Strain estimation in 3D by fitting linear and planar data to the March model

Abstract

The probability density function associated with the March model is derived and used in a maximum likelihood method to estimate the best fit distribution and 3D strain parameters for a given set of linear or planar data. Typically it is assumed that in the initial state (pre-strain) linear or planar data are uniformly distributed on the sphere which means the number of strain parameters estimated needs to be reduced so that the numerical technique succeeds. Essentially this requires that the data are rotated into a suitable reference frame prior to analysis. The method has been applied to a suitable example from the Dalradian of SW Scotland and results obtained are consistent with those from an independent method of strain analysis. Despite March theory having been incorporated deep into the fabric of geological strain analysis, its full potential as a simple direct 3D strain analytical tool has not been achieved. The method developed here may help remedy this situation.