Application of Information Theory to the Formation of Granitic Rocks

Abstract

Information theory, proposed originally by Shannon (1948), has been applied to the formation of granitoid rocks. Application of the theory allows the four main elements involved in granite formation viz.: partial melting (M), melt segregation (S), magma ascent (A) and emplacement (E) to be analysed qualitatively as a single, holistic process. The information content (chemical, isotopic and mineralogical) is contained in the magma, and the received message is the crystallised pluton. Noise added (e.g., by tectonism, weathering or sample collection) can lead to distortion or even irretrievable loss of information. Against this is the energy introduced into the system by the observer. Defining the message to be transmitted during granitoid formation as the initial composition of the partial melt (H _s ), the total information or entropy content (H′) preserved in an exposed granitic pluton can be expressed symbolically as:

$$ H' = \left[ {{H_S} - N - \Lambda } \right] + R + \delta $$

where N and Λ represent information loss by noise and weathering, counteracted by redundancy R and input from the investigators δ. The processes involved in granitoid formation, as identified by the application of information theory, are likely to be cyclic. By defining a total assembly time for a pluton, based on the rate of each key granite-forming process, information theory suggests that the rate-limiting step in pluton formation is the process of partial melting of the protolith — ultimately the rate of thermal diffusion necessary to accomplish this. Analysis suggests that total melt volume and melting rate in the source will control both the segregation mechanism and magma ascent rate.