[R-sig-Geo] equations for cross variograms (Applied Spatial Data Analysis with R)

[Edzer Pebesma]

Tom Gottfried wrote:
> Hi all,
>
> two questions about the equations on page 206 of the ASDAR book:
>
> 1) is it possible, that in the first one, there is "1/2" missing before the expression of the
> expected value? I looked in some books and papers and it's always there.
>   
Yes, it's missing. Luckily it's not missing in the software (I believe!)
>
> 2) is there any literature that could help me understand the second equation (for non-collocated
> data). Mostly the pseudo-cross semivariance is mentioned for use with non-collocated data and is
> expressed as half the variance of differences such as
>
> gamma_ij(h)=1/2 Var[Z_i(x+h) - Z_j(x)]
>
> Is this the same as what is expressed by the second equation on page 206 of the ASDAR book and thus
> what is calculated by gstat::variogram?
>   
No, you found another mistake in the book. The correct equation for
non-collocated data should be

gamma_ij(h) = 1/2 E(((Z_1(s) - m_1) - (Z_2(s+h) - m_2))^2)

which is equivalent with what you give, when Z_1 and Z_2 have constant
means m_1 and m_2 respectively. Again, this is what the software does.
> Thank you very much!
>   
Thank you, we'll update the Errata pages on www.asdar-book.org.
> Tom
>
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>   

-- 
Edzer Pebesma
Institute for Geoinformatics (ifgi), University of Münster
Weseler Straße 253, 48151 Münster, Germany. Phone: +49 251
8333081, Fax: +49 251 8339763 http://ifgi.uni-muenster.de/
http://www.springer.com/978-0-387-78170-9 e.pebesma at wwu.de