Over 270 single-hole [Guzman et al., 1996] and 44 cross-hole pneumatic injection tests [Illman et al., 1998; Illman, 1999] have been conducted at the Apache Leap Research Site (ALRS) near Superior, Arizona. In this paper, we describe a geostatistical analysis of the single-hole data and type-curve as well as numerical inverse interpretations of one cross-hole test, PP4. Our geostatistical analysis yields information about the spatial structure of air permeabilities measured on a nominal scale of 1 m, as well as of other variables such as fracture density. Our type-curve and inverse interpretations of cross-hole test PP4 yield information about pneumatic connections, directional air permeabilities, and airfilled porosities on scales ranging from a few meters to a few tens of meters. The numerical model can be applied simultaneously to pressure data from multiple borehole intervals (and multiple cross-hole tests), which amounts to "pneumatic tomography" of the rock. Our analyses suggest that (a) pneumatic pressure behavior of unsaturated fractured tuffs at the ALRS can be interpreted by treating the rock as a continuum on scales ranging from meters to tens of meters; (b) this continuum is representative primarily of interconnected fractures; (c) its pneumatic properties nevertheless correlate poorly with fracture density; and (d) air permeability exhibits multiscale random variations in space.