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On Pulses whose Travel Times are not True Minima

Published online by Cambridge University Press:  24 October 2008

Harold Jeffreys
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Extract

In the construction of the seismological tables it has been found that the times of several pulses at a given distance show a well-marked maximum frequency for each, about which the bulk of the observations are spread with a standard deviation of 1·5−3 sec. For others there was only a vague concentration, spread over about half a minute (Jeffreys and Bullen, 1936–40). The theoretical times of the latter type could all be calculated from those of the former by using the principle of stationary time for small variations of the path, and the observed times might be either shorter or longer than the theoretical ones. There was a complete association between the type of distribution of the residuals and the nature of the path. Whenever the time as calculated was a minimum for all small variations of the path, the distribution of residuals was of the former type; when it was stationary without being either a true minimum or a maximum it was of the latter.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 39 , Issue 1 , March 1943 , pp. 48 - 51
Copyright
Copyright © Cambridge Philosophical Society 1943

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References

REFERENCES

Jeffreys, H.Operational methods in mathematical physics. (Camb. Univ. Press, 1931.)Google Scholar
Jeffreys, H. and Bullen, K. E.Mon. Not. Roy. Astr. Soc., Geophys. Suppl. (several papers) (1936–1940).Google Scholar