Geological process understanding in space and time

Geological patterns in space and time are dependent on a number of processes that scale differently depending on whether or not they are linear or non-linear and on the involved constants (rate constants, diffusion constants). In order to predict geological processes and their occurrence in space and time one needs to understand at what spatio-temporal scales they are active. Quite often the slowest process is dominating the time scale of pattern evolution, therefore cross-over points in space and time are of special interest, where the dominance of one processes over another switches. When two processes are competing during the formation of a pattern, the cross-overs are critical points where the behavior of the system changes. Here we are exploring five important processes namely elastic wave propagation, fluid pressure diffusion, temperature diffusion, matter diffusion and reactions. While elastic wave propagation and reactions scale linearly, fluid pressure-, temperature-, and matter-diffusion have non-linear scaling behavior, which can be illustrated best in a log-log diagram of time versus space. In such a diagram the diffusion processes have a steeper slope than the two linear processes. Fluid pressure diffusion is 3 to 4 orders of magnitude faster than temperature diffusion, which itself is 3 orders of magnitude faster than matter diffusion (in a fluid). For example if a reactive fluid enters a fault, in a second the fluid pressure equilibrates on a m-scale, the temperature on a mm-scale and matter on the micro-meter scale. During fault slip that happens due to fluid overpressure, elastic wave propagation and fluid pressure diffusion act at the same time scale on micrometers but then diverge with fluid pressure diffusion equilibrating in seconds on the m-scale while elastic wave propagation reaches km-scale at the same time. We will discuss these scaling relations in details with examples from a variety of geological processes.