Figure 26-5. Relationship among the travel-time curves, the ray-path diagram, and the 

 associated idealized seismogram for the two layer case with no dip between the lower 

 and higher velocity layers. The idealized reflection depicted at a later time on the 

 seismic record illustrates the reflection event from a deeper reflecting horizon of little 

 or no dip. 



Several interesting observations can be made from this figure. When the horizontal 

 distance from shotpoint to seismometer is zero, the direct wave arrival time is zero and 

 the reflected wave arrival time would be twice the depth to the interface divided by 

 the average velocity within the layer. The slope of the reflected travel-time curve is 

 zero at x = and the slope of the direct wave travel-time curve equals the reciprocal 

 of the velocity in the upper layer. At distances less than x ir , only the direct wave and 

 reflected wave arrivals are present thus to best record reflections from this interface, 

 spreads would be confined within x ir . Note that as the distance outward from the shot- 

 point increases, the reflection arrival time also increases even though the depth to the in- 

 terface has remained constant — this time increment constitutes the spread stepout (AT g ) . 



The refracted wave arrival first appears at the distance of initial refraction (x ir l, 

 and at this distance the arrival time of the refracted wave and the arrival time of the re- 

 flected wave are equal. The direct wave is also present but it has arrived sooner — i.e. at x ir 

 the fastest way to go from shotpoint to receiver is along a direct path. At x lr the slopes 

 of the refracted and reflected travel-time curves are the same and equal to the reciprocal 

 of the velocity of the higher speed (lower) layer. 



Both the direct and refracted waves arrive simultaneously when the seismometer 

 is positioned at the critical distance (x c ). Within x e the first arrivals (often called 

 first breaks) are from a direct wave — outward from x c the first breaks are from 

 a refracted wave; thus for most refraction prospecting the seismometers would be 

 spread at a distance greater than x c so that undisturbed arrival times may be used 

 for substitution into the computing equations of the refraction method. 



As the distance increases beyond x c the distance-depth ratio becomes larger and 

 thus the reflection travel-time curve approaches (becomes asymptotic to) the direct 

 travel-time curve. No indications are given on the travel-time curves relative to energy 

 content as such; neither are there depicted in this figure any of the bothersome multiple 

 arrivals (waves which have bounced about within the upper layer prior to being 

 recorded) nor are there shown any of other wave types, e.g. surface waves, which 

 would be present. 



This ray-path diagram shows only a few of the rays present yet a sufficient number 

 are presented such that the significant geometric relationships are demonstrated. Both 

 the direct and reflected waves travel wholly within the upper layer, whereas the re- 

 fracted wave travels from the shotpoint down through the upper layer to the higher 

 velocity layer then along it and finally up through the lower velocity layer to the 

 seismometer. If the velocities of the layers are known, then measurements to a given 

 scale can be made along the applicable paths to give the arrival times — thus a 

 theoretical travel-time curve could be constructed from a ray-path diagram. 



Since each channel records the arrival times at different distances from the shotpoint, 

 a multitrace record is in essence a travel-time curve; and as such, the record itself can 

 often be used directly to supply the needed travel-time information. 



567 



