Two methods for determining the time of origin, depth of focus, and the average velocities from the focus to the surface are described. The first stage in the first method is to determine the time of origin using a modification of the Wadati method. As was pointed out in 1973 by Kisslinger and Engdahl, the relation between (ts − tp and tp is nonlinear and it is necessary to allow for this nonlinearity by including a term in tp2 in the analysis. Thereafter the depth of focus and the average velocity can be found by a modification of the procedure used to determine the depth to a reflector in seismic reflection prospecting. It is necessary to allow for the sphericity of the Earth in this analysis.
In the second method, the depth of focus is determined first by analyzing (ts − tp)2 as a function of x2, x being the epicentral distance. The average velocity of separation of S and P waves is also determined at this stage. Thereafter the time of origin and the average P and S velocities are determined. The results of the analysis of the calculated travel times for three models show that systematic errors in the depth of focus using these procedures are less than 2 km over the depth range of 60 to 640 km.
Preliminary results of the analysis of a limited set of Japanese earthquakes by these methods give estimates of depth smaller than those given by ISC for depths less than 300 km. For deeper earthquakes, these methods give foci deeper than the ISC, but in these cases the observations close to the epicenter are inadequate for reliable analysis.