# scikit-gstat用户手册：前言

## General

scikit-gstat的用户指南文档旨在为用户提供该Python模块功能的使用指南，以及对地理统计学概念的基础性介绍。主要的用例是将这种描述交给学习地理统计学并需要使用scikit-gstat的学生但在介绍变异函数之前，必须先回答一个更普遍的问题，即地质统计学究竟是什么。

Note

## What is geostatistics 什么是地质统计学?

The basic idea of geostatistics is to describe and estimate spatial covariance, or correlation, in a set of point data. While the main tool, the semi-variogram, is quite easy to implement and use, a lot of important assumptions are underlying it.

The typical application of geostatistics is an interpolation. Therefore, although using point data, a basic concept is to understand this point data as a sample of a (spatially) continuous variable that can be described as a random field , or to be more precise, a Gaussian random field in many cases.

The most fundamental assumption in geostatistics is that any two values  and  are more similar, the smaller  is, which is a separating distance on the random field. In other words: close observation points will show higher covariances than distant points. In case this most fundamental conceptual assumption does not hold for a specific variable, geostatistics will not be the correct tool to analyse and interpolate this variable.

One of the most easiest approaches to interpolate point data is to use IDW (inverse distance weighting). This technique is implemented in almost any GIS software. The fundamental conceptual model can be described as:

where  is the value of  at a non-observed location with  observations around it. These observations get weighted by the weight , which can be calculated like:

where   is the unobserved point and  is one of the sample points. Thus, is the 2-norm of the vector between the two points: the Euclidean distance in the coordinate space (which by no means has to be limited to the  case).

This basically describes a concept, where a value of the random field is estimated by a distance-weighted mean of the surrounding points. As close points shall have a higher impact, the inverse distance is used and thus the name of inverse distance weighting.

In the case of geostatistics this basic model still holds, but is extended. Instead of depending the weights exclusively on the separating distance, a weight will be derived from a variance over all values that are separated by a similar distance.

This has the main advantage of incorporating the actual (co)variance found in the observations and basing the interpolation on this (co)variance, but comes at the cost of some strict assumptions about the statistical properties of the sample. Elaborating and assessing these assumptions is one of the main challenges of geostatistics.

## Geostatistical Tools 地理统计学工具

Geostatistics is a wide field spanning a wide variety of disciplines, like geology, biology, hydrology or geomorphology. Each discipline defines their own set of tools, and apparently definitions, and progress is made until today.

It is not the objective of scikit-gstat to be a comprehensive collection of all available tools. The objective is more to offer some common and also more sophisticated tools for variogram analysis. Thus, when using scikit-gstat, you typically need another library for the actual application, like interpolation. In most cases that will be gstools. However, one can split geostatistics into three main fields, each of it with its own tools:

scikit-gstat的目标不是要成为所有可用工具的全面集合。它的目的更多的是为变异函数分析提供一些常用的和更复杂的工具。因此，在使用scikit-gstat时，你通常需要另一个库来实现实际应用中的其他功能，比如插值。在大多数情况下，gstools将可以胜任。然而，人们可以把地理统计学分成三个主要领域，每个领域都有自己的工具。

• variography: with the variogram being the main tool, the variography focuses on describing, visualizing and modelling covariance structures in space and time.

• 变差法：以变异函数为主要工具，变差法的重点是对空间和时间的协方差结构进行描述、可视化和建模。

• kriging: is a family of interpolation methods, that utilize a variogram to estimate the kriging weights as sketched above.

• kriging：包含一系列插值方法，利用变异函数来估计kriging的权重。

• geostatistical simulation: is aiming on generate random fields that fit a given set of observations or a pre-defined variogram or covariance function.

• 地质统计学模拟：旨在生成符合给定的观察值或预定的变异函数或协方差函数的随机场。