The interpretation of the Wadati diagram with relaxed assumptions

The usual interpretation of the graph of ( S-P ) versus P in terms of the ratio of P - and S -velocities ( α/β ) and the origin time is valid only if α/β is the same in all media along the wave path. The properties of the graph have been derived for the cases in which α/β differs in layers by amounts that are small but representative of the range found in crustal rocks. For data at regional distances large compared to the depth, the slope yields a good approximation to α/β in the lowest layer traversed by the waves. The P -axis intercept is no longer the origin time. For a hypocenter in a half-space overlain by one layer, the origin time error is approximately proportional to the difference in α/β in the two media. If the origin time is known independently, for example, from a location program with good data and a good velocity model, the error in origin time given by the Wadati diagram can be used to verify the model. The technique was applied to a tightly clustered group of earthquakes well-placed with respect to the network centered on Amchitka Island. The P -velocities were well-determined, but Poisson's ratio had been arbitrarily taken as 0.25. The results called for a decrease of σ to 0.24 in the source layer (10.2-22.6 km) and an increase to 0.28 in the material above. The premonitory decrease in α/β proposed as a predictive phenomenon by Semyenov was marginally detected for one event during the 12 months following April, 1971. Conditions in an island arc make the application of the technique difficult. The time duration of the minimum relative to the magnitude of the earthquake agrees well with the results of other investigations.