Earthquakes descaled: on waiting time distributions and scaling laws

Recently, several authors have used waiting time distributions for large earthquake data sets to draw conclusions regarding the physics of earthquake processes. We show, theoretically and by simulation, that a characteristic kink in observed waiting time distributions does not have the physical significance of separating correlated and uncorrelated earthquakes. It also follows from our discussion that the Omori law is not trivially related to a proposed scaling law and that caution must be taken before the spatial scaling exponent of the law is interpreted as a fractal dimension of seismicity.