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[1] Power variograms of statistically isotropic or anisotropic fractal fields (common in earth science) are weighted integrals of variograms representing statistically homogeneous fields (modes) having mutually uncorrelated increments. Large-and small-scale cutoffs were previously assumed proportional to length scales of the sampling window and data support. We verify this assumption numerically for two-dimensional isotropic fractional Brownian motion (fBm). It was previously concluded semi-empirically that, for Hurst coefficient H = 0.25, the constant of proportionality is m = 1/3. We confirm this but find m to vary with mode type and H. We find that due to lack of ergodicity, sample fBm variograms generated on finite windows exhibit directional dependence and differ sharply between realizations. Many realizations are required to obtain an average sample variogram resembling the theoretical power model, especially for persistent fields. We propose generating fBm on finite windows using truncated power variograms and provide guidance for doing so effectively. Citation: Cintoli, S., S. P. Neuman, and V. Di Federico (2005), Generating and scaling fractional Brownian motion on finite domains, Geophys. Res. Lett., 32, L08404,

A gravity current originated by a power-law viscous fluid propagating in axisymmetric geometry on a horizontal rigid plane below a fluid of lesser density is examined. The intruding fluid is considered to have a pure power-law constitutive equation. The set of equations governing the flow is presented, under the assumption of buoyancy-viscous balance and negligible inertial forces. The conditions under which the above assumptions are valid are examined and a selfsimilar solution in terms of a nonlinear ordinary differential equation is derived for the release of a fixed volume of fluid. The space-time development of the gravity current is discussed for different flow behavior indexes.