Erratum to The Relationship between and ⁠: A Review and Application to Induced Seismicity in the Groningen Gas Field, The Netherlands

In response to induced earthquakes associated with conventional gas production in the Groningen gas field in the Netherlands, several networks of seismic monitoring instruments have been installed in the region (Dost et al., 2017). The recordings recovered from these networks have been of fundamental importance to the development of ground‐motion prediction models that underpin hazard and risk modeling to inform decision making regarding mitigation measures (van Elk et al., 2019). In late 2018, it was discovered that the surface accelerographs of the G‐network had been installed with a calibration error such that the majority of the instruments were recording half of the correct ground‐motion amplitudes. The error was swiftly corrected via the website of Royal Netherlands Meteorological Institute (KNMI), which operates the networks. The calibration error explains, for example, the relatively low amplitudes observed in some of the KNMI network recordings in figure 3 of Bommer, Dost, et al. (2017).

After discovery of the calibration error, work immediately began to assess the impact on the ground‐motion models that have been developed as part of the induced seismic hazard and risk modeling effort in Groningen. The early ground‐motion model of Bommer et al. (2016) was not affected because it was developed using only recordings from the KNMI B‐network. The subsequent ground‐motion models for the prediction of peak ground acceleration (PGA), peak ground velocity (PGV), and acceleration response spectra combined recordings from the B‐ and G‐networks but fortuitously did not use the surface accelerographs of the G‐network. Rather, from these stations, recordings from the 200 m geophones were used instead, a decision partly motivated by the improved signal‐to‐noise ratios of the deeper recordings. Another key consideration was the desire to bypass uncertainty in the amplification factors relative to the buried reference rock horizon at ∼800  m depth because the G‐network stations had not benefited from the same in situ near‐surface shear‐wave velocity measurements as were conducted for the B‐network accelerographs (Noorlandt et al., 2018).

Two elements of the more recent ground‐motion models did make use of the surface accelerograph recordings from both the B‐ and G‐networks, but in neither case did the calibration error have any impact at all. The model for predicting ground‐motion durations (Bommer, Stafford, et al., 2017) uses the significant duration definition, which is determined as the interval between accumulation of 5% and 75% of the total Arias intensity, a metric that is entirely insensitive to amplitude scaling of the record. The component‐to‐component variability model (Stafford et al., 2019)—used to transform the geometric mean amplitudes predicted for the hazard into the arbitrary horizontal component used in the risk calculations—was derived from ratios of the two horizontal components of each accelerogram, which are also completely independent of amplitude scaling. The study by Stafford et al. (2019) additionally proposed a model for spatial correlations among response spectral ordinates in the Groningen field that made use of recordings from the G‐network. The inclusion of these records will have influenced the results of that study but most likely only by a small amount given that the results were obtained by averaging over multiple datasets and modeling approaches and that some of these analyses were entirely independent of the G‐network. The seismic risk calculations for the Groningen field (van Elk et al., 2019) currently approximate spatial correlation through rules for sampling variability within and between site‐response zones (Rodriguez‐Marek et al., 2017) rather than directly implementing the model of Stafford et al. (2019).

Another element of the ground‐motion modeling that made use of the surface accelerograph recordings is the relationship between local and moment magnitudes in Groningen, as presented by Dost et al. (2018). This relationship—which in the magnitude range of relevance (⁠�L≥2.5⁠) is one of equivalence between the two scales—is invoked for assigning seismic moments to events as part of the inversions of Fourier amplitude spectra for source, path, and site parameters, as well as in calibrating the upper branches of the ground‐motion logic tree to match predictions from ground‐motion prediction equations derived for tectonic earthquakes. Because recordings from surface accelerographs of the G‐network were included in the calculation of seismic moments, many of the moment magnitude values required correction: the changes in values are illustrated in Figure 1, and a corrected version of the electronic supplement is now presented as Ⓔ Table S1 (available in the supplemental content to this erratum). As can be appreciated in Figure 1, the impact has mainly affected smaller magnitudes because the larger earthquakes in the database were predominantly recorded by the accelerographs of the B‐network. The correction of the data resulted in a small change to the quadratic relationship between the two magnitude scales, as illustrated in Figure 2. The corrected equation is

(1)�=0.0469�L2+0.6387�L+0.6375.

As would be expected, the corrected relationship predicts slightly larger moment magnitudes for local magnitudes smaller than �L 2.5, but the conclusion of equivalence, on average, at higher magnitudes is unchanged. The quadratic form of equation (1) is only a convenient way to express the relationship in a single formula, and in practice, it is probably appropriate to assume a linear relationship (⁠�w=�L⁠) for larger magnitudes; consequently, the apparent divergence from this model that would be implied by extrapolation of the cyan curve in Figure 2 to larger magnitudes can be safely ignored.

In light of this finding, it may be concluded that the Groningen ground‐motion models have been entirely unaffected by the unfortunate calibration error. However, for any application involving smaller‐magnitude induced earthquakes in the Groningen field, the updated model presented herein should now be used.