Page 188 - Modern Spatiotemporal Geostatistics

Modifications of BME Analysis 169

Fable 9.1. The g a functions corresponding
to case presented in Example 9.2.

samples (assumed to have point support) and the block. In view of the support
effect between samples (xi) and block (xv), the BME system of equations
l
consists of Equations 9.5, 9.8, and 9.9 with XA = Xv = V~ f v dux(u).
The corresponding g a functions (a = 0, 1, 2) are shown in Table 9.1.
The Lagrange multipliers p a are found from the solution of the following system
of equations

where The
left-hand sides of Equation 9.10 are computed experimentally in terms of the
varioerams as follows (/in = 1}

where and are the point (sample)-block and the block-block averaged
variograms, respectively. Equation 9.8 now becomes

and using the relationships in Table 9.1, the last equation reduces to the fol-
lowine integral reoresentation

which is solved with respect to the Xv that is the desired BME block
estimate.
BME's treatment of the support effect does not suffer from the limitations
of classical geostatistics approaches (e.g., the problematic inference of the