Abstract
The fractal model proposed in Brenes (2013), Brenes & Alvarado (2013), Brenes (2014) y Brenes (2016) is now expanded to include the empirical log-logistical relationship proposed in Connor et al. (2003) for Soufriere volcano, providing it with a theoretical basis. Such a theoretical derivation suggests a thermo-dynamical view of the eruption process.References
ANGELL, C. A., 1995: Formation of glasses from liquids and biopolymers.- Science, 267: 1924-1935.
BRENES, J., 2013: Aplicación de la teoría de fragmentación/transporte secuencial a los depósitos de las erupciones 1723 y 1963-65 del Irazú, Costa Rica. Caso dispersión negativa.- Rev. Geol. Amér. Central, 48: 63-85.
BRENES, J., & ALVARADO, G. E., 2013: Aplicación de la teoría de fragmentación/transporte secuencial a los depósitos de las erupciones 1723 y 1963-65 del Irazú, Costa Rica. Caso dispersión positiva y modelo fractal.- Rev. Geol. Amér. Central, 48: 87-98.
BRENES, J., 2014: Aplicación del modelo de fractura fractal de Balankin al modelo fractal de actividad volcánica - Rev. Geol. Amér. Central, 50: 83-98
BRENES-ANDRE, J., 2016: Incorporación del modelo de Landau al modelo fractal de una erupción.- Rev. Geol. Amér. Central, 54: 125-142.
CONNOR, C. B., SPARKS, R. S. J., MASON, R. M., BONADONNA, C. & YOUNG, S. R., 2003.- Exploring links between physical and probabilistic models of volcanic eruptions: The Soufrie`re Hills Volcano, Montserrat.- Geophys R. Lett. 30, 1701, doi:10.1029/2003GL017384, 2003
CONNOR, C. B., MCBIRNEY, A. R. & FURLAN, C., 2006: What is the probability of explosive eruption at long-dormant volcano?.- En: MADER, H. M., COLES, S. G., CONNOR, C. B., CONNOR, L. J. (eds): Statistics in Volcanology. Special Publications of International Association of Volcanology and Chemistry of the Earth’s Interior 1 (IAVCEI).- Geological Soc. London, London: 39-46.
CORNELIUS, R. R. & VOIGHT, B., 1994-. Seismological aspects of the 1989-1990 eruption of Redoubt volcno, Alaska: The materials failure forecast method (FFM) with RSAM and SSAM seismic data.- J. Volcan. Geotherm. Res. 62; 469-498.
DENLINGER, R. P. & HOBLITT, R. P. 1999. Cyclic eruptive behaviour of silicic volcanoes.- Geology, 27: 459-462.
FOKIN, V. M., KALINIA, A. M. M. & FILIPOVICH, V. N. 1981- Nucleation in silicate glasses and effect of preliminary heat treatment on it.- J. Cryst. Growth, 52: 115
GUNN, L. S.; BLAKE, S.; JONES, M. C. & RYMER, H., 2014: Forecasting the duration of volcanic eruptions: an empirical probabilistic model.- Bull Volcanol 76:780, DOI 10.1007/s00445-013-0780-8
LU, Y-C., MAIY, Y-W. & XIEZ, H., 2005: A sudden drop of fractal dimension: a likely precursor of catastrophic failure in disordered media.- Philosophical Magazine Letters, 85: 33-40.
MELNIK, O. & SPARKS, R. S. J., 1999: Non-linear dynamics of lava dome extrusion.- Nature, 402: 37-41.
SHORE, J. D., HOLZER, M., & SETHNA, J. P., 1992: Logarithmically slow domain growth in nonrandom frustrated systems: Ising models with competing interactions. Phys. Rev. B, 46: 11376-404.
SPARKS, R. S. J., MURPHY, M. D., LEJEUNE, A. M., WATTS, R. B., BARCLAY & YOUNG, S. R., 2000: Control on the emplacement of the andesite dome of the Soufriere Hills Volcano, Monserrat, by degassing-induced crystallization.- Tera Nova, 12: 14-20.
VARLEY, N., JOHNSON, J., RUIZ, M., REYES, G. & MARTIN, K., 2006: Applying Statistical Analysis to Understanding the Dynamics of Volcanic Explosions.- En MADER, H. M., COLES, S. G., CONNOR, C. B. & CONNOR, L. J. (eds): Statistics in Volcanology. Special Publications of International Association of Volcanology and Chemistry of the Earth’s Interior 1 (IAVCEI). Geol. Soc. London, London: 57-76.
VOIGHT, B., 1988: A method for prediction of volcanic eruptions.- Nature, 332: 125-130
VOIGHT, B., 1989: A relation to describe rate-dependent material failure.- Science, 243: 200-203
WEIBULL, W., 1951: A statistical distribution of wide applicability.- J. Appl. Mech, 18: 293-297