We agree with Bürgmann and colleagues' comment that additional parameters might play a role in explaining and interpreting the observed changes in b-values, such as the suggested activation of different faulting regimes. Maps of b-values always represent volumetric averages and are generally prone to missing shifts of origin locations within the sampled rock volume. However, we reduced this limitation by using distance-weighted sampling of events1, 2, which accounts for the relative hypocentre/plate interface distance and focuses on processes along the interface.

Bürgmann and colleagues select earthquakes with a variance reduction of greater than 80% from the F-net seismic catalogue. However, the variance reduction changes significantly with time and specifically decreases after the Tohoku-oki earthquake. Thus the selection process biases the catalogue by excluding a third of pre- and more than half of post-Tohoku-oki events, independent of event magnitude (30% post-Tohoku-oki for variance reduction of greater than 70%). In our view, the relative fractions of mechanism types (and their b-values) cannot be established with confidence from these subsets.

Aside from these doubts, the b-value time series that Bürgmann and colleagues infer from the relative mechanism fractions reproduces our documented mainshock-related b-value increase1 with smaller amplitude. The inferred smaller amplitude is consistent with the range of b-values observed between different focal mechanism types3. However, this amplitude is significantly lower than those we document in our analysis of the temporal and spatial variation of b-values. Moreover, the fraction-inferred time series reproduces only a slight hint of the recent b-value decrease we observed. Although not shown by Bürgmann et al., the b-values of the individual mechanism types change significantly following the Tohoku-oki magnitude 9 event. That is, despite the above quality limitations, the reverse and normal faulting b-values early after the mainshock are strongly increased, but have significantly recovered at the end of the study period. We find that the amplitude of these changes within each mechanism type is larger than the amplitude inferred from the changes in relative mechanism fractions. This indicates that the relative fractions in focal mechanisms play a secondary rather than dominating role in the overall temporal b-value signal.

The analysis by Bürgmann and colleagues confirms our original comment1 — traditionally considered mechanisms of stress relaxation cannot explain the b-value recovery observed following the Tohoku-oki earthquake. Whatever the physical mechanism, the b-value is a measure for the likelihood of large versus small events, and this is recovering quickly in northeast Japan. Whether an additional independent parameter exists that for some time can limit the maximum magnitude along this frequency-magnitude distribution is speculative.

Although not fully understood, our b-value observations1 are not the first and only evidence indicating non-characteristic behaviour of megathrust events4, 5, 6. The evolution of faulting style7 points to a similarly fast, but probably heterogeneous recovery of stress along the northeastern Japan plate interface, supporting our interpretation.