Equally inclined orthogonal geophones

Problems in Exploration Seismology and their Solutions

Series	Geophysical References Series
Title	Problems in Exploration Seismology and their Solutions
Author	Lloyd P. Geldart and Robert E. Sheriff
Chapter	13
Pages	485 - 496
DOI	http://dx.doi.org/10.1190/1.9781560801733
ISBN	ISBN 9781560801153
Store	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 $x$-, $y$-, and $z$-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 $(l,m,n)$ and $l=m=n$. Because $l^{2}+m^{2}+n^{2}=1$ [Sheriff and Geldart, problem (15.9a)],

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

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

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Also in this chapter

• S-wave conversion in marine surveys
• Equally inclined orthogonal geophones
• Guided (channel) waves and normal-mode propagation
• Vertical seismic profiling
• Effect of velocity change on VSP traveltime
• Mapping the vertical flank of a salt dome
• Poission’s ratio from P- and S-wave traveltimes

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