Geostatistics

Geostatistics is the branch of statistics focusing on spatial or spatiotemporal datasets. Developed originally to predict probability distributions of ore grades for mining operations, this is the currently applied in diverse disciplines including petroleum geology, hydrogeology, hydrology, meteorology, oceanography, geochemistry, geometallurgy, geography, forestry, environmental control, landscape ecology, soil science, together with agriculture esp. in precision farming. Geostatistics is applied in varied branches of geography, especially those involving the spread of diseases epidemiology, the practice of commerce as well as military planning logistics, and the developing of excellent spatial networks. Geostatistical algorithms are incorporated in many places, including geographic information systems GIS.

Background

Geostatistics is intimately related to interpolation methods, but extends far beyond simple interpolation problems. Geostatistical techniques rely on statistical models that are based on random function or random variable picture to model the uncertainty associated with spatial estimation and simulation.

A number of simpler interpolation methods/algorithms, such(a) as inverse distance weighting, bilinear interpolation and nearest-neighbor interpolation, were already well known before geostatistics. Geostatistics goes beyond the interpolation problem by considering the studied phenomenon at unknown locations as a kind of correlated random variables.

Let x be the value of the variable of interest at alocation x. This value is unknown e.g. temperature, rainfall, piezometric level, geological facies, etc.. Although there exists a value at location x that could be measured, geostatistics considers this value as random since it was not measured, or has not been measured yet. However, the randomness of x is not complete, but defined by a cumulative distribution function CDF that depends oninformation that is requested about the value x:

Typically, whether the value of is invited at locationsto x or in the multiple-point simulationpseudo-genetic techniques.

By applying a single spatial framework on an entire domain, one makes the given that is a stationary process. It means that the same statistical properties are applicable on the entire domain. Several geostatistical methods manage ways of relaxing this stationarity assumption.

In this framework, one can distinguish two modeling goals:

A number of methods equal for both geostatistical estimation and chain realizations approaches. Several mention books supply a comprehensive overview of the discipline.