Glossary

Earthquakes and crustal deformation

Crustal deformation cycle:
The crustal loading cycle is often divided into four phases. This structure has been assembled from observations in many places, but a complete cycle in one location has never been observed:
preseismic : The most elusive to characterise. It implies that crustal deformation just prior to a large event is anomalous compared to the interseismic deformation.
coseismic :
postseismic :
interseismic :

Earthquake predictability :
time-independent hazard : Earthquakes are random (Poisson) in time, uses past locations of inferred events.
time-dependent hazard : Assumes earthquakes are the result of ruptures in the Earth's crust, induced by high levels of tectonic strain. This leads to theories such as characteristic earthquakes.
forecast : Assumes earthquakes are probabilistically predictable in the medium and short term with better accuracy due to their tendency to cluster in space and time. i.e. since since any small earthquake has a small probability of being a foreshock to a large event, the probability of the latter increases whenever the former is observed.
deterministic prediction : Seeks to make predictions high in accuracy and reliability in size, location and time.

Omori's Law:
Fusakichi Omori (1868-1923), States that aftershock frequency decreases by roughly the reciprocal of time after the main shock, given by a power law. This assumes that the crack propagation velocity tends to infinity. The modified Omori's Law assumes that the inertial limiting velocity is the speed of sound and introduces a small correction due to the finite rupture propagation duration.

Plastosphere: moldable part
Ductile lower lithosphere.

Schizosphere: broken part
Brittle upper lithosphere.

Orogenesis and wedge growth

Orogenesis :
The growth of mountain belts.

Pro- and retro-sides of a doubly-vergent wedge :
Doubly-vergent wedges grow over convergent subduction zones as accretionary wedges or mountain belts. The pro-side refers to the side on the wedge that overlies the subducting plate, whilst the retro-side refers to the side of the wedge that overlies the over-riding plate.

Self organisation and statistical mechanics

Autopoiesis:
The process by which systems maintain their organisation and regenerate their components in the course of their operation.

Algebraic decay vs. exponential decay of s:
Algebraic: s ^{- β}, where β is some decay exponent
Exponential: e^-s/s0, where s0 is a characteristic length-scale

Boltzmann distribution :

Competition and cooperation:
Types of interaction between two or more elements of a system. Competition refers to each element striving to maximise its use of a finite and / or non-renewable resource. Cooperation refers to the elements engaged in a mutually beneficial exchange.

Criticality :
At the critical point, a local distortion will propagate through the entire system. The effect decays geometrically rather than exponentially.

Detailed balance :
The transition rates in a Markov process between all pairs of states are equal.

Deterministic vs complex vs stochastic models :
Consider the case of a process controlled by a single variable x with variability dx ,
Deterministic : dx<<x , always
Complex : dx<<x , in some particular cases
Stochastic : dx<<x , never

Emergent properties :
Behaviour not explicable in terms of the individual, single elements. The appearance of qualitatively new phenomena on higher levels of a hierarchical system.

Ensembles :
Statistical Ensemble is a very large set of similar systems, considered all at once.
Canonical Ensemble is an ensemble of dynamically similar systems, each of which can share its energy with a large heat reservoir, or heat bath
Grand Canonical Ensemble generalises the Canonical emsemble by allowing systems to share particles as well as energy.

Ergodic :
1. Where a sequence or sizable sample is representative of the whole.
2. Relating to the probability that a state will never recur.
In an ergodic population, any single individual is representative of the entire population. The salient characteristics of this individual are essentially identical with any other member of the group.

Evolution:
A process of change in some direction.

Extensive vs. intensive property :
Proportional to the size of the system vs. independent of the size of the system. e.g. Entropy and Helmholtz free energy are extensive.

Finite-size scaling :
Properties of a system which vary as a function of the size of the system.

Instability:
The inability of a system to keep its state.

Lyapunov exponent :
The Lyapunov characteristic exponent gives the rate of exponential divergence from perturbed initial conditions.

Maximum entropy

Maximum entropy production
The tendency of a system which is in a steady state, that is held away from equilibrium by an external forcing, to produce entropy at the maximum rate possible.

Noise, 1/f :

Non-equilibrium:
System state with inflow of matter, energy and/or information causing it to stay away from its most probable state under the hypothetical condition of isolation.

Point process

Poisson process

Resilience:
Measure of a system's ability to remain within a domain of stability in response to fluctuations of the system by a disturbance, and the ability of the system to return to that stable domain having once left.

Self-organisation :
The ability of certain non-equilibrium systems to develop structures and patterns in the absence of external control or manipulation.

Self-organisated criticality (SOC):
When a system drives itself to criticality, unlike systems in thermodynamic equilibrium which must be tuned to their critical point. The ability of a system to evolve in such a way as to approach a critical point then maintain itself at that point.

Spinodal line :
Represents the classical limit between stability and meta-stability. A system that is on the limit of having only one potential minima.