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

{\displaystyle {\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 ${\displaystyle \sigma }$.
Event ${\displaystyle t_{\hbox{P}}}$ ${\displaystyle t_{\hbox{S}}}$ ${\displaystyle \alpha /\beta }$ ${\displaystyle (\alpha /\beta )^{2}}$ ${\displaystyle \sigma }$
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