# Equally inclined orthogonal geophones

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 13.2

Determine the inclination angles for three orthogonal geophones that are equally inclined to the vertical.

### Solution

The three orthogonal geophones define a rectangular coordinate system with the ${\displaystyle x}$-, ${\displaystyle y}$-, and ${\displaystyle z}$-axes along the geophones axes. We take a straight line through the origin of this system such that it is equally inclined to each axis, and rotate the coordinate system so that the straight line is vertical. The direction cosines of the vertical line are ${\displaystyle (l,m,n)}$ and ${\displaystyle l=m=n}$. Because ${\displaystyle l^{2}+m^{2}+n^{2}=1}$ [Sheriff and Geldart, problem (15.9a)],

{\displaystyle {\begin{aligned}3l^{2}=1,\quad l=1{\sqrt {3}},\cos ^{-1}(1/{\sqrt {3}})=54.74^{\circ }.\end{aligned}}}

Thus the geophones must be inclined ${\displaystyle 54.74^{\circ }}$ to the vertical.