10 to 20 meters (Figures 3^, 36 and 37). The range of wave height H, 

 plotted against earthquake magnitude M in Figure Ul, appears to accord 

 with the trend of Japanese data, and with an empirical relationship 

 established in earlier studies (Wilson, et al, 1962; Wilson, 196h) . 

 This relationship is 



log^Q H = 0.75 M - 5.0 (6) 



and may he expected to give a rough idea of tsunami heights expected 

 from an earthquake of given magnitude within a range of 500 miles of 

 a coastline. 



3. Progression and Dispersion of the Tsunami Across the Pacific 

 Ocean 



We may briefly enquire into the immediate development following 

 the upheaval of the water surface over the Continental Shelf (Figure i+2a). 

 Under the effects of gravity, and with the energy communicated from the 

 uplift and thrust of the land, the positive wave will start to separate 

 in two as shown in Figure U2b. 



Propagation landward of the negative wave will start a negative 

 reflection from the coast with some loss of energy from entrapment, 

 scattering, and absorption in the greatly indented coastline, as well as 

 leakage into Cook Inlet and Prince William Sound (cf. discussion of this 

 subject by Munk, I961). The positive wave propagating seaward over the 

 shelf into deep water loses some energy at once to a negative reflection 

 which propagates back toward the coast (cf. Lamb, 1932; Johnson, et al, 

 1951 ; LeMehaute, I960; Dean, I96U). The progress of these reflections 

 in the early moments of tsunami transmission is shown schematically in 

 Figure U2. In this process a little-understood mechanism of energy trans- 

 fer to higher frequencies takes place, and amplification results throiigh 

 sympathetic resonance at the natural frequencies of shelf oscillation. 

 The interference of the coast and shelf-edge reflections with each other 

 probably accounts for the beat oscillation revealed in Figure 38c. The 

 oscillation is essentially of the "leaky" mode type discussed by Snodgrass. 

 Munk, and Miller (1962), and by Munk (1962), because the direction of 

 propagation of the reflections in the gross sense is normal to the coast 

 and to the shelf edge. 



The main tsunami meanwhile emerges from the Continental Shelf and 

 spreads across the Pacific Ocean in the manner inferred from Figure 27. 

 Its energy will be supplemented by small additional amounts of energy 

 continuously transmitted to deep water from the shelf oscillation. 



The tsunami was recorded at tide gage stations throughout the 

 Pacific arena and facsimile reproductions of marigrams , together with 

 arrival times, have been published by the U. S. Coast & Geodetic Survey 

 (C&GS, 196i+ ; Spaeth and Berkman, I965, I967). A selection from these are 

 reproduced here in diagrams (a) of Figures k3 to 66, which refer to sta- 

 tions encompassing most of the peripheral boundary of the Pacific Ocean. 



62 



