Chap. 9] ♦ SEISMIC METHODS 477 



also in igneous rocks does the velocity of elastic waves change with depth; 

 however, this change is less in the latter than in the former, since igneous 

 rocks have a lesser initial porosity. By laboratory experiments, Adams 

 and Gibson have shown that the compressibility of granites and gabbros 

 drops at first rapidly with an increase in pressure and remains uniform later 

 for greater pressures. The greatest change in compressibility occurs for 

 the first thousand megabaryes, which is equivalent to the first 4 km of 

 depth. 



E. Physical Rock Properties Related to Seismic Intensity 



To fully characterize the elastic behavior of rocks and formations con- 

 sideration must be given to the intensity of elastic vibrations in addition 

 to the velocity of propagation. The following physical parameters are 

 significant in this connection: (1) specific acoustic resistance, (2) spreading 

 and dispersion, and (3) absorption and dissipation of energy. 



1. Acoustic (radiation) impedance. The seismic or acoustic intensity I 

 may be defined as the average rate of flow of energy through a unit section 

 normal to the direction of propagation, or it may be defined as average 

 power transmission per unit area. Power being the flow of energy per 

 second, the intensity is equal to the average energy content, or energy 

 density, W, multiplied by the velocity of an acoustic or seismic wave, 



I = Tf v. (9-33a) 



Since the kinetic energy is |mv^ or, for a simple harmonic motion with the 

 maximum amplitude A and frequency w, = ^iuAW, the energy density 

 per unit volume is |AVs. By substitution of ^t^^ for co^, W = 2x^Ay^5, 

 so that eq. (9-33a) becomes 



I = 2t'AVi.5./. (9-336) 



If in this equation the factor R is substituted for the product Vj5, the 

 intensity 



I = 27ryA'R. (9-33c) 



The intensity is thus proportional to the square of the amplitude and 

 to the square of the frequency. Hence, vibrations of high frequency may 

 be accompanied by great intensities, although their amplitude is small. 

 Further, the intensity depends on the factor R, which by analogy with 

 the electrical relation (power = /^R) may be designated as acoustic resist- 

 ance (in the presence of a reactive component, acoustic impedance). The 

 acoustic resistance referred to unit dimensions is the specific acoustic 

 resistance. Following are the specific acoustic resistances for a number 

 of substances: steel, 390- 10*; rubber, 0.5-10*; water, 15-10*; and air, 42. 



