SPECSIM2: a program for spectral simulation of anisotropic two-dimensional random fields

Abstract

The authors describe the structure and implementation of SPECSIM2, an ANSI Fortran-77 program for simulating anisotropic two-dimensional random fields via a spectral approach. This new program overcomes the limitation of the previously published version (Pardo-Igúzquiza and Chica-Olmo, Comput. Geosci. 20 (4) (1994) 597), which was confined to the direct generation of isotropic fields with any anisotropy imposed by a subsequent co-ordinate transformation. The diagonal symmetry of the two-dimensional covariance function with respect to the origin, i.e. C(x,y)=C(−x,−y) and C(x,−y)=C(−x,y), implies that its Fourier transform (i.e. the spectral density) is real (the imaginary part vanishes). This observation leads to a straightforward direct simulation of anisotropic fields by the spectral method. Examples are given to demonstrate the performance of the method using semi-variograms with or without nugget effects and with simple or nested structures, as well random fields with several structures that have different anisotropy angles.