A Description of Seismicity Based on Non-extensive Statistical Physics: A Review

A Non-Extensive Statistical Mechanics View on Easter Island Seamounts Volume Distribution

“…To have an estimation of V o we select the volume where the power law approximation of P(>V) takes the value P(>V) = 1 leading to V = V q ( 2−q q−1 ) 3 2 . We observe that β < 1 leading to 1.5 < q, in agreement with previous published results on earth physics processes in a broad range of scales from laboratory up to geodynamic one [16,17]. For V q = 24 km 3 as estimated for the fitting of Q-exponential (see Figure 2) we lead to V o = 20 km 3 which is similar with the cut off used in [40].…”

“…The distribution shows power law features as other distributions on Earth sciences mentioned in [11,16,17,[40][41][42][43][44] with q values in the range 1.5 < q < 2. Since Equation (7a) can fit the ESC dataset well with Q ≈ 2.20 leading to a q = 1.54, we lead to a q-value which is a quantitative measure of the scale of the spatial interactions in ESC seamount system.…”

“…This approach applied in a broad selection of problems (see [15][16][17] and references there in) where crossover statistics appears (i.e., a change of Q parameter to a different one). In this frame a crossover formulation of non-extensive statistical physics introduced where two entropic indices introduced to describe a crossover to another type of behavior at large values of the investigated physical parameter, in our case the seamount volume V. In this case we should have [39] …”

“…Non-extensive statistical physics (NESP) is the appropriate methodology to describe effects where long-range dependence effects are important. Non-extensive statistical physics (NESP), originally was introduced in [14], recently summarized in [15], while its validity in Earth Sciences is reviewed in [16,17]. NESP is based on Tsallis entropy, a generalization of the classic Boltzmann-Gibbs entropy and has the main advantage that it considers all-length scale correlations among the elements of a system, leading to a very common in Earth Sciences asymptotic power-law behavior.…”

“…Since they are key components of Earth physics processes, Tsallis statistical mechanics is suitable to explore the distribution of seamounts in ESC. Its applicability in Earth and planetary physics has been demonstrated in a series of recent publications on seismicity [16][17][18][19][20][21], natural hazards [22,23], plate tectonics [24], geomagnetic reversals [25], rock physics [26], applied geophysics [27], and Earth's and Mars' fault-length distributions [28][29][30].…”