This Mathematica-Demo considers a well studied simple example of two-dimensional random field, namely an AR1XAR1 field. Simulating a such 2D process is quite fast, once a value for the underlying range-parameter is chosen. It is well known that the classic Maximum likelihood (ML) principle can be easily implemented here, even for large data size, by using the known expression of the inverse of the correlation matrix of an 1D AR(1) process and its determinant, and by exploiting the properties of the Kronecker product. It can be verified here the calculation of the profile log-likelihood is very fast even when computed over a fine grid of range-values. This demonstration studies the "energy variance matching" alternative to ML (GE-EV method, which is the "no-noise" version of CGEM-EV) which was already implemented in a series of Mathematica-Demos for different contexts in the 1D case (Matérn autocorrelations and the powered-exponential autocorrelation). Of course (since GE-EV requires even less computations than ML) the implementation of GE-EV is also very fast here. As is was already observed for other (isotropic) random fields in an extensive simulation study published in Spatial Statistics, ML and GE-EV methods give quite close results, except for the settings with ''large'' range. Anyway, in these "extreme" settings, the proximity of the two methods is restored provided we only focus on the estimation of the product "standard-deviation X inverse-range", which plays here the role of a "microergodic coefficient", as it was the case for "the diffusion coefficient" specific to each of the above-mentioned 1D cases.