Figure 6
Scaling relations of the slip model before and after convolution. (a) Example of a convolution leading to AAE(t) (in blue) from an avalanche profile V(t) (in red) and a transfer function T(t) = \(\cos \left( {wt} \right)e^{ - qt}\) (in black). (b) Examples of 6 convoluted avalanche profiles for different source functions V(t) with different durations, and the same transfer function. Both convoluted and original profiles are normalized with respect to their maxima. (c–f) scaling relations \(E \sim A_{max}^{x}\) (c), \(S \sim A_{max}^{\gamma }\) (d), \(A_{max} \sim D^{\chi }\)(e) and \(A_{max} \sim R^{\xi }\) (f) for the original V(t) profiles (red points) and after the convolution AAE(t) (blue points). For e) and f) the exact exponent values in mean field theory are Χ=1 and ξ=1.
