14 EWING [chap. 1 



associated with the transformations. Sv waves in the low-velocity sediments 

 have been observed occasionally in shallow water (Drake et al., 1959) but have 

 not been reported in deep-water measurements. 



The lines whose intercepts are 14.5 and 16.0 are determined by reflected- 

 rofracted and doubly refracted compressional waves from Layer 5. Ray paths 

 associated with these arrivals are shown by dashed lines. The reflected-refracted 

 arrival has only two possible paths for each shot, i.e. the reflection through 

 the water layer can occur at either the shot end, as shown, at the detector end, 

 or both. The extra trip to the surface taken by the doubly refracted arrival 

 can occur at any place between the point of initial horizontal refraction and 

 the point of re-emergence leading directly to the detector. For uniform, horizon- 

 tal layering, the doubly refracted arrival can be very strong, because the 

 energy travelling any of the possible paths will arrive at the detector in phase 

 and at the same time as that taking any other path. The strength of this 

 arrival, therefore, gives an indication of the uniformity of the layering. Both 

 of the arrivals just discussed propagate horizontally at the speed of the com- 

 pressional wave in Layer 5, hence their slopes on the time-distance graph are 

 the same as that of the singly refracted wave in that layer. The intercept of 

 the reflected-refracted line is equal to that of the once refracted line plus 

 the delay time corresponding to a reflection through the water layer at the 

 angle indicated. The intercept of the doubly refracted line is obviously twice 

 that of the singly refracted hne. Reflected-refracted and multiply refracted 

 arrivals are often seen for each layer. For simplicity, only those associated 

 with the Layer 5 wave are shown. 



Note that in the time-distance graph for the case just considered, the 

 refraction lines have been drawn solid over the region where arrivals can be 

 received and dashed in the region of fictitious arrivals, i.e. the change from 

 dashed to solid line occurs at the critical distance for each type of arrival and 

 for each layer. 



It is of interest now to consider the case in which the velocity in the upper 

 layer of sediments (Layer 2) is not uniform throughout but increases with 

 depth in the layer. From the results of many measurements, it is known that, 

 owing to compaction, cementation, etc., the sediments do have appreciable 

 velocity gradients, particularly in the upper few hundreds of meters. The 

 effect of gradient in deep-sea sediments was reported first by Hill (1952) when 

 he found that, in an area of the eastern Atlantic, no arrivals corresponding to 

 reflections from the sea floor were observed (at low frequencies), whereas 

 arrivals, somewhat delayed, could be accounted for as having followed paths 

 refracted by a velocity gradient in the sediments. Velocity-depth relationships 

 have since been determined empirically for both shallow-water and deep- 

 water sediments (Nafe and Drake, 1957), and studies have been made on 

 artificial compaction (Laughton, 1954), indicating velocity gradients of 0.5- 

 2 sec~i in a variety of sediment types. Although it is well known that velocity 

 gradients are present in the water layer, they are small compared with those in 

 sediments, and for siin]>]icity we will assume constant velocity in the water. 



