Quantifying magma mixing with the Shannon entropy: Application to simulations and experiments

Author(s)

Perugini, D. ^[1] ; De Campos, C. P. ^[2] ; Petrelli, M. ^[1] ; Morgavi, D. ^[1] ; Vetere, F. P. ^[1] ; Dingwell, D. B. ^[2]

Affiliation

^[1] Univ Perugia, Dept Phys & Geol, I-06100 Perugia - Italy

^[2] Univ Munich, Dept Earth & Environm Sci, D-80333 Munich - Germany

• Document type: Journal article
• Source: LITHOS; v. 236, p. 299-310, NOV 2015.
• Web of Science Citations: 5

Abstract

We introduce a new quantity to petrology, the Shannon entropy, as a tool for quantifying mixing as well as the rate of production of hybrid compositions in the mixing system. The Shannon entropy approach is applied to time series numerical simulations and high-temperature experiments performed with natural melts. We note that in both cases the Shannon entropy increases linearly during the initial stages of mixing and then saturates toward constant values. Furthermore, chemical elements with different mobilities display different rates of increase of the Shannon entropy. This indicates that the hybrid composition for the different elements is attained at different times generating a wide range of spatio-compositional domains which further increase the apparent complexity of the mixing process. Results from the application of the Shannon entropy analysis are compared with the concept of Relaxation of Concentration Variance (RCV), a measure recently introduced in petrology to quantify chemical exchanges during magma mixing. We derive a linear expression relating the change of concentration variance during mixing and the Shannon entropy. We show that the combined use of Shannon entropy and RCV provides the most complete information about the space and time complexity of magma mixing. As a consequence, detailed information about this fundamental petrogenetic and volcanic process can be gathered. In particular, the Shannon entropy can be used as complement to the RCV method to quantify the mobility of chemical elements in magma mixing systems, to obtain information about the rate of production of compositional heterogeneities, and to derive empirical relationships linking the rate of chemical exchanges between interacting magmas and mixing time. (C) 2015 Elsevier B.V. All rights reserved. (AU)

• FAPESP's process: 09/50493-8 - Crustal and lithospheric mantle models under the Paraná and Chaco-Paraná basins by merging satellite gravity gradiometry, terrestrial gravimetry and geomagnetic and electromagnetic soundings
• Grantee: Icaro Vitorello
• Support type: Research Projects - Thematic Grants
• FAPESP's process: 15/11850-0 - 8th Hutton Symposium on Granites and related rocks
• Grantee: Valdecir de Assis Janasi
• Support type: Research Grants - Organization of Scientific Meeting