Open AccessS ‐wave travel times for a spherically averaged earth
Author(s) -
Uhrhammer Robert
Publication year - 1978
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1978.tb04272.x
Subject(s) - confidence interval , weighting , statistics , geodesy , travel time , mathematics , residual , variance (accounting) , distribution (mathematics) , geology , physics , mathematical analysis , algorithm , accounting , transport engineering , acoustics , engineering , business
Summary. Shear‐wave travel times in a spherically averaged earth are estimated using ‘differential’ S minus P ( S – P ) travel‐time measurements and detailed statistical procedures. Fourteen earthquakes and 48 stations are specially selected, yielding 302 S ‐ P times for 6° < Δ < 111°. Analysis of variance techniques are used to estimate simultaneously azimuthally varying source and station adjustments while constructing an S – P travel‐time model. A method of weighting the equations of condition based on the distribution of stations and epicentres is developed to reduce the effects of systematic errors due to non‐random sampling of the Earth. The resulting S ‐ P travel times are added to the 1939 Jeffreys–Bullen and the 1968 Herrin P travel times as a function of distance to obtain shear‐wave travel‐time models. Confidence intervals for the models are estimated from the variance of the observed S – P travel times. The standard error for a single observed S – P travel time (6° < Δ < 111°) is 2.1 s and the residual distribution is not significantly different from a normal distribution at the 95 per cent confidence level. For 30° < Δ < 80° the mean S travel time is 1.3 s later than the corresponding mean for Jeffreys–Bullen tables, which is significant at the 95 per cent confidence level.