# Poission’s ratio from P- and S-wave traveltimes

Series Geophysical References Series Problems in Exploration Seismology and their Solutions Lloyd P. Geldart and Robert E. Sheriff 13 485 - 496 http://dx.doi.org/10.1190/1.9781560801733 ISBN 9781560801153 SEG Online Store

## Problem 13.7

Find Poisson’s ratio for the five events in Figure 13.7a.

### Solution

Poisson’s ratio $\sigma$ can be obtained from the ratio $V_{\hbox{P}}/V_{\hbox{S}}$ using equation (10.2) Table 2.2a. Since $z=V_{\hbox{P}}t_{\hbox{P}}=V_{\hbox{S}}t_{\hbox{S}}$ , $V_{\hbox{P}}/V_{\hbox{S}}=t_{\hbox{S}}/t_{\hbox{P}}$ , we can get $(V_{\hbox{P}}/V_{\hbox{S}})$ from the traveltimes and then get $\sigma$ using equation (10,2) (see Table 2.2a), that is,

{\begin{aligned}\sigma ={\frac {(V_{\hbox{P}}/V_{\hbox{S}})^{2}-2}{2[(V_{\hbox{P}}/V_{\hbox{S}})^{2}-1]}}.\end{aligned}} Measurements and calculations are listed in Table 13.7a. Figure 13.7a.  Comparison of P- and S-wave records (courtesy of CGG.) (i) P-wave record; (ii) S-wave record displayed at double the speed to facilitate comparison.
Table 13.7a. Determination of $\sigma$ .
Event $t_{\hbox{P}}$ $t_{\hbox{S}}$ $\alpha /\beta$ $(\alpha /\beta )^{2}$ $\sigma$ 1 0.39 0.96 2.46 6.05 0.40
2 0.62 1.50 2.42 5.86 0.40
3 0.74 1.65 2.23 4.97 0.37
4 0.80 1.83 2.29 5.24 0.38
5 0.99 2.16 2.18 4.75 0.37