Solid Earth Discussions www.solid-earth-discuss.net 1869-9537 2 1 2010 10.5194/sed-2-43-2010 http://www.solid-earth-discuss.net/2/43/2010/ http://www.solid-earth-discuss.net/2/43/2010/sed-2-43-2010.html http://www.solid-earth-discuss.net/2/43/2010/sed-2-43-2010.pdf 43 67 2010-03-04 The stochastic quantization method and its application to the numerical simulation of volcanic conduit dynamics under random conditions E. Peruzzo e.peruzzo@sns.it M. Barsanti F. Flandoli P. Papale Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126, Pisa, Italy Dipartimento di Matematica Applicata, Università di Pisa, Via Buonarroti 1c, 56127, Pisa, Italy Istituto Nazionale di Geofisica e Vulcanologia, Sezione di Pisa, Via della Faggiola 32, 56126, Pisa, Italy Invited contribution by E. Peruzzo, one of the EGU Young Scientists Outstanding Poster Paper (YSOPP) Award winners 2009. Stochastic Quantization (SQ) is a method for the approximation of a continuous probability distribution with a discrete one. The proposal made in this paper is to apply this technique to reduce the number of numerical simulations for systems with uncertain inputs, when estimates of the output distribution are needed. This question is relevant in volcanology, where realistic simulations are very expensive and uncertainty is always present. We show the results of a benchmark test based on a one-dimensional steady model of magma flow in a volcanic conduit. Bennett, W. R.: Spectra of quantized signals, Bell Syst. Tech. J., 27, 446–472, 1948. Graf, S. and Luschgy, H.: Foundations of quantization for probability distributions, Springer, Berlin-Heidelberg, 2000. Gray, R. M. and Neuhoff, D. L.: Quantization, IEEE T. Inform. Theory, 44(6), 2325–2383, 1998. Neri, A., Esposti Ongaro, T., Menconi, G., De' Michieli Vitturi, M., Cavazzoni, C., Erbacci, G. and Baxter, P. J.: 4-D simulation of explosive eruption dynamics at Vesuvius, Geophys. Res. Lett., 34, L04309, doi:10.1029/2006GL028597, 2007. Oliver, B. M., Pierce, J. and Shannon, C. E.: The philosophy of PCM, P. IRE, 36, 1324–1331, 1948. Panter, P. F. and Dite, W.: Quantizing distortion in pulse-count modulation with nonuniform spacing of levels, P. IRE, 39, 44–48, 1951. Papale, P., Neri, A. and Macedonio, G.: The role of magma composition and water content in explosive eruptions. 1 Conduit ascent dynamics, J. Volcanol. Geoth. Res., 87, 75–93, 1998. Papale, P.: Dynamics of magma flow in volcanic conduits with variable fragmentation efficiency and nonequilibrium pumice degassing, J. Geophys. Res., 106, 11043–11065, 2001. Sparks, R. S. J.: Forecasting volcanic eruptions, Earth Planet. Sc. Lett., 210, 1–15, 2003. Todesco, M., Neri, A., Esposti Ongaro, T., Papale, P., Macedonio, G., Santacroce, R. and Longo, A.: Pyroclastic flow hazard assessment at Vesuvius (Italy) by using numerical modelling: I. Large-scale dynamics, B. Volcanol., 64, 155–177, 2002. Valentine, G. A. and Wohletz, K. H.: Numerical models of Plinian eruption columns and pyroclastic flows, J. Geophys. Res, 94, 1867–1887, 1989. Wand, M. P. and Jones, M. C.: Kernel smoothing, Chapman and Hall, Boca Raton, 1995. Wilson, L., Sparks, R. S. J. and Walker, G. P. L.: Explosive volcanic eruptions: IV. The control of magma properties and conduit geometry on eruption column behaviour, Geophys. J. Roy. Astr. S., 63, 117–148, 1980.