Tsunamis 



where A = 4,2 if the ground motion is upward or A = 5.6 if it is 

 downward. The corresponding results for other values of L can 

 easily be found (the calculation requires only the use of the method 

 of stationary phase). The dependence on the shelf slope, 9, is that 

 which would be found for monochromatic waves whereas the depen- 

 dence on X is a consequence of the dispersion during the deep 

 water propagation. 



IV. DEEP OCEAN TOPOGRAPHY 



If there were systematic variations in the water depth between, 

 say, the Aleutians and the equatorial Pacific, one might expect that 

 the relative intensities of the Tsunamis (with Aleutian source) which 

 were incident on different Pacific islands might differ because of 

 mid-ocean refractive effects. Exhaustive studies of this effect have 

 certainly not been completed but the indications are that this is not 

 a major reason for the different response at (for example) Wake and 

 Hawaii. One might also anticipate that the irregular deep ocean 

 topographical variations could seriously modify the wave which 

 propagates across the ocean. This possibility has been analyzed 

 treating each event as a member of an ensemble of phenomena each 

 of which take place over a topography which is itself a member of a 

 stochastically described collection of random topographies. This is 

 motivated loosely by the fact that the one-dimensional topography 

 between any given source and any given target differ from that associ- 

 ated with any other source-target pair, and the fact that the topog- 

 raphies are so poorly known that little else can be done. The result 

 of this study indicates that the ratio of intensity at Xq of the wave 

 over the irregular bottom to that over constant depth is characterized 

 by 



e +1 



where € is the ratio of the average irregularity height to the average 

 depth and L = ZttN where N is the number of wave lengths of the 

 monochromatic wave whose scattering is being studied. For wave 

 lengths in the spectral region of major interest, the effect of this 

 facet of the wave propagation seems to be of relatively small im- 

 portance too. 



V. ISLAND TOPOGRAPHY 



When the wave encounters an island, the lateral scale of that 

 island has the same order of magnitude as much of the important 

 part of the wave length spectrum. Thus , the pretense that the wave 

 climbs a plane shelf must be corrected. The refractive effects so 



