After sending the message, I checked the relation and noticed a few missing
terms.
COV[Y(si),Y(sj)]=E{[Y(si)-m(si)][Y(sj)-m(sj)]}=E{[W(si)][W(sj)]}=
COV[W(si),W(sj)]
--
With Best Wishes
Mohammad J. Abedini Department of Civil and Environmental EngineeringSchool of
Engineering, Shiraz UniversityOffice Phone #: Direct: 0711-6474604, Ext.:
0711-(613)3132Cell Phone #: 09173160456
Subject: Inquiry
From: Mohammad Abedini <[email protected]>
Date: Mon, 06/01/2015 09:38 PM
To: [email protected]
Dear Colleagues
It is quite a while where our geo-mailing list
is not active and we have to delineate the source of this problem.
Anyway, I would greatly appreciate it if I could have
your comments and assessment regarding the following issue:
Generally speaking, any random function can be
written as Y(s)=m(s)+W(s). where m(s)=E[Y(s)].
1. When m=cte independent of spatial location,
then, the covariance of Y at two spatial locations is the same as covariance of
W at
the same two spatial locations.
2. When m is not constant, a few geostatisticians
argue that covariance of Y at two spatial locations cannot be defined and of
course it is not equal to covariance of W at the same two locations.
3. I am not quite convinced why covariance of Y at
two spatial locations is not defined. I am wondering if this lack of
availability
is at theoretical level and/or at computational level. Assuming its
availability, look at the following mathematical manipulation:
COV[Y(si),Y(sj)]=E{[Y(si)-m(si)][Y(sj)-(sj)]}=E{[W(si)][W(sj)]}=
COV[W(si),Y(sj)]
This implies that the covariance of Y and W is the
same.
Your critical assessment of the above
assertion would be greatly appreciated.
--
With Best Wishes
Mohammad J. Abedini Department of Civil and Environmental EngineeringSchool of
Engineering, Shiraz UniversityOffice Phone #: Direct: 0711-6474604, Ext.:
0711-(613)3132Cell Phone #: 09173160456
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