What Statistical Test Determines Concentricity in Spherical Geophysics Data?

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SUMMARY

The discussion focuses on determining the concentricity of lineations in spherical geophysics data using statistical tests. The user describes a method involving the rotation of data sets to align with the z-axis and fitting a z-plane to each lineation by averaging z values. The goal is to minimize the sum of the squares of the residuals to identify the 'best fit' pole. The user seeks a hypothesis test or goodness-of-fit test to validate whether the lineations are best represented by concentric circles around this pole.

PREREQUISITES
  • Understanding of spherical coordinate systems and data rotation
  • Familiarity with statistical concepts such as residuals and goodness-of-fit tests
  • Knowledge of geophysical data analysis techniques
  • Experience with fitting models to data sets
NEXT STEPS
  • Research "Chi-Squared Goodness-of-Fit Test" for assessing model fit
  • Explore "ANOVA for Spherical Data" to compare multiple poles
  • Learn about "Maximum Likelihood Estimation" for parameter fitting
  • Investigate "Circular Statistics" for analyzing angular data distributions
USEFUL FOR

This discussion is beneficial for geophysicists, data analysts, and researchers involved in spherical data analysis and model fitting, particularly those interested in statistical validation of geophysical models.

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

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