Semivariance

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In spatial statistics, the empirical semivariance is described by

\hat\gamma(h)=\frac{1}{2}\cdot\frac{1}{n(h)}\sum_{i=1}^{n(h)}(z(x_i+h)-z(x_i))^2

where z is a datum at a particular location, h is the distance between ordered data, and n(h) is the number of paired data at a distance of h. The semivariance is half the variance of the increments z(x_i+h)-z(x_i), but the whole variance of z-values at given separation distance h (Bachmaier and Backes, 2008).

A plot of semivariances versus distances between ordered data in a graph is known as a semivariogram rather than a variogram. Many authors call 2\hat\gamma(h) a variogram, others use the terms variogram and semivariogram synonymously. However, Bachmaier and Backes (2008), who discussed this confusion, have shown that \hat\gamma(h) should be called a variogram, terms like semivariogram or semivariance should be avoided.

See also[edit]

References[edit]

  • Bachmaier, M and Backes, M, 2008, "Variogram or semivariogram? Understanding the variances in a variogram". Article doi:10.1007/s11119-008-9056-2, Precision Agriculture, Springer-Verlag, Berlin, Heidelberg, New York.
  • Clark, I, 1979, Practical Geostatistics, Applied Science Publishers
  • David, M, 1978, Geostatistical Ore Reserve Estimation, Elsevier Publishing
  • Hald, A, 1952, Statistical Theory with Engineering Applications, John Wiley & Sons, New York
  • Journel, A G and Huijbregts, Ch J, 1978 Mining Geostatistics, Academic Press

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