# Spatial distribution of points

#### nicolaslecorvec

##### New Member
Hi,

I'm working on spatial distribution of points (being location of volcanoes). I found so far a linear correlation between the mean distance between nearest neighbours and the density in a semi-log plot.

I'm looking for ideas and ways to study these fields of points/volcanoes.

Cheers,

N.

#### ohammer

##### Member
Hi,

I'm working on spatial distribution of points (being location of volcanoes). I found so far a linear correlation between the mean distance between nearest neighbours and the density in a semi-log plot.

I'm looking for ideas and ways to study these fields of points/volcanoes.

Cheers,

N.
There is a fairly large literature on spatial point pattern analysis of volcanoes and similar structures. The standard machinery to throw at it is Ripley's K to identify overdispersion and clustering at different scales, and 2D kernel density estimation to make a pretty density map. From Ripley's K you can compute fractal dimension (not extremely useful, but the scale range of fractality has been used to estimate crust thickness).

An overall test for overdispersion/clustering (across all scales) can be computed from nearest neighbour analysis.

It may also be interesting to find and test for linear alignments of points, which may be interpreted as fault lines.

All of these functions are available in Past, and most of them in packages for R such as spatstat, spatial and splancs. None of the R packages contain lineament analysis, as far as I know.

#### nicolaslecorvec

##### New Member
Hi,

Thank you for your answer. Actually I've already done all that (fractal, lineaments, and poisson nearest neighbors). I'm trying to find out if tectonic environement act on the distribution of volcanoes in volcanic fields. I just started to play with the results of the PNN analysis, and so far it looks quite random. Except when I plot for each field (25 of them), the mean distance between the NN =f(density). I can fit in power equation in the form of y=ax^-b. I'm not familiar with the statistical interpretation of such trend.. that's why i was writing here to get some advice.

cheers

#### ohammer

##### Member
Hi,

Thank you for your answer. Actually I've already done all that (fractal, lineaments, and poisson nearest neighbors). I'm trying to find out if tectonic environement act on the distribution of volcanoes in volcanic fields. I just started to play with the results of the PNN analysis, and so far it looks quite random. Except when I plot for each field (25 of them), the mean distance between the NN =f(density). I can fit in power equation in the form of y=ax^-b. I'm not familiar with the statistical interpretation of such trend.. that's why i was writing here to get some advice.

cheers
OK. I'm not quite sure if I understand - is it not obvious that NN distance should fall as the inverse square root of density?

I would be interested to know what technique you used for lineament analysis? (I have worked a little on this: Hammer, Ø. 2009. New methods for the statistical detection of point alignments. Computers & Geosciences 35:659-666).