From the point (H/H = 1; r/d = l) in Figure 70, lines have "been 

 drawn which represent proportionalities, H « t~^, for the values n = 1/3, 

 1/2, 2/3, 5/6, 1. Theoretical studies of decay of impulsively generated 

 waves have variously shown that one or another of these laws may he 

 involved. As summarized by Wilson, et al (1962), Wilson (196U), one- 

 dimensional (x, horizontal) dispersive waves decay according to the law 

 x~l/2 in the hody of the waves and as x~l/3 at the wave front. Kajuira 

 (1963) confirms the latter result for the leading wave of a tsunami 

 provided that 



(b/d) (6 /dTi /t)l/3 < 1 (13) 



where b is the half-breadth of a rectangular source area and wave propaga- 

 tion is in the direction of the breadth (see also Van Dorn, I965). 



It must be assumed that, at least for the first six stations listed 

 in Table III, and possibly for the first twelve, the tsunami advanced on 

 the American seaboard with a one-dimensional propagation. We find that 

 the data points for stations along the Americas show a certain disposition 

 to accord in the mean with the laws H °= r~-^'^ and H == r~-^'^. Further, 

 those that seem to accord with the first law represent data drawn largely 

 from high waves at the front of the beats for situations in which energy 

 lost to other frequency excitations was fairly low. 



Of the data points that seem to accord better with the H <x r"-'-'^ law, 

 there was considerable loss of energy to higher frequencies. Had this 

 loss not occurred, they would place higher in Figure 70. San Francisco 

 and Rincon Island, for example, might qualify then for the H cc r~^'^ law, 

 particularly as the highest waves are close to the front of the beat (see 

 Figures 50, 5l). Also, the data points for Ushuaia, Tierra del Fuego , 

 and the Palmer Peninsula, Antarctica, drawn from wave heights deep in the 

 body of the beat (Figures 55, 56), would then conform better to the law 

 of H oc r-1/2^ 



Since the data of Table III for the North American coastline appear 

 to obey the H ** r~l/3 law, we may use Kajuira's condition. Equation (l3), 

 to place a bound on the half-breadth of the tsunami source region. If 

 we take an approximately median value for the data represented by the 

 upper set of points (Figiore 70) as r/d = 1000 and note that time t in 

 Equation (l3) can be expressed in terms of r via Equation (l2), then 

 Equation (l3) resolves to 



b/d < (r/6d)l/3 (lU) 



Using r/d = 1000 and adopting d = 5000 feet for the first seven data 

 points, we find 



b < 10 km (15) 



In terms of what we know about the actual source region, this condition 

 appears unduly restrictive. 



102 



