Consider now the wave rays generated shoreward. If the wave ray 

 generated from the point at distance £ along the faultline is con- 

 sidered for the straight, uniform section of shoreline (Fig. 37), the 

 wave ray will reflect from the shoreline and be directed at the angle 

 otj at the position shown in the figure. This wave ray will turn 

 parallel to the shoreline (i.e., parallel to the bottom contours) at 

 the edge of the shelf. Therefore, 35.5 percent of the energy gener- 

 ated shoreward in the example will also be trapped. Note that the 

 energy generated shoreward would have a tendency to form a Mach-stem 

 along the shoreline if 3 is greater than 45°. 



A caustic, by definition, is a line tangent to a family of wave 

 rays. For the waves generated seaward, a caustic will be formed by 

 those wave rays refracted back to the shoreline (i.e., the trapped 

 wave rays), after they have reflected from the shoreline. For the 

 wave rays generated landward from the faultline, a caustic is formed 

 after reflection as shown by the dashline in Figure 37. 



************************************ 



As illustrated in Figure 37, wave rays trapped on a shelf may diverge 

 apart. These wave rays may reconverge at various points along the coast- 

 line, producing high waves at the points of convergence. 



Chao (1970), Chao and Pierson (1970), and Pierson (1972) discuss the 

 case of short -period waves reflected from a shoreline, where several wave 

 crests exist between the point of reflection and the caustic. The wave 

 rays follow similar paths to those discussed above, but the wave crests 

 propagating shoreward from the caustic will interact with the wave crests 

 propagating seaward from the coastline, producing many peaks and nodes 

 between the coastline and the caustic. 



For the straight coastline shown in Figure 35, the traveltime, t, 

 along the wave ray between the shoreline and the caustic can be easily 

 determined. Where the distance s is measured along the wave ray, 



ds 

 dt 



(244) 



but 



so that 



d s - -^~ (245) 



s cos a 



Jo Jo 



V 



dx 



(246) 



Also, from shallow-water assumptions, 



c = v^d = /g(d + Sx) (247) 



115 



