112 



T. I. Oblogina 



for a single ■wave equation. This problem has been solved in several works C^'^). 

 The solutions obtained, however, are unsuitable for studying the dynamic 

 properties of diffracted waves, since the very construction of these solutions 

 makes it difficult to extract an expression for the displacement field near 

 the wave fronts which is suitable for purposes of calculation. 



The problem of plane -wave diffraction from the edge of a tapering stratum 

 is solved below by the Smirnov-Sobolev method of functional invariants; 

 the dynamic hodographs and theoretical seismograms for diffi-acted waves 

 are calculated. 



Fig. 9. Diagram to aid formulation of diffraction problem for a plane wave from the 

 edge of a "tapering stratum". 



Solution. The function 9^0 depends solely on the ratios ;r/i,y/i. As Sob olev 

 shows, by substitution of the variables ^ = xjt t] = yjt the wave equation 



° 9t^ 9x^ ' 9y^ 

 is converted into an equation of mixed type, 



{a,H'-l) n,,+^<hn,n+^< ^'-1) 9'o..+ 2«o^l<. 

 + 2ao2 72990^ = 0. 



(9) 



(10) 



The above equation in the hyperbolic region is reduced by substituting 

 the variables according to the formulas: 



