Multifaceted nature of hydrogeologic scaling and its interpretation

Geology is ubiquitously heterogeneous, exhibiting both discrete and continuous spatial variations on a multiplicity of scales. It is therefore natural to expect that hydrogeologic and other geophysical variables would do likewise. We present evidence that hydrogeologic variables exhibit isotropic and directional dependencies on scales of measurement (data support), observation (extent of phenomena such as a dispersing plume), sampling window (domain of investigation), spatial correlation (structural coherence), and spatial resolution (descriptive detail). We then show that it is possible to interpret these multiple scale dependencies within a unified theoretical framework. This and similar theoretical frameworks may be applicable to a wider range of geophysical scale issues.