Re: AI-GEOSTATS: Extreme values?
- Dear Chaosheng Zhang
This problem can be looked in various perspectives. You have to fit the data in the broader
picture and objectives.
First, what do your soil samples represent? How were they collected, what was their size? Are
they spot samples, multiple takes in a cross pattern with x metres between takes up to y
meters away from the centre? Etc.?
A significant part of nuggets effects when dealing with rock or soil materials may be sampling
and sample preparation generated. If these samples were assayed by AA, what was the size
of the portion used? If one gram, it is much more liable to generating a nugget effect than with 5
or 10 grams whenever pulverisation size was not fine enough and uniform.
Second, what is the purpose of your study. Academic work? Detection, remediation-
restoration, etc.? The high values might have physical significance in the later perspective
and smothing them may not be the ideal solution. Lead and Arsenic contamination cannot be
neglected or minimized.
In an industry or regulation perspective, the recommendation in that case might be to to carry
out additional sampling around the hot spots to delineate them better, say samples at 100 m
spacing, as well as checking the original hot spots, with a sampling method designed to be
representative. I am afraid I may not be easing you out of your problem, but such is physical
Chapter 8 in Jeff Myer's book "Geostatistical Error Management," deals with sampling and
Chapter 16 with sampling strategy. I published a text on "Sampling Quality Control" in a
mineral exploration and development perspective in Exploration and Mining Geology, Vol 7,
No 1-2, p. 107-116 (1998). This issue has several other papers on sampling. If it is not
available to you, I could send you a file copy of my paper.
Geoconseil Marcel Vallée Inc.
706 Routhier Ave
Québec, Québec G1X 3J9
Tel: (1) 418 652 3497
Fax: (1) 418 652 9148
14/12/01 06:33:35, Chaosheng Zhang <Chaosheng.Zhang@...> wrote:
>Dear Marcel Vallée,--
>Thanks. I think the sampling density is good enough to reveal the spatial
>structure, and the extreme samples are located within the "hot spots". The
>problem is that the few values are still extremely high within the "hot
>spots". This may be what the "nugget effect" means.
>I'm just wondering if these few extreme values should really be "discarded"/
>"censored" or replaced. However, this could get some criticism as they may
>If it is hard to find the best way, I will have to "replace" all the extreme
>values with 99% or 98% percentiles. But I'm not sure if it is appropriate to
>----- Original Message -----
>From: "Marcel Vallée" <vallee.marcel@...>
>To: <ai-geostats@...>; "Chaosheng Zhang" <Chaosheng.Zhang@...>
>Sent: Thursday, December 13, 2001 10:40 PM
>Subject: Re: AI-GEOSTATS: Extreme values?
>> Dear Chaosheng Zang
>> The sampling interval is so wide that the high values could easily be
>>related to "hot spots" of
>> higher grade contamination, i..e dumping areas for particular kinds of
>>slags, mineralized waste, etc. A property map might help.
>> Have you contoured the data? If so, the sampling interval is so wide that
>>real hot spots of
>> environmental significance might not show 2D distribution on such a wide
>sampling grid, however.
>> Marcel Vallée, Eng,, Geo.
>> Geoconseil Marcel Vallée Inc.
>> 706 Routhier Ave
>> Québec, Québec G1X 3J9
>> Tel: (1) 418 652 3497
>> Fax: (1) 418 652 9148
>> Email: vallee.marcel@...
>> 13/12/01 08:01:48, Chaosheng Zhang <Chaosheng.Zhang@...> wrote:
>> > Date: Thu, 13 Dec 2001 13:01:48 +0000
>> > From: Chaosheng Zhang <Chaosheng.Zhang@...>
>> > Subject:AI-GEOSTATS: Extreme values?
>> > To: ai-geostats@...
>> > Dear all,
>> > My question is: How to deal with the extreme/outlying values in a data
>> > I am dealing with heavy metal concentrations in soils from a mine area.
>>>The sample number is 223, and the samples are spatially evenly distributed
>>>with the sampling interval of 400 metres. There are several samples with
>>>extremely high values, which makes me feel uncomfortable. The
>>>percentiles of the dataset are listed as follows (in mg/kg):
>> > Zn Cu Pb Cd As
>> > Min 4 1 25 0.0 2
>> > 5% 35 6 35 0.1 6
>> > 10% 40 7 41 0.2 7
>> > 25% 65 13 62 0.3 9
>> > 50% 122 18 168 0.6 15
>> > 75% 338 27 821 1.5 28
>> > 90% 907 56 2799 2.8 58
>> > 95% 1986 116 4490 4.2 80
>> > 96% 2462 151 4698 4.9 82
>> > 97% 3493 178 5413 6.2 91
>> > 98% 4697 207 7609 8.3 111
>> > 99% 6712 247 11750 12.4 184
>> > Max 11473 1293 16305 48.5 1060
>> > When doing geostatistical and statistical analyses, we need some confidence
>> > in dealing with the these very high extreme values which account for less
>> > than 2% of the total sample number.
>> > Any suggestions?
>> > Cheers,
>> > Chaosheng Zhang
>> > ===================================
>> > Dr. Chaosheng Zhang
>> > Department of Geography
>> > National University of Ireland
>> > Galway
>> > IRELAND
>> > Tel: +353-91-524411 ext. 2375
>> > Fax: +353-91-525700
>> > Email: Chaosheng.Zhang@...
>> > ===================================
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- Chaosheng Zhang -
I think Marcel Vallee is headed in the right direction on your problem.
There is a good chance that the problem is one of sample and or subsample
support. As mentioned, if you sampled within a foot or tow of a location
that displays an extreme or "outlier" value, you may find values an order of
magnitude or more below the outlier. Similarly, you may also have
"inliers", where a sample nearby a location with a low concentration may
contain a significantly higher value. Of course, no one gets excited about
the inliers that may be unrepresentative, but we get very excited about the
The possibility of extreme values should be planned for in the initial stage
of the sampling program. Pierre Gy's work has revealed that the physical
size, volume, and orientation of a sample and subsample (i.e. the support)
are crucial to the concentration estimate obtained. You are asking a lot to
have a 10-g sample represent 400 meters between sample locations in any
case. Unless the support of the original sample and all subsampling stages
was sufficient, there is little chance that the samples are highly
representative of the true concentration. Mine areas typically are very
heterogeneous and proper sampling support when sampling is essential.
Perhaps you can provide some details. If the underlying data are not
representative due to improper suppoort, you are trying to "contour an
illusion", and typically the results are not pleasing.
The way in which the data are used in decision-making is also important.
For instance, if your purpose is to delineate hot spots for risk assessment,
extreme values do not pose a problem as they will be addressed. You may,
however, be very interested in getting your best information at an economic
cutoff value or risk threshold, since the decision for treatment of values
high above or way below the action level is easy.
Westinghouse Safety Management Solutions
2131 S. Centennial Ave., SE
Aiken, SC 29803
From: Chaosheng Zhang [mailto:Chaosheng.Zhang@...]
Sent: Thursday, December 13, 2001 8:02 AM
Subject: AI-GEOSTATS: Extreme values?
My question is: How to deal with the extreme/outlying values in a data set?
I am dealing with heavy metal concentrations in soils from a mine area. The
sample number is 223, and the samples are spatially evenly distributed with
the sampling interval of 400 metres. There are several samples with
extremely high values, which makes me feel uncomfortable. The percentiles of
the dataset are listed as follows (in mg/kg):
Zn Cu Pb Cd As
Min 4 1 25 0.0 2
5% 35 6 35 0.1 6
10% 40 7 41 0.2 7
25% 65 13 62 0.3 9
50% 122 18 168 0.6 15
75% 338 27 821 1.5 28
90% 907 56 2799 2.8 58
95% 1986 116 4490 4.2 80
96% 2462 151 4698 4.9 82
97% 3493 178 5413 6.2 91
98% 4697 207 7609 8.3 111
99% 6712 247 11750 12.4 184
Max 11473 1293 16305 48.5 1060
When doing geostatistical and statistical analyses, we need some confidence
in dealing with the these very high extreme values which account for less
than 2% of the total sample number.
Dr. Chaosheng Zhang
Department of Geography
National University of Ireland
Tel: +353-91-524411 ext. 2375
[Non-text portions of this message have been removed]