Open AccessA New Method of Deriving Seismic Velocity Distributions from Travel‐time Data
Author(s) -
Bullen K. E.
Publication year - 1960
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.1960.tb00394.x
Subject(s) - computation , seismic velocity , travel time , distribution (mathematics) , set (abstract data type) , mathematics , data set , geology , mathematical analysis , geodesy , computer science , algorithm , seismology , statistics , transport engineering , engineering , programming language
Summary A law of the form v = arζo gives a useful first approximation to the seismic velocity distribution in various parts of the Earth. A method is here devised of finding the corrections to numerical values given by the law which are needed to fit a given set of seismic travel‐time data. The method provides an alternative to the classical Herglotz method of determining seismic velocity distributions, and can be specially powerful in regions where the proportionate deviations from the above velocity law are small or moderate. The method is exact in spite of the non‐linear form of the first approximation. Auxiliary notes are given which facilitate computation in particular cases, for example when the form T = a Δ‐ b Δ 3 has been used to represent part of the travel‐time data. For purposes of illustration, the method is applied to determining the P velocity distribution for the whole region E of the Earth. The method incidentally illustrates anew the importance of the parameters 5 and a (defined below) in ray theory.