SEISMIC METHODS 



725 



boundary between the low velocity layer and the high-speed consolidated 

 material. This variation requires a slight modification of the system to 

 make it applicable for measuring the thickness of the surface layer at each 

 seismometer location. 



Consider a shock wave origin at the point P, Figure 443. The wave 

 thus generated reaches the point Q with a velocity Vc and emerges at the 

 point C, traveling from Q to C with the velocity F„. The time Tpqc for the 

 wave to travel from F to C by this path may be expressed 



TpQC- y^ + y^ 



(79) 



Fig. 443. — Method of differences. 



where Wc is the thickness of the low velocity layer at the seismometer 

 station C. Wc may be taken as a first approximation of that portion of the 

 ray path QC or RC through the low velocity layer, because of the near- 

 vertical incidence associated with the high contrast in velocities (F„ as 

 compared with Vc)- 



Similarly, for a shock wave origin at the point S, Tsrc may be expressed 



TfSRC 



SR Wc 

 Vc Vu 



Adding Equations 79 and 80 and solving for Wc 



PS 



W. 



-K 



T 



PQC 



+ TsRO ~ 



Vc 



V. 



(80) 



(81) 



After Wc has been estimated by Equation 81, then the order of the magni- 

 tude of the distance, QR, which was neglected in placing PQ + SR = PS, 

 may be approximated by the expression 



QR = 2Wc^ 



(82) 



i.e., tan" 



Wc 



= sm 



-1 



Wc 



= sm' 



Vc 



QR/2 ^"' QR/2 



and a corresponding correction applied to the distance PS in making a 



PS 

 second approximation of Wc- The quantity — may be checked expenment- 



ally by recording the travel times at both points A and B. 



