exploration of mineral deposits.^ Such transmitters 

 were not wholly successful because of the limitations of the high frequencies 

 just discussed. Comparing 400-cycle propagation with explosion-gener- 

 ated waves in a profile across the Hawkinsville salt dome, L. G. Howell, 

 et al,^** found shorter travel times for the explosion waves, which would 

 indicate that the latter penetrated the cap rock whereas the audio-fre- 

 quency waves tended to travel near the surface. It is probable, therefore, 

 that for exploration purposes the lower frequencies, such as those used in 

 dynamic soil-testing vibrators, have better possibilities. 



In mine rescue work and trench warefare there is, naturally, no choice 

 in regard to the frequency characteristics of the sound source. As a mat- 

 ter of fact, the higher frequency pomponents have to be utilized if the drill- 

 ing or digging tools and associated activities are to be identified. The 



1" A. Leighton, U. S. Bur. Mines Tech. Paper No. 277 (1922). 

 "2 L. G. Howell, C. H. Kean, and R. R. Thompson, Geophysics, 6(1), 1-14 (Jan., 

 1940). 



i« U. S. Patent 1,240, 328. 

 "* Loc. cil. 



