Help needed for spatial statistics - linearity problem

I am a final year Environmental Geoscience BSc student, currently engaged in a dissertation project on synsedimentary fracturing in carbonates. I have hit a snag in my data analysis, and have not yet been able to find a solution in the literature I have read. My project supervisor has referred me to an expert who, as yet, hasn't answered any of my emails.

I have a single dataset of the locations of geological features (blue holes) that may be indicative of fracturing. I need to prove that these features are distributed in a linear way.

The problem is, each the features is expected to occur on one of several lines running parallel to the carbonate bank margin. I need a technique to relate the different data to the line that is relevant, without arbitrary selection of data points.

The questions I have are therefore:

Is there a non-arbitrary method for selecting data for regression analysis?

Is there a technique for correlating parts of a single dataset with several
linear trends?

I would greatly appreciate it if someone could suggest a source where I might find the answers to these questions, or the name of a suitable technique.