Multifractal characterization of airborne geophysical data at the Oak Ridge facility

Abstract

Scaling analyses on geophysical measurements of electrical conductivity, gamma radiation, and magnetic fields, at the Oak Ridge Reservation were conducted. The electrical conductivity and magnetic data exhibited multifractality in the north-south and eastwest directions. The radiation data were observed to be non-scaling; a variogram with a sill was found to be more appropriate. The scaling of the EC and magnetic was generally within a range smaller than the maximum distance selected, as periodicity dominated at the larger distances. The electrical conductivity had anisotropy in the scaling of their variograms. But the magnetic data appear to have an isotropic scaling. The underlying statistics of the fields were near Gaussian for the electrical conductivity, but essentially Gaussian for the magnetic data. In environmental hydrogeology, knowledge of the spatial distribution of the intrinsic permeability, K, is very helpful in understanding the transport and spreading of contaminant plumes. Our previous studies have shown that the subsurface permeability, K, is multifractal. Detailed measurement of K is costly. Hence, large data sets of value collected both on a fine scale and over large distances are rare. In this study, we hypothesize that geophysical data could be used indirectly as a surrogate measurement for K, for obtaining statistical information on scale limited K data, and perhaps, directly at sites where K and electrical conductivity are correlated.

Scaling and multifractal fields in the solid earth and topography

“…15 shows the corresponding B fields. See also Tennekoon et al (2005) for scaling analyses of geomagnetic fields and Fedi (2003) for multifractal analysis of borehole susceptibilities.…”

Multifractal characteristics of the jet turbulent intensity depending on the outfall nozzle geometry

“…These measures are useful for describing the experimental observations, as reported by Frisch and Parisi (1985), Meneveau and Sreenivasan (1987), and Puthenveettil et al (2005). Multifractal is also used to characterize the wetland topography (Tchiguirinskaia et al 2000), airborne geophysical data (Tennekoon et al 2005), and to generate complex hydrologic spatiotemporal datasets (Cortis et al 2009(Cortis et al , 2010. For river networks, Seo et al (2014) examined the peak flow distribution on stochastic network models.…”

Characterization of Pore Water Flow in 3‐D Heterogeneous Permeability Fields

“…However, it has been increasingly recognized that geophysical fields are better represented by multifractals, which are characterized by an infinite hierarchy of exponents (Falconer, ; Frisch & Parisi, ). Multifractality has been observed in numerous geophysical fields, such as turbulence (Anselmet et al, ), hydrologic basins (Veneziano & Iacobellis, ), rainfall (Gupta & Waymire, ), and magnetic susceptibility and K40 emissions (Tennekoon et al, ); nevertheless, it has not been considered in investigating local‐scale deformation of pore‐water flow in heterogeneous media. For our investigation, we select the Universal Multifractal (UM) model to generate multifractals, which captures both Gaussian and non‐Gaussian statistics (Pecknold et al, ; Schertzer & Lovejoy, ).…”