# Effects of weathered layer (LVL) and permafrost

Series Geophysical References Series Problems in Exploration Seismology and their Solutions Lloyd P. Geldart and Robert E. Sheriff 5 141 - 180 http://dx.doi.org/10.1190/1.9781560801733 ISBN 9781560801153 SEG Online Store

## Problem 5.10a

Assume that raypaths have angles of approach of $10^{\circ }$ , $20^{\circ }$ , $30^{\circ }$ , $40^{\circ }$ , and $60^{\circ }$ in the subweathering where the velocity is 2400 m/s. For a weathered layer 10 m thick with velocity 500 m/s, how do travel-times through the weathered layer compare with that for a vertically traveling ray? What are the horizontal components of the raypaths in the LVL?

### Solution

Referring to Figure 5.10a,

{\begin{aligned}\sin \theta _{1}=\left(V_{1}/V_{2}\right)\sin \theta _{2}=0.208\sin \theta _{2},\\\Delta t=0.010/\left(0.500\cos \theta _{1}\right){\rm {s,}}\\\Delta x=\left(10\tan \theta _{1}\right){\rm {m.}}\end{aligned}} Table 5.10a. Traveltimes and $\Delta x$ for raypaths in the LVL and permafrost.
Incident In low-velocity layer In permafrost
$\theta _{2}$ $\theta _{1}$ $\Delta x$ (m) $\Delta t$ (ms) $\theta _{1}$ $\Delta x$ (m) $\Delta t$ (ms)
$0^{\circ }$ $0.0^{\circ }$ 0.0 20.0 $0.0^{\circ }$ 0 27.8
$10^{\circ }$ $2.1^{\circ }$ 0.4 20.0 $15.1^{\circ }$ 27 28.8
$20^{\circ }$ $4.1^{\circ }$ 0.7 20.1 $30.9^{\circ }$ 60 32.4
$30^{\circ }$ $6.0^{\circ }$ 1.1 20.1 $48.6^{\circ }$ 113 42.0
$40^{\circ }$ $7.7^{\circ }$ 1.4 20.1 $74.6^{\circ }$ 363 104.6
$42^{\circ }$ $8.0^{\circ }$ 1.4 20.1 $90.0^{\circ }$ $60^{\circ }$ $10.4^{\circ }$ 1.8 20.3

Substituting the values of $\theta _{2}$ , we get the results in Table 5.10a. The traveltimes in the LVL vary by only 0.5% over most of the range of $\theta _{2}$ , and, even for $\theta _{2}=60^{\circ }$ , change by only 1.5%.

## Problem 5.10b

For permafrost 100 m thick with a velocity of 3600 m/s, answer the questions in part (a).

### Solution

We repeat the calculations of part (a) changing $V_{1}$ to 3.60 km/s and layer thickness to 100 m. The results are also shown in Table 5.10a. Because rays now have large horizontal components, the changes in $\Delta x$ and $\Delta t$ are considerable. This large ray bending makes corrections for permafrost very difficult. If $\theta _{2}>42^{\circ }$ , upcoming waves are totally reflected.