Hwang and Divoky (1970, 1972) use a simplified monotonic displace- 

 ment history to describe ground motion. They propose that, to a first 

 approximation, horizontal displacement of a sloping bottom can be repre- 

 sented as purely vertical displacement. 



Houston, et al . (1975b) use an elliptical -shaped generating area, 

 with an instantaneously displaced water surface, as input data for a 

 standard design tsunami in a numerical solution. They define the sur- 

 face displacement as a modified elliptic paraboloid, having a parabolic 

 cross section parallel to the major axis of the ellipse, and a triangular 

 cross section parallel to the minor axis of the ellipse. The numerical 

 propagation of the wave uses the same procedure as used in Brandsma, 

 Divoky, and Hwang (1975) . The potential energy of the uplifted water 

 surface for this type of surface displacement is given by 



E = 4 (££U4/V-x*) 5/2 dx (25) 



\6 / a dT o 



where 



x = measured along the major axis of the ellipse 



a = the length of the semimajor axis 



y = measured along the minor axis of the ellipse 



b = the length of the semiminor axis 



z = the vertical direction upward from the undisturbed water surface 



c = the maximum uplifted elevation at coordinates (x = o, y = o, 

 z = c) 



p = the density of the seawater (taken as 1.026 grams per cubic 

 centimeter) 



IV. TSUNAMI PROPAGATION 



After determining the initial disturbance of the water surface, as 

 discussed in Section III, the propagation of the tsunami to nearby or 

 distant shorelines must be analyzed. Because tsunamis are long-period 

 waves with long wavelengths in relation to both the water depth and the 

 wave height, long-wave equations can be used. 



1. Small -Amplitude Waves . 



The simplest means of analyzing the wave motion, where the ratio of 

 the wave height to water depth, H/d, is small, is to use the following 

 small -amplitude solutions to the wave equations: 



38 



