What Statistical Test Determines Concentricity in Spherical Geophysics Data?

[arlosaur]

I am doing a geophysics project where I am analyzing a number of lineations on a globe / sphere. That is, I have a data set with many (70 - 180) sets of data points that are grouped together in lineations. I am trying to determine if the lineations are best described by concentric circles about a specific pole. To do this for every longitude/latitude value on the sphere I rotate the entire data set so that the chosen axis of rotation is now the z-axis. I then fit a z-plane through each lineation, which amounts to averaging the z values for each lineation after rotation. I also calculate the sum of the squares of the residuals (z_i - <z>)^2 for each lineation. I then calculate the 'best fit' pole by choosing the pole which minimizes the sum of the squares of the residuals of each lineation with their respective best-fit plane.

Now I wish to come up with a hypothesis test or a goodness-of-fit test to determine if the lineations are best described by concentric circles about this pole (as opposed to two or three poles or something else altogether).

Any ideas? Thanks.

 

[ssd]

Goodness of fit applies to the graduation of a probability distribution only.