ArcGIS Tutorial: Important Concepts for geostatistical simulations

　　Simulation Concepts

In a broad sense, simulations refer to the process of replicating reality using models. In Geostatistical, a simulation is an implementation of a random function (surface) that has the same geostatistical elements (measured using mean, variance, and Semivariogram) as the sample data that generated the simulation. More specifically, Gaussian geostatistical simulations (GGS) apply to continuous data and assume that the transformation of data or data has a normal (Gaussian) distribution. The main assumption that GGS relies on is that the data is static-mean, variance, and spatial structure (SEMIVARIOGRAM) does not change in the data space domain. Another major assumption of GGS is that the stochastic function of modeling is a multivariate Gaussian random function.

Compared with kriging, GGS has advantages. Because Kriging is based on the local mean of the data, it produces a smooth output. On the other hand, the representation of local variability generated by GGS is better because GGS adds the missing local variability in kriging back to its resulting surface. For the variability in the predicted values added to a specific location by the GGS implementation, the average value is zero, so that many GGS implementations tend to have an average of kriging predictions. This concept is described. Various implementations are represented as a set of stacked output layers, and the value of a particular coordinate position is subjected to a Gaussian distribution whose mean is equal to the kriging estimate at that location, and the degree of diffusion is given by the kriging variance at that location.

　　

The Extract value to table tool can be used to generate data for a graphic in, and it is useful for post-processing of output generated by GGS.

The use of GGS is increasingly presenting a trend in geostatistical practice, which is not the pursuit of the best unbiased predictions for each of the non-sampled locations (as demonstrated by kriging), but rather a special description of the uncertainty of decision analysis and risk analysis, which is more appropriate for presenting the global trends in the data ( Deutsch and Journel 1998, Goovaerts 1997). Simulations also overcome the problem of conditional deviations in kriging estimates (high-value area predictions are usually low, while low-value areas are typically high).

For the spatial distribution of the properties studied, geostatistical simulations can generate multiple representations of the same probability. The uncertainties of the non-sampled locations can be measured based on these representations, which are spatially selected together, rather than being selected individually (as measured by kriging variance). In addition, the kriging variance is usually independent of the data value and is usually not used as a measure of the estimated precision. On the other hand, you can use multiple simulation implementations (the implementation is built with a simple kriging model with a normal distribution of input data, that is, the data is normally distributed or has been transformed with a normal score transformation or other type of transformation) to estimate the estimated accuracy by constructing the distribution for the estimated value of the sample location. The distribution of these uncertainties is critical for risk assessment and decision analysis using estimated data values.

GGS assumes that the data is normally distributed, but in practice, this is rarely the case. Perform a normal score transformation on the data so that the data conforms to the standard normal distribution (mean = 0, variance = 1). The normal distribution data is then simulated and the result is reversed to obtain the analog output in the original unit. When using simple kriging for normal distribution data, the kriging estimates and variances provided by this kriging fully define the conditional distribution for each location in the study area. This allows you to draw a mock implementation of a random function (unknown sample surface) with only the two parameters of each location, which is why GGs is based on a simple kriging model and a normal distribution data.

The Gaussian geostatistical simulation tool supports two types of simulations:

1. The conditional simulation follows the data value (unless the measurement error is included in the kriging model). Because the simulation generates values at the Grid cell Center, if this value does not correspond exactly to the location of the sample point, the measured value of the sample location may be different from the analog value. The conditional simulation will also replicate the mean, variance, and semivariogram of the data in the average mode (that is, on many implementations averaging). The simulated surface looks much like the kriging prediction map, but it will show more spatial variability.

2. The non-conditional simulation does not follow the data values, but copies the mean, variance, and semivariogram of the data in an average way. The simulated surface shows a spatial structure similar to the gold map, but high and low values are not necessarily present in the input data where there are high or low values.

ArcGIS Tutorial: Important Concepts for geostatistical simulations