Open AccessThe Tau Method for Inversion of Travel Times—II Earthquake Data
Author(s) -
Bessonova E. N.,
Fishman V. M.,
Shnirman M. G.,
Sitnikova G. A.,
Johnson L. R.
Publication year - 1976
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.1976.tb01634.x
Subject(s) - inversion (geology) , inverse theory , geology , geodesy , function (biology) , inverse , mathematical analysis , inverse problem , travel time , hypocenter , geometry , seismology , mathematics , physics , surface wave , optics , induced seismicity , engineering , evolutionary biology , biology , transport engineering , tectonics
Summary Further development of the theory and practice of the method for solving the inverse problem of seismology suggested in Bessonova et al . is described in this paper. The problem is formulated as follows: the travel times of body waves are given at a discrete set of points, and we are required to find in the ( V, Y ) plane ( V is the velocity and Y is the depth) the closed area which contains all velocity‐depth curves corresponding to the given data. A spherically symmetric model is assumed and a lower limit for the velocity in the low velocity zones is postulated. The method is based on the use of the function τ( p ) = T ( p ) – pX ( p ), p being the ray parameter, T the travel time, and X the epicentral distance. A new formula which expresses the velocity‐depth curve in terms of the function τ( p ) is used to construct the required area. A statistical method of interpretation allows us to construct the confidence region which contains the velocity‐depth curve at a given confidence level. Application of the method is illustrated using earthquake data to investigate the velocity distribution in the mantle.