Abstract
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.
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References
Baloga S (1987) Lava flows as kinematic waves. J Geophys Res 92:9271–9279
Baloga S, Pieri D (1986) Time-dependent profiles of lava flows. J Geophys Res 91:9543–9552
Baloga S, Taylor GJ, Bruno BC (1992) The character of lava flow margins. Lunar Planet Sci XXIII:57–58
Bruno BC, Taylor GJ, Rowland SK, Lucey PG, Self S (1992) Lava flows are fractals. Geophys Res Lett 19:305–308
Campbell DK (1987) Nonlinear science. Los Alamos Science 15:218–262
Cas RAE, Wright JV (1987) Volcanic successions. Allen & Unwin, London, 528 pp
Crisp J, Baloga S (1990) A method for estimating eruption rates of planetary lava flows. Icarus 85:512–515
Eichelberger JC (1975) Origin of andesite and dacite: Evidence of mixing at Glass Mountain in California and at other circum-Pacific volcanoes. Geol Sci Am Bull 86:1381–1391
Fink JH (1980) Surface folding and viscosity of rhyolite flows. Geology 8:250–254
Fink JH, Fletcher RC (1978) Ropy pahoehoe: Surface folding of a viscous fluid. J Volcanol Geotherm Res 4:151–170
Garcia L (1991) The fractal explorer. Dynamic Press, Santa Cruz 108 pp
Gudmundsson A, Oskarsson N, Gronvold K, Saemundsson K, Sigurdsson O, Stefansson R, Gislason SR, Einarsson P, Brandsdottir B, Larsen G, Johannesson H, Thordarson Th (1991) The 1991 eruption of Hekla, Iceland. Bull Volcanol 54:238–246
Guest JE, Sanchez J (1969) A large dacitic lava flow in northern Chile. Bull Volcanol 33:778–790
Hayward J, Orford JD, Whalley WB (1989) Three implementations of tractal analysis of particle outlines. Comp & Geosci 15:199–207
Hulme G (1974) The interpretation of lava flow morphology. Geophys J R Astron Soc 39:361–383
Hulme G, Fielder G (1977) Effusion rates and rheology of lunar lavas. Philos Trans R Soc London A 285:227–234
Kilburn CRJ (1981) Pahoehoe and aa lavas: A discussion and continuation of the model of Peterson and Tilling. J Volcanol Geotherm Res 11:373–382
Kilburn CRJ (1990) Surfaces of aa flow fields on Mount Etna, Sicily: Morphology, rheology, crystallization, and scaling phenomena. In: Lava flows and domes (Fink JH, ed), Springer Verlag, Berlin: 129–156
Longley PA, Batty M (1989) Fractal measurement and line generalization. Comp & Geosci 15:167–183
Lopes RMC, Kilburn CRJ (1990) Emplacement of lava flow fields: Applications of terrestrial studies to Alba Patera, Mars. J Geophys Res 95:14383–14397
Mandelbrot BB (1967) How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science 156:636–638
Mandelbrot BB (1983) The fractal geometry of nature. Freeman, San Francisco, 468 pp
Mueller J-C (1987) Fractal and automated line generalization. Cartographic J 24:27–34
Peterson DW, Tilling RI (1980) Transition of basaltic lava from pahoehoe to aa, kilauea volcano, Hawaii: field observations and key factors. J Volcanol Geotherm Res 7:271–293
Richardson LF (1961) The problem of contiguity: an appendix to statistics of deadly quarrels. General Systems Yearbook 6:139–187
Rowland SK, Walker GPL (1990) Pahoehoe and aa in Hawaii: volumetric flow rate controls the lava structure. Bull Volcanol 52:615–628
Shaw HR (1969) Rheology of basalt in the melting range. J Petrology 10:510–535
Shaw HR, Swanson DA (1970) Eruption and flow rates of flood basalts. In: Proceedings of the Second Columbia River Basalt Symposium (Gilmour EH, Stradling D eds), Eastern Washington State College Press, Cheney, 271–299
Shaw HR, Wright TL, Peck DL, Okamura R (1968) The viscosity of basaltic magma: An analysis of field measurements in Makaopuhi lava lake. Am J Sci 266:225–264
Smith AL, Carmichael ISE (1968) Quaternary lavas from the Southern Cascades, Western USA. Contrib Min Petrol 19:212–238
Thorpe RS, Francis PW, O'Callaghan L (1984) Relative roles of source composition, fractional crystallization and crustal contamination in the petrogenesis of Andean volcanic rocks. Philos Trans R Soc London A 310:675–692
Turcotte DL (1991) Fractals in geology: What are they and what are they good for? Geol Sci Am Today 1, 1:3–4
Ulrich GE, Bailey NG (1987) Geologic Map of SP Mountain part of San Francisco Volcanic Field, North-Central Arizona. USGS Misc Field Map MF-1956
Wadge G, Lopes RMC (1991) The lobes of lava flows on Earth and Olympus Mons, Mars. Bull Volcanol 54:10–24
Walker GPL (1973) Lengths of lava flows. Philos Trans R Soc London A 274:107–118
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Bruno, B.C., Taylor, G.J., Rowland, S.K. et al. Quantifying the effect of rheology on lava-flow margins using fractal geometry. Bull Volcanol 56, 193–206 (1994). https://doi.org/10.1007/BF00279604
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DOI: https://doi.org/10.1007/BF00279604