nondispersive equations are commonly used to study tsunami propagation in the 

 deep ocean. 



18. The validity of these equations over the continental shelf may be 

 questioned. Several investigators, however, find that their use is justified. 

 Tuck (1979) found that "...linear long-wave equations are adequate to describe 

 most of the tsunami generation, propagation, and reception processes." In 

 studying tsunami propagation from the deep ocean to the nearshore regions, 

 Goring (1978) concluded that "... because of the small relative height of 

 tsunamis and their large lengths relative to the lengths of the continental 

 slope, the propagation of tsunamis from the deep ocean to the continental 

 shelf-break [sic] and for some distance onto the shelf will be predicted as 

 well by the linear nondispersive theory as by the nonlinear theories." 



19. Studies of the behavior of tsunamis over real bathymetry have indi- 

 cated also that linear nondispersive equations are appropriate. Numerical 

 studies by Houston (1978) have shown that linear nondispersive equations 

 govern tsunami generation, propagation over the deep ocean, and interaction 

 with the Hawaiian Islands. Houston (1980) found from numerical experiments 

 that nonlinear advection terms had no significant effect on tsunamis propa- 

 gated from the deep ocean to the shoreline in the southern California region. 

 Alexeev et al. (1978) studied the generation and propagation of tsunamis in 

 the region of the South Kuril Islands. They obtained nearly identical tsunami 

 elevation time-histories at Kunashir Island using linear and nonlinear equa- 

 tions. The evidence suggests that the equations used in this study accurately 

 modeled tsunami propagation in the Gulf of Alaska. 



20. The initial condition used in the model was that the initial defor- 

 mation of the water surface was the same as that of the permanent vertical 

 displacement caused by the tectonic deformation of the seabed, except that 

 sharp irregularities in the profile were smoothed out. The justification 

 for the smoothing is given by Wilson (1969). This type of initial condition 

 has been used by many investigators, including Houston and Garcia (1974), 

 Brandsma, Divoky, and Hwang (1978), and Aida (1981). 



21. The model equations were solved by a system of finite difference 

 approximations. The finite difference scheme was similar to that presented by 

 Reid and Bodine (1968). The outline of the grid used for the computations is 

 shown in Figure 3. Spacing between grid points was 0.065 deg along parallels 

 and 0.04 deg along meridians. The along-meridian spacing corresponds to an 



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