# 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 ${\displaystyle 10^{\circ }}$, ${\displaystyle 20^{\circ }}$, ${\displaystyle 30^{\circ }}$, ${\displaystyle 40^{\circ }}$, and ${\displaystyle 60^{\circ }}$ 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,

{\displaystyle {\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 ${\displaystyle \Delta x}$ for raypaths in the LVL and permafrost.
Incident In low-velocity layer In permafrost
${\displaystyle \theta _{2}}$ ${\displaystyle \theta _{1}}$ ${\displaystyle \Delta x}$ (m) ${\displaystyle \Delta t}$ (ms) ${\displaystyle \theta _{1}}$ ${\displaystyle \Delta x}$ (m) ${\displaystyle \Delta t}$ (ms)
${\displaystyle 0^{\circ }}$ ${\displaystyle 0.0^{\circ }}$ 0.0 20.0 ${\displaystyle 0.0^{\circ }}$ 0 27.8
${\displaystyle 10^{\circ }}$ ${\displaystyle 2.1^{\circ }}$ 0.4 20.0 ${\displaystyle 15.1^{\circ }}$ 27 28.8
${\displaystyle 20^{\circ }}$ ${\displaystyle 4.1^{\circ }}$ 0.7 20.1 ${\displaystyle 30.9^{\circ }}$ 60 32.4
${\displaystyle 30^{\circ }}$ ${\displaystyle 6.0^{\circ }}$ 1.1 20.1 ${\displaystyle 48.6^{\circ }}$ 113 42.0
${\displaystyle 40^{\circ }}$ ${\displaystyle 7.7^{\circ }}$ 1.4 20.1 ${\displaystyle 74.6^{\circ }}$ 363 104.6
${\displaystyle 42^{\circ }}$ ${\displaystyle 8.0^{\circ }}$ 1.4 20.1 ${\displaystyle 90.0^{\circ }}$
${\displaystyle 60^{\circ }}$ ${\displaystyle 10.4^{\circ }}$ 1.8 20.3

Substituting the values of ${\displaystyle \theta _{2}}$, we get the results in Table 5.10a. The traveltimes in the LVL vary by only 0.5% over most of the range of ${\displaystyle \theta _{2}}$, and, even for ${\displaystyle \theta _{2}=60^{\circ }}$, 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 ${\displaystyle V_{1}}$ 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 ${\displaystyle \Delta x}$ and ${\displaystyle \Delta t}$ are considerable. This large ray bending makes corrections for permafrost very difficult. If ${\displaystyle \theta _{2}>42^{\circ }}$, upcoming waves are totally reflected.

Figure 5.10a.  Raypath bending at LV base.