This paper investigates the effects of spatial autocorrelation structures in low resolution data on downscaling without ground measurements or secondary data, as well as the potential of geostatistical downscaling. An advanced geostatistical downscaling scheme applied in this paper consists of two analytical steps: the estimation of the point-support spatial autocorrelation structure by variogram deconvolution and the application of area-to-point kriging. Point kriging of block data without variogram deconvolution is also applied for a comparison purpose. Experiments using two low resolution thematic maps derived from remote sensing data showing very different spatial patterns are carried out to discuss the objectives. From the experiments, it is demonstrated that the advanced geostatistical downscaling scheme can generate the downscaling results that well preserve overall patterns of original low resolution data and also satisfy the coherence property, regardless of spatial patterns in input low resolution data. Point kriging of block data can produce the downscaling result compatible to that by area-to-point kriging when the spatial continuity in block data is strong. If heterogeneous local variations are dominant in input block data, the treatment of the low resolution data as point data cannot generate the reliable downscaling result, and this simplification should not be applied to donwscaling.