Proposal of the spatial dependence evaluation from the power semivariogram model

Abstract

In Geostatistics, the use of measurement to describe the spatial dependence of the attribute is of great importance, but only some models (which have second-order stationarity) are considered with such measurement. Thus, this paper aims to propose measurements to assess the degree of spatial dependence in power model adjustment phenomena. From a premise that considers the equivalent sill as the estimated semivariance value that matches the point where the adjusted power model curves intersect, it is possible to build two indexes to evaluate such dependence. The first one, SPD*, is obtained from the relation between the equivalent contribution (α) and the equivalent sill (C* = C0 + α), and varies from 0 to 100% (based on the calculation of spatial dependence areas). The second one, SDI*, beyond the previous relation, considers the equivalent factor of model (FM*), which depends on the exponent β that describes the force of spatial dependence in the power model (based on spatial correlation areas). The SDI*, for β close to 2, assumes its larger scale, varying from 0 to 66.67%. Both indexes have symmetrical distribution, and allow the classification of spatial dependence in weak, moderate and strong.