The heterogenous conductivity field is characterized by the following set of statistical parameters: mean, correlation scales (x-, y-, z-directions), and variance. Also important for generating the random field is the Seed value, directions of geometric anisotropy, and the Nugget effect. (see below)
LambdaX - Correlation scale in the x-direction (left-to-right, or west-to-east).
LambdaY - Correlation scale in the y-direction (north-to-south).
LambdaZ - Correlation scale in the z-direction (vertical, or into the earth).
Correlation scale = a measure of the spatial distance across which the aquifer properties (e.g., conductivity) are supposed to be correlated. This parameter can be different in all three directions, making the aquifer anisotropic. However, in most cases, the horizontal correlations scales are assumed to be constant. Vertical correlation scale is generally smaller than horizontal correlation scales. Correlation scales give an idea about the "texture" or "pattern" of variability.
Seed - A random number for initiating the simulation process. The seed input affects the random drawing of a value from the probability distribution.
Theoretical variance - a measure of how far the set of random numbers (e.g., hydraulic conductivity values) are spread out from their mean (or average) value. A higher variance means higher variability of aquifer properties and vice versa.
Theoretical mean - Average value calculated from the theoritical distribution.
Angle (Rotate around Z) - Angle of rotation about of the geometric anisotropy the z-axis, if LambdaZ is not oriented parallel to the +z-axis
Angle (Rotate around X) - Angle of rotation of the geometric anisotropy about the x-axis, if LambdaX is not oriented parallel to the +x-axis
Angle (Rotate around Y) - Angle of rotation of the geometric anisotropy about the y-axis, if LambdaY is not oriented parallel to the +y-axis
Nugget - Random noise that may represent small-scale (sub-cell) variability, "measurement error", sampling variation, etc. Formally, it is the difference between a sampled value and a potential repeat sample at the same location.