Self-Organisation and Dissipation in Real and Synthetic Earthquake Populations
Al-Kindy, Fahad H Y
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Energy released from the Earth’s crust in the form of earthquakes commonly follows a powerlaw gamma type probability distribution. This spontaneous organisation is in apparent contradiction to the second law of thermodynamics that states that a system should naturally evolve to a state of maximum disorder or entropy. However, developments in the field of modern thermodynamics suggest that some systems can undergo organisation locally, at the expense of increasing disorganisation (or entropy) globally through a process of entropy production. The primary aim of this thesis is to investigate self-organisation in the Earth’s seismogenic lithosphere as a driven, far-from-equilibrium, self-organising ‘dissipative structure’ in a very near critical steady-state and the underlying general mechanisms involved. The secondary aim is to test in more detail the applicability of the Bak, Tang and Wiesenfeld (BTW) model of Self-Organised Criticality (SOC) in describing Earth’s seismicity. This is done by: 1. Mathematical derivation of analytical solutions for system energy and entropy using the tools of equilibrium statistical mechanics; 2. The study of conservative and non-conservative versions of the BTW numerical model and 3. Analysis of temporal and spatial properties of earthquake data from the Harvard Centroid Moment Tensor catalogue and the Global Heat Flow Database. The modified gamma distribution predicts analytically that entropy S is related to the energy probability distribution scaling exponent B and the expectation of the logarithm of seismic energy hlnEi in the form of the gamma entropy equation S » BhlnEi. This solution is con- firmed for both numerical model results and real earthquake data. Phase diagrams of B vs. hlnEi suggest that the universality in B need not be maintained for a system to remain critical provided there is a corresponding change in hlnEi and S. The power-law systems examined are different from equilibrium systems since the critical points do not occur at global maximum entropy. For the dissipative BTW model at a steady-state, the externally radiated energy follows out-of-equilibrium power-law gamma type statistics, but, the internal energy has two icharacteristics that are indicative of equilibrium systems; a Gaussian type energy probability distribution and a Brownian noise power-spectrum for the internal energy fluctuations. This suggests an observer dependency in assessing criticality. The internal and external entropies calculated for the model are negatively correlated suggesting that driven systems self-organise at the expense of increasing entropy globally through a process of dissipation. A power-law dependency of mean radiated energy hEi on dissipation 1¡® is confirmed for a locally driven dissipative system in the form hEi » (1¡®)¡0:975. The BTW model shows spatial heterogeneity whilst maintaining universality in contradiction to previous assumptions. The quantitative analysis of real data reveals that earthquakes are more predictable spatially then temporally. Regionalisation using the Flinn-Engdahl classification shows that mid-ocean ridges are more organised (lower entropy) than subduction zones. A regional study of three different scaling exponents suggests that universality in earthquake scaling is violated, in contradiction to the original model of SOC. A model of self-organised sub-criticality (SOSC) is proposed as an alternative model for Earth seismicity. Overall, the results suggest that the tools of equilibrium thermodynamics can be applied to a steady-state far-from-equilibrium system such as the Earth’s seismogenic lithosphere, and that the resulting self-organisation occurs at the expense of maximising dissipation and hence entropy production.