DIFFRACTED SEISMIC WAVES 



115 



zontal component w^ and the vertical component v^ of the displacement: 



y2aQ^.x{v-h)Im0'{Oo') 1 



k'here 



(20) 



(21) 



Here t^ is the time of the first onsets of the diffracted wave. Formulas (20) 

 are valid in the neighbourhood of its front, except for the vicinity of the 

 singular point B (Fig. 9), where they do not apply. 



We can now give the shape of the incident wave in the form of a smooth 

 pulse 



G' (0 == 4 h 



{t-T). 



(22) 



To obtain the components of displacement u-^^ and v-^ for such a pulse, 

 we must, as is known, integrate according to a parameter 



i-^ {t, x,y) = J u{t — r, X, y) dG, 

 



(23) 



where u is the function for the case of a single pulse, which we know already, 

 and T is the parameter. 



Performing the integration, we get 





(24) 



where 



/{t-a^r) = 4.T^ {At {\^t-]/At-T) - ^ [At^r-~ {At-~T)^I^]] - 



