446 



SEISMIC METHODS 



[Chap. 9 



The factor k is the incompressibility factor or bulk modulus; its reciprocal, 

 K, is the compressibility. In terms of Young's modulus : 



k = 



3(1 - 2a) 



If Poisson's ratio a is j, A; = |E. 



(6) Tangential stresses produce a change in the angles of an elastic body 

 and preserve the surfaces. In the x-z plane of an elementary parallelo- 



1 



■^, 



(a) 



-^x. 



(b) 



Fig. 9-2. (a) Shear deformation by X,; (6) shear deformation by Z,; (c) resultant 



deformation. 



piped, the tangential stresses Xz and Zx produce the strains du and dw 

 and the "shear" angles ^Pxz and (p^x , which are related to the stresses by a 

 proportionality factor that is the reciprocal of the rigidity, ft. Thus, as 

 shown in Fig. 9-2, ^L ~ (l/l*)^^ and (p[x ~ (l/l»)Zx . Since X^ and Z, 

 are interchangeable, the resultant change of shape is given by 



2(pxt = Xg; 



and, similarly, for the other planes. 



2<Pyt = Y, 



It 



(9-11) 



