h scatter plot
A h scattergram (engl. H-scattergram or h-scatterplot ) is a scatter plot , which is primarily in the geostatistics is applied to the spatial variability of a position-dependent ( geo-referenced display) measured variable.
meaning
The importance of the h-scatter diagrams results from their property of clearly showing extreme deviations of individual pairs of measured values with regard to their spatial variability.
Their comparison also results in the directional dependency of the similarity or dissimilarity of measured values, that is to say the distinction between an isotropic or anisotropic behavior of the measured variable.
Via the squared, orthogonal distances of y = x, they are also the basis of an experimental semivariogram in which each h-scatter diagram is represented by two values.
description
It relates a measured value z at the point x i with a measured value at the point x i + h , where h is a freely selected distance or vector. Both measured values are entered in a Cartesian coordinate system, with z (x i ) on the x-axis and z (x i + h) on the y-axis. If this distance is zero or if the values are identical despite the distance, then all points lie on the diagonal y = x , since z (x i ) = z (x i + h) applies. If this is not the case, the result is a point cloud, the size or non-uniformity of which generally increases with increasing h , so the points are more and more poorly clustered. At the same time, the number of points generally decreases, since from a certain size of h , fewer and fewer measured values are sufficiently far apart. Since only in the case of exact measuring grids with constant measuring intervals between the individual measuring points also a larger number of them have the same distance, an interval or a class Δh is used instead of a discrete value h in the case of uneven measuring networks . As a rule of thumb , at least 30 to 50 value pairs should be within the class Δh . In order to take into account the range of the data, distances h are used that are at most as large as half the smallest extent of the investigation area.
adoption
The following assumption flows into the h-scatter diagram:
- z (x i ) - z (x i + h) = d (h)
ie the difference between the measured values does not depend on the location. It does not matter whether the distance between x 1 and x 2 or that of x 4 and x 5 equals h or Δh .
Cross h scatter plot
A cross h scatter diagram is a scatter diagram that compares two different attributes a and b with one another, e.g. B. the concentrations of various substances. It is formed analogously to the h scatter diagram, but with
- z a (x i ) and z b (x i + h) .
For h = 0 it is a common scatter plot between two data sets.