I'm intruding into foreign territory here, since I don't have experience in exploring for gas fields etc., (though I have had to deal with patches of contamination, which is the same sort of thing on a small scale). So apologies if I blunder around and tread on toes!
Be that as it may, a point which has occurred to me in reading this thread is that the distribution being observed is the distribution of size conditional on being discovered, and the probability of being discovered may be expected to increase with size. So the frequency f(x) of occurrence of a size x in nature is attenuated by a factor equal to the probability that an item of size x will be discovered -- g(x) say. The frequency of x in the observed data is f(x | D), say, and so f(x | D) = f(x)*g(x) from which f(x) = f(x | D)/g(x). From this point, provided there is a reasonaboly justifiable model for g(x) (to within a constant of proportionality, e.g. simply g(x) = x), you can "demodulate" the observed data to infer the "wild" data. There has for many decades been a similar problem in classical geometrical probability (the ancestor of spatial statistics and morphometry), namely to infer the distribution of (e.g.) areas of cells given the observed distribution of the sizes of transects by lines, or of counts of sampling points intersecting them, leading to an integral equation. Maybe all this is old hat in the areas you are investigating, but since it did not seem to be even implicit in the discussion so far I thought I would bring it to the surface. Best wishes to all, Ted. On 01-Sep-05 Chris Hlavka wrote: > Beatrice - This is a vexing problem that I've tried to deal with in > sizes of features in satellite imagery (Hlavka, C. A. and J. L. > Dungan, 2002. Areal estimates of fragmented land cover - effects of > pixel size and model-based corrections. International Journal of > Remote Sensing23(4): 711-724.) The affine (count versus continuous) > nature of the digital imagery is at least part of the problem. I've > used probability plots to assess type of distribution. > > In gas field work, there is evidence that the apparent lognormality > of field-sizes is due to lower rates of discovery of smaller fields > than larger fields - especially for older surveys. It has been > noted that newer field data was closer to Pareto than older data and > thus inferred that the actual distribution is Pareto. -- Chris > > > >>Hello list >> >>I am a PhD student looking at developing a statistical model to predict >>the size-distribution of an area's oil and gas fields. >> >>It is clear that previous investigators prefer either a Pareto power >>law >>or a lognormal distribution to approximate field-size distributions. >> >>The data I am using does not look like it comes from a Pareto >>distribution >>- which I explain as being a result of undersampling - which previous >>investigators have reported - that undersampling occurs because the >>small >>fields are not sampled or recoded. However by using basin-modelling >>software to simulate oil and gas fields (for the same basin that my >>discovered empirical data comes from) I notice that this sample is also >>undersampled - that is fields under a certain size are not being >>simulated >>- which is probably due to the resolution of my input data but what is >>interesting is that the undersampling actually occurs throughout all >>the >>size ranges - including the medium to larger sizes - which I would not >>have expected. Like the discovery dataset (n = 25) the simulated >>dataset >>(n = 140) looks like it is more from a lognormal distribution than a >>Pareto distribution. >> >>My conclusion is that without being able to say that a Pareto is better >>than a lognormal and vise-versa it appears only logical to use both >>distributions. >> >>Geologically there does not seems to be a reason why a modal size >>(greater >>than what is detectable by exploration methods) of fields should exist >>- >>which would be the case if the data was from a lognormal distribution >>- >>except if the distribution is highly right skewed (at the small field >>size) and the mode is actually just below the detection of size. >> >>Geologically there does seem reason for fields to become so small that >>they become entities (that trap oil and gas) - and this relationship >>may >>be better approximated by a Pareto. >> >> >>The Pareto and lognormal form is similar but maybe one is better to >>approximate field sizes than the other. >>My question is do you think a Pareto distribution better approximates >>an >>oil and gas size distribution than a lognormal (or vise-versa) and if >>so >>why. >> >> >>I am currently working on goodness of fit test to throw some more light >>on >>this - but if anyone has any thing to say I'd appreciate some comments. >> >>Thank you, >> >>Kind regards >> >>Beatrice >> >>Geological and Nuclear Sciences >>New Zealand >>www.gns.cri.nz >> >> >>* By using the ai-geostats mailing list you agree to follow its rules >>( see http://www.ai-geostats.org/help_ai-geostats.htm ) >> >>* To unsubscribe to ai-geostats, send the following in the subject >>or in the body (plain text format) of an email message to >>[EMAIL PROTECTED] >> >>Signoff ai-geostats > > > -- > *************************************** > Chris Hlavka > NASA/Ames Research Center 242-4 > Moffett Field, CA 94035-1000 > (650)604-3328 FAX 604-4680 > [EMAIL PROTECTED] > *************************************** -------------------------------------------------------------------- E-Mail: (Ted Harding) <[EMAIL PROTECTED]> Fax-to-email: +44 (0)870 094 0861 Date: 02-Sep-05 Time: 09:16:02 ------------------------------ XFMail ------------------------------
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