Pat McGroin
25-10-2007, 10:42 AM
Hi Everyone,
I am trying to understand if fitcircle will provide me with the correct
output for the following problem, and if not, whether somebody
could point me in the right direction for solving this problem. For
those of you who have worked in structural geology, I am trying to
find how much rotation is needed to restore two sets of tilted
surfaces to the same direction. The rotation is accommodated
initially on a vertical plane. Some do that with a Wulff stereonet
(which I did as well), but I am trying to solve the question
numerically.
The problem consists is finding a small circle which:
1. Passes through 2 given points (poles of dipping surfaces) on a
sphere
2. Is parallel to the sphere's rotation axis (the plane defining the cap
on the sphere is perpendicular to the equatorial plane, thus its pole
is defined by some longitude angle and 0 latitude).
The ultimate information I need to retrieve from the computation
are:
1. Since a small circle is the trace of a cone on the sphere, what is
the azimuth of the axis of this cone ?
2. What is the angular distance between the two poles used to fit
the small circle, ie the angular distance along the small circle? I
know it is r*alpha, but what is the value of the radius r?
3. What is the shortest angular distance between the small circle
and the "north pole" of the sphere; in other words, what is the
northernmost latitude reached by the small circle?
The man pages for fitcircle say that fitcircle computes either the
great or small circle passing through a cloud of observations. What
it doesn't say is what small cricle is fitted. My understanding is that
there is an infinite number of small circles passing through two
points on a sphere. Which one is provided by fitcircle -S ?
If fitcircle won't achieve this computation, could you point me to
some other way to achieve this purpose numerically ?
Cheers
Trip
I am trying to understand if fitcircle will provide me with the correct
output for the following problem, and if not, whether somebody
could point me in the right direction for solving this problem. For
those of you who have worked in structural geology, I am trying to
find how much rotation is needed to restore two sets of tilted
surfaces to the same direction. The rotation is accommodated
initially on a vertical plane. Some do that with a Wulff stereonet
(which I did as well), but I am trying to solve the question
numerically.
The problem consists is finding a small circle which:
1. Passes through 2 given points (poles of dipping surfaces) on a
sphere
2. Is parallel to the sphere's rotation axis (the plane defining the cap
on the sphere is perpendicular to the equatorial plane, thus its pole
is defined by some longitude angle and 0 latitude).
The ultimate information I need to retrieve from the computation
are:
1. Since a small circle is the trace of a cone on the sphere, what is
the azimuth of the axis of this cone ?
2. What is the angular distance between the two poles used to fit
the small circle, ie the angular distance along the small circle? I
know it is r*alpha, but what is the value of the radius r?
3. What is the shortest angular distance between the small circle
and the "north pole" of the sphere; in other words, what is the
northernmost latitude reached by the small circle?
The man pages for fitcircle say that fitcircle computes either the
great or small circle passing through a cloud of observations. What
it doesn't say is what small cricle is fitted. My understanding is that
there is an infinite number of small circles passing through two
points on a sphere. Which one is provided by fitcircle -S ?
If fitcircle won't achieve this computation, could you point me to
some other way to achieve this purpose numerically ?
Cheers
Trip