where the coefficients a and b are determined by a least squares 

 analysis of the available data for the generating area. To calculate 

 probabilities tsunamis may be placed in groups; e.g., a group of tsunamis 

 shown with magnitude 3.75 actually includes all tsunamis with magnitudes 

 from 3.5 to 4.0, etc. To analyze the probability of an individual tsunami 

 having a magnitude greater than or equal to 3.5, the probabilities would 

 be summed 



2 



Z n(3.75 + 0.5j) = n(3.75) + n(4.25) + n(4.75) (5) 



3=0 



which would include all tsunamis with magnitudes from 3.5 to 5.0. It 

 should be noted that the stress in rock cannot exceed some maximum value; 

 the rock will fracture when the stress reaches that value. 



Abe (1975) and Geller (1976) show from empirical results that the 

 fault length of earthquakes is approximately equal to twice the fault 

 width. Using these results and the model of Haskell (1969), Geller gives 

 a maximum earthquake magnitude, M, of 8.22. Because of variations in 

 the assumed fault length-to-width ratio, actual earthquake magnitudes 

 may exceed this value slightly; Geller lists a magnitude of 8.5 for the 

 1964 Alaska earthquake. However, as noted by Geller, the maximum magni- 

 tude occurs because the conventional magnitude scale is saturated and 

 ceases to give a meaningful measure of the earthquake size. 



It is assumed that tsunamis do not occur with magnitudes greater 

 than 5.0 where the tsunami magnitude has some relationship to earthquake 

 magnitude as mentioned previously. If tsunami magnitude is related to 

 seismic moment, defined by Kanamori (1972) as a function of rigidity, 

 fault area and average fault slip, Kanamori and Cipar (1974) indicate 

 that the 1960 Chilean earthquake had the largest seismic moment ever 

 reliably determined (2 x 1030 dyne -centimeters) . 



The method for grouping tsunamis (eq. 5) has been utilized by Houston 

 and Garcia (1974), using statistics for the entire trench along the Chilean 

 coast. Applying revised information for that particular generating area, 

 a major source of tsunamis in the western United States (Houston and 

 Garcia, 1978), a = 0.074 and b = 0.63. Taking the value m = 3.5 for the 

 magnitude of a design tsunami (to be used for determining potential runup 

 in coastal areas), the probability for a tsunami with a magnitude of 3.5 

 or greater being generated in any given year is 



n(3.5) = 0.074 [ e "0 • 63 (3 .75) + e -0. 63(4.00) + e - . 63 (4 . 75)] (6) 



which gives a value of 0.0166 or a recurrence interval of 60 years. For 

 a 412-year period for the Chilean coast, the prediction would be seven 

 tsunamis of magnitude 3.5 or greater. This agrees with historical records 

 of tsunamis in this area. 



24 



