# Define empirical dissertation

Sample observations are denoted Z ( s i ) = z i {\displaystyle Z(\mathbf {s} _{i})=z_{i}} . Samples may be taken at k {\displaystyle k} total different locations. This would provide as set of samples z 1 , … , z k {\displaystyle z_{1},\ldots ,z_{k}} at locations s 1 , … , s k {\displaystyle \mathbf {s} _{1},\ldots ,\mathbf {s} _{k}} . Generally plots show the semivariogram values a function of sample point separation h {\displaystyle h} . In the case of empirical semivariogram, separation distance bins h ± δ {\displaystyle h\pm \delta } are used rather than exact distances, and usually isotropic conditions are assumed (., that γ {\displaystyle \gamma } is only a function of h {\displaystyle h} and does not depend on other variables such as center position). Then, the empirical semivariogram γ ^ ( h ± δ ) {\displaystyle {\hat {\gamma }}(h\pm \delta )} can be calculated for each bin: