To determine the probability of runup of a given height at a given 

 location along the coastline, it is necessary to propagate tsunamis 

 across the ocean by numerical means from each segment of the trench for 

 all tsunami magnitudes (i.e., i = 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, and 

 5.0). The wave train of each tsunami must be superimposed on segments 

 of the tidal cycle of an interval equal to the duration of the wave train. 

 This superposition must be made for each tidal segment of that interval 

 for a 1-year period, and the probability of the resulting runup determined. 

 Tidal variations are discussed by Harris (in preparation, 1980). A cumu- 

 lative probability can then be established for runup at a particular site. 



Determining the probability of tsunami runup at a particular coastal 

 location for tsunamis generated in the Aleutian Trench area, would require 

 the numerical generation of 84 tsunamis (12 segments of trench and 7 

 intensities of each segment). As shown by Houston and Garcia (1974), each 

 runup value has an associated probability, and the totality of runup val- 

 ues at a given shoreline point defines a probability distribution from 

 which the cumulative probability distribution, Pg(Z), can be obtained 

 for runup greater than or equal to a particular value. 



By approximating the probability fg (Z) of the astronomical tide by 

 a Gaussian distribution (Petrauskas and Borgman, 1971; Houston and Garcia, 

 1974) , the probability of runup to a given elevation is given by 



P(Z) = [I f (A) P 5 (Z - A) dA (10) 



Probabilities for tsunami runup can then be determined at each coastal 

 point, combining the tsunami with the astronomical tide. 



An analysis similar to that used for the Aleutian Trench could be 

 applied to tsunamis generated in other source areas. For the west coast 

 of the United States (excluding Hawaii) , only the Aleutian Trench and the 

 Peru-Chile Trench appear to produce significant tsunami runup, although 

 Holden (1898) indicates some occurrence of tsunamis from sources along 

 the California coastline. Using numerical results obtained for tsunamis 

 generated along the Aleutian and Peru-Chile Trenches, Houston and Garcia 

 (1978) have determined probable 100- and 500-year tsunami flood elevations 

 for the west coast of the continental United States . 



II. THE GENERATION OF TSUNAMIS 



Tsunami-type waves can be generated from a number of sources, includ- 

 ing shallow-focus submarine earthquakes, volcanic eruptions, landslides 

 and submarine slumps, and explosions. Each of these sources has its own 

 generating mechanism, and the characteristics of the generated waves are 

 dependent of the generating mechanism. The tsunami waves which travel 

 long, transoceanic distances are normally generated by the tectonic 

 activity associated with shallow-focus earthquakes. However, large waves 

 can be generated locally by the other generating mechanisms. 



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