  Seismicity and faulting within the Earth crust are characterized by many
scaling laws that are usually interpreted as qualifying the existence of
underlying physical mechanisms associated with some kind of criticality in the
sense of phase transitions. Using an augmented Epidemic-Type Aftershock
Sequence (ETAS) model that accounts for the spatial variability of the
background rates $\mu(x,y)$, we present a direct quantitative test of
criticality. We calibrate the model to the ANSS catalog of the entire globe,
the region around California, and the Geonet catalog for the region around New
Zealand using an extended Expectation-Maximization (EM) algorithm including the
determination of $\mu(x,y)$. We demonstrate that the criticality reported in
previous studies is spurious and can be attributed to a systematic upward bias
in the calibration of the branching ratio of the ETAS model, when not
accounting correctly for spatial variability. We validate the version of the
ETAS model which possesses a space varying background rate $\mu(x,y)$ by
performing pseudo prospective forecasting tests. The non-criticality of
seismicity has major implications for the prediction of large events.
