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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