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EXAMPLE PROBLEM 18************** 



GIVEN : A tsunami is generated by uplifting along a faultline located on 

 a coastal shelf (Fig. 37). The faultline is oriented so that the angle 

 between the coastline and the faultline is B = 40°. The faultline 

 extends to the outer edge of the shelf which is 100 kilometers (62.14 

 miles) from the toe of the shoreline slope. The shelf has a uniform 

 slope seaward of S = 0.003 and a 30-meter water depth at the toe of the 

 shoreline slope. The uplifting is uniform along the faultline so that 

 it acts as a line source. 



FIND : The percentage of the wave energy trapped on the shelf. 



SOLUTION : The depth of water at the outer edge of the shelf is 



d = d + Sx = 30 + 0.003(100,000) 



= 330 meters (1,083 feet) . 



Looking first at wave rays traveling seaward from the faultline, at the 

 inner end of the faultline, using equation (237), 



d d 

 v = s £ 



^ S sin 2 a 2 S 



30 30 



0.003 sin 2 40° 0.003 



x„ = 14,200 meters (8.83 miles) 



At the outer end of the faultline, taking d s as the depth of water 

 at the faultline, i.e., where the wave ray originates 



330 330 



P 0.003 sin 2 40° 0.003 



Xp = 156.23 kilometers (97.08 miles) 



which is beyond the limits of the shelf. Noting that x„ varies 

 linearly with d g , from proportionality the length I of the part 

 of the faultline (of length Lr) contributing trapped energy is 



Lf(100 - 14.2) 



(100 + 156.23 - 14.2) 

 0.355 hf 



or 35.5 percent of the energy generated seaward in the example is 

 trapped. 



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