With this email I would like to ask you 2 questions about spatial point

patterns. I'm working on a PhD, studying carbonate mounds at the

seafloor W of Ireland. We found a large province of these mound

structures, where we estimate there are more than 1000 of them. In part

of the province we could map the mounds accurately thanks to a 3D

seismic data set. This resulted in 387 mounds in an area of about 300 to

350 km2 (depending on where exactly we draw the boundary of the

province), which I suppose is a nice subset of the whole province, on

which we can do some statistical analyses. For example, I would like to

study the spatial positions of the mounds : are they clustered, or

rather regularly spaced?

This brings me to the first point : I used Ripley's K-function,

including edge correction, as described by Cressie (1993, Statistics for

spatial data). However, it turned out that the calculated K-values and

the resulting plots were very sensitive to the estimated 'intensity'

(lambda). A difference in intensity of 1.21 mounds/km2 or 1.26

mounds/km2 made a difference in interpreting the mounds to be clustered

or completely randomly spaced. And although the province on the whole is

quite sharply delineated, the 'exact' position of the boundary is

subject to interpretation, which affects the province's surface area,

and hence the estimation of lambda. (note that changing the postion of

the boundary, but not the intensity value, did not affect very much the

resulting K-values)

When I tried to calculate the K-function in study areas inside the mound

province, I received quite different results for the different study

areas chosen. I have the feeling that part of this is caused by a slowly

changing intensity. This would mean that the process is not

stationary...

* Therefore my question : is the K-function a good technique to study

the spatial point pattern? (as I understood from Cressie (1993) it is

one of the best ones?)? How sensitive is it to the estimation of lambda?

And to non-stationarity? Any suggestions?

The second point then goes one step further. Apart from the mound

position, I also registered some morphological characteristics, such as

mound height, cross-sectional area,... I could consider these data as a

marked point process, is that correct?

Now I would like to find out if there are zones with bigger and smaller

mounds, which maybe could be related to depth, slope angle of the

horizon on which they are seated etc. I made some plots already with

different symbols for different height classes etc, but I could not

really see a special pattern at first sight, and it would be interesting

to put things in numbers, I suppose.

* Hence my second question : should I consider these marked points as

irregular lattice data? And then calculate a semivariogram, maybe

interpolate a surface? I have the feeling there is quite a lot of

variability in mound height over small areas. How do I express this

best?

I must admit that, although I obtained the basics of (geo)statistics,

I'm not a (geo)statician at all, hence some of the derivations in

geostatistical handbooks go a bit far... I am mainly interested in the

application of the techniques in order to obtain information about the

behaviour of the mounds.

In any case, thank you very much for any help, and looking forward to

your suggestions!

Veerle

--

Veerle Huvenne

Renard Centre of Marine Geology

University of Ghent

Krijgslaan 281, S8

9000 Gent, Belgium

+32/9/264.45.84

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