If the incremental areas are equal, i.e., A 2 = A 2 = . . . = A^, then 

 equation (13) can be rewritten as 



h? 



H=l2 



Pg A. .E -£ (14) 



or, alternatively, 



n 



h 



E = pg n A. E — U 5 ) 



* £-1 2n 



Noting that the total area, A, is given by 



A = 



n < 











and that 













n h " 



■>? 



+ 



hi* . . 



2n 



. + h 2 



n 



(h 2 ) 



v aye? 



E — = 

 i=l 2n " 



2 



equation (15) becomes 













E = 



Pg 



A 



(h 2 ) 



a-oq 







2 



(16) 



(17) 



(18) 



where (h 2 ) is the average value of the square of the uplifted heights. 



avg 



For the 1964 Alaskan earthquake the height of uplifting varied con- 

 siderably over the area of uplifting, and had a maximum in excess of 15 

 meters (49 feet) at a point near Montague Island (Malloy, 1964). The 

 tsunami had a calculated potential energy of 2.26 x 10 22 ergs (1.67 x 10 15 

 foot-pounds) . 



When using equation (18) it must be remembered that the average of 

 the height squared, (h 2 )avg> i- s not equal to the average height squared, 

 (h ay ^) 2 . This is easily illustrated by the following example problem. 



************* EXAMPLE PROBLEM i*************** 



GIVEN : An area of uplifting is divided into five equal-sized areas of 

 2.3 x 10 12 square centimeters (2.48 x 10 9 square feet), with upliftings 

 of 30, 60, 90, 120, and 150 centimeters, respectively. 



FIND: 



(a) The value of (h , ) 2 , 



(b) the value of (h 2 ) ay(? , and 



(c) the potential energy of the uplifted seawater. 



33 



