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Geostatistics, as mentioned in the introductory topic What is geostatistics?, is a collection of methods that allow you to estimate values for locations where no samples have been taken and also to assess the uncertainty of these estimates. These functions are critical in many decision-making processes, as it is impossible in practice to take samples at every location in an area of interest.
It is important to remember, however, that these methods are a means that allows you to construct models of reality (that is, of the phenomenon you are interested in). It is up to you, the practitioner, to build models that suit your specific needs and provide the information necessary to make informed and defensible decisions. A big part of building a good model is your understanding of the phenomenon, how the sample data was obtained and what it represents, and what you expect the model to provide. General steps in the process of building a model are described in The geostatistical workflow.
Many interpolation methods exist. Some are quite flexible and can accommodate different aspects of the sample data. Others are more restrictive and require that the data meet specific conditions. Kriging methods, for example, are quite flexible, but within the kriging family there are varying degrees of conditions that must be met for the output to be valid. Geostatistical Analyst offers the following interpolation methods:
- Areal interpolation
- Diffusion interpolation with barriers
- Disjunctive kriging
- Empirical Bayesian kriging
- Gaussian geostatistical simulations
- Global polynomial
- Indicator kriging
- Inverse distance weighted
- Kernel interpolation with barriers
- Local polynomial
- Ordinary kriging
- Probability kriging
- Radial basis functions
- Simple kriging
- Universal kriging
Each of these methods has its own set of parameters, allowing you to customize each model for a particular dataset and the requirements for the output that it generates. To provide some guidance in selecting which to use, the methods have been classified according to several different criteria, as shown in Classification trees of the interpolation methods offered in Geostatistical Analyst. After you clearly define the goal of developing an interpolation model and fully examine the sample data, these classification trees may be able to guide you to an appropriate method.