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优化的插值法与固定地点样品数据点吗?

我想找到一个优化的空间插值方法,处理固定地点样本数据点。说如果我有固定地点采样站点和每天收集数据,然后使用这些数据来创建插值的表面。有方法,预处理这些采样站点之间的空间关系,然后将这种空间关系集成到插值方法加快整个插补过程?我用谷歌搜索了一些信息,但找不到我想要的。谁能让我在正确的方向吗?谢谢。

回答

一个好地方是地质统计学[1]。这是统计学的一个分支关注空间或时空数据集。在其早期,地质统计学也称为区域化变量理论。地质统计学最初是由[乔治Matheron][2],一名法国数学家和地理学家——尽管当我第一次听到他在1980年代他被形容为一个采矿工程师。Matheron开发地质统计学找到一个更好的方法来更准确地确定矿石储量。他的其他目的是试图确定矿石储量(我的水平精度。e x盎司黄金的信心y %)。自1960年代初始开发地质统计学的矿石储量的开采,这项技术已经被用于其他领域有一个数据样本之间的空间联系,这样的森林,污染周围的污染金属冶炼厂、土壤科学、地球化学等的一个关键地质统计学的工具是(方差图)[3]。变差函数是用于确定样本的距离可以看作是相互独立的。变异函数的数学可以看起来有些混乱,但变异函数可以简单地来解释。考虑一行100等距的样本点,说1米。 - Determine the variance for all data points 1 m apart, i.e 1 & 2, 2 & 3, ... 19 & 20 ... - Next calculate the variance for all points 2 m apart: 1 & 3, 3 & 5, ... 17 & 19, also 2 & 4, 4 & 6, ... 18 & 20 ... - Then find the variance for samples 4 m apart and then 5 m apart and 10 m, 20 m, 25 m and 50 m The sample distances must be factors of the total distance. You can find the variance for samples 3 m apart because 3 doesn't divide into 100 evenly, but if there were only 99 samples then things are totally different. The distance between samples is known as the lag distance. On a plot of variance versus lag distance, for low lag values the curve will rise. Where the curve flatten out is the distance at which samples can be regarded as being independent of each other. The variogram has its roots in the [correlation diagrams][4]. For data on a 2D grid, it is prudent to obtain a suite of variograms along the directions north-south, east-west, northwest-southeast and northeast-southwest to obtain an initial variance rosette. Any trend in the data will be seen from this and a better variogram orientation can then be tried. Where the distance between samples is strictly not uniform, but within accepted tolerances, adjustments will need to be made to the data. Also if data is clustered within areas, the data will need to be declustered first. When data points are being considered it is common for a search ellipse to be used and for the search ellipse to be orientated. For example, is the data set is soil contamination samples around a metal smelter, or seed dispersal from trees, the search ellipse would be orientated so the major axis would be aligned with the direction of the prevailing winds. Because of the amount of calculations involved and the size of some data set, particularly metal grades in geological ore bodies, computers are heavily involved with geostatistical analyses. An initial reference on geostatistics is [Isobel Clark, 1979, Practical Geostatistics, Applied Science Publishers][5] If you want to estimate a value between sample points then either some form of weighting of samples will need to be used. Within geostatistics, [kriging][6] is usually used, but there are many forms of kriging, just to name a few: ordinary, disjunctive, log-normal, indicator. What some people also do is to use other forms of weighting such as [inverse distance][7] squared, or [inverse distance][8] to another power, usually between 1.5 and 3, but inverse distance squared is the more common of these. The results from kriging and inverse distance squared are then compared. The two techniques will rarely give the same results, but the results should be similar. [1]: https://en.wikipedia.org/wiki/Geostatistics [2]: http://en.wikipedia.org/wiki/Georges_Matheron [3]: https://en.wikipedia.org/wiki/Variogram [4]: http://www.aaec.ttu.edu/faculty/eelam/3401/CourseMaterials/Notes_Fall07/Notes_Regr1_Elam08-31-07.pdf [5]: http://www.kriging.com/pg1979_download.html [6]: http://www.kriging.com/whatiskriging.html [7]: https://en.wikipedia.org/wiki/Inverse_distance_weighting [8]: https://www.rockware.com/rockworks/help/solid_model_inverse.htm

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