Quantifying the effect of rheology on lava-flow margins using fractal geometry

This study aims at quantifying the effect of rheology on plan-view shapes of lava flows using fractal geometry. Plan-view shapes of lava flows are important because they reflect the processes governing flow emplacement and may provide insight into lava-flow rheology and dynamics. In our earlier investigation (Bruno et al. 1992), we reported that flow margins of basalts are fractal, having a characteristic shape regardless of scale. We also found we could use fractal dimension (D, a parameter which quantifies flow-margin convolution) to distinguish between the two endmember types of basalts: a a (D: 1.05–1.09) and pahoehoe (D: 1.13–1.23). In this work, we confirm those earlier results for basalts based on a larger database and over a wider range of scale (0.125 m–2.4 km). Additionally, we analyze ten silicic flows (SiO₂: 52–74%) over a similar scale range (10 m–4.5 km). We note that silicic flows tend to exhibit scale-dependent, or non-fractal, behavior. We attribute this breakdown of fractal behavior at increased silica contents to the suppression of small-scale features in the flow margin, due to the higher viscosities and yield strengths of silicic flows. These results suggest we can use the fractal properties of flow margins as a remote-sensing tool to distinguish flow types. Our evaluation of the nonlinear aspects of flow dynamics indicates a tendency toward fractal behavior for basaltic lavas whose flow is controlled by internal fluid dynamic processes. For silicic flows, or basaltic flows whose flow is controlled by steep slopes, our evaluation indicates non-fractal behavior, consistent with our observations.