https://orcid.org/0000-0002-6129-8459
In our recently published paper titled ‘Locating tectonic tremors with uncertainty estimates: time- and amplitude-difference optimization, wave propagation-based quality control and Bayesian inversion’, we inadvertently employed improper methods for coordinate conversion between geographic and Cartesian coordinates. Consequently, this led to a slight distortion in the inversion results and figures.
Specifically, we mistakenly utilized the normal Mercator (NM) projection to define the station locations in Cartesian coordinate. This inappropriate choice resulted in an artificial stretch of inter-station distances, reaching a maximum of 21 per cent. The correct approach involves using the Transverse Mercator (TM) projection to maintain accurate inter-station distances. Analysis described in Section 3.2 is subject to this change. Under the artificial stretch of distance, the S-wave velocity (|${V}_S$|) was consistently overestimated. We subsequently revised the analyses described in Section 3.2, modifying the selection criteria for |${V}_S$| to 0.15–0.35 km/s. With this updated criterion, we retained 1460 of tremors. We also revised the Bayesian inversion analysis in Section 3.3 using the newly obtained 1460 events and corrected station locations. As a result, we found that this adjustment had minimal impact on the results, except for |${V}_S$| estimation.
Another issue is that while we adopted the NM projection to determine station locations in Cartesian coordinate, station and event locations shown in Figs 4, 7, 9, and 10 of the original paper underwent conversion from Cartesian to geographical coordinates using the TM projection. Consequently, station and event locations in these figures were systematically shifted outward relative to the map centre.
All necessary corrections to the paper are detailed below. These changes do not affect the performance of our proposed method and the overall pattern seen in the tremor distribution. Hence, our main conclusion remains the same.
Figure 4: Station locations in Figs 4(a), (b), (d), and (e) have been rectified. Distance plots of Figs 4(c) and (f) are also affected.
Wave propagation pattern from a specific event inferred from (a–c) relative arrival times and (d–f) relative logarithmic amplitudes. (a) Relative arrival time are shown in map view. The grey line denotes the trench. (b) Standard deviations of the error on the relative arrival times. (c) Relative arrival times plotted against propagation distances. The error bar denotes the standard deviation. The blue dashed line represents a regression line. (d–f) The same as (a–c), but relative logarithmic amplitudes are shown. Note that the effect of geometrical spreading is removed in (f).
Figure 5: Plots have shifted toward lower |${V}_S$| due to the shrinking of distances in Cartesian coordinate. Accordingly, we adjusted the acceptable range for |${V}_S$|.
Estimations of the S-wave velocity (|${V}_{S}$|) and attenuation strength (|${B}$|) based on the wave propagation pattern. Each red dot shows the results from different events. The dashed curves are contours of the quality factor (|${Q}_{S}$|) from 100 to 1000. A dominant frequency of 5 Hz was assumed. The acceptable ranges of |${V}_{S}$| and |${B}$| are highlighted in pale blue.
Figure 6: The update of the inversion analysis requires a change in this figure.
(a) Likelihood evolution. Black dots show the likelihood of MCMC samples by 20 non-tempered chains. The underlying grey dots show the results of independent inversion without parallel tempering for which 100 non-tempered chains were employed. The yellow-shaded area highlights iterations after the burn-in period. (b) Histograms of the likelihood sampled by non-tempered MCMC chains at the 6 000 000th iteration. The black and grey histograms show the results with and without the tempering scheme, respectively.
Figure 7: The update of the inversion analysis requires a change in this figure. Station and event locations are shifted inward relative to the map centre.
Inversion results. (a, b) Hypocentres. Each blue dot shows the median hypocentre of the MCMC samples for each event. The error bars represent the 95 per cent confidence interval derived from MCMC samples. The inverted triangles are seismic stations. The thick grey line in (a) represents the trench. The thick grey line in (b) represents the bathymetry along 136.5° E. (c, d) Median estimates of (c) delay factors and (d) amplification factors of the MCMC samples. (e, f) Probability distributions of the (e) S-wave velocity and (f) quality factor. Red and grey histograms show the posterior and prior distributions, respectively.
Figure 8: The update of the inversion analysis requires a change in this figure.
Histograms of the hypocentre uncertainties (i.e. the range of 95 per cent confidence interval) in the (a) east–west, (b) north–south, and (c) vertical directions. The differently coloured histograms show the hypocentre uncertainties from different inversion settings: the complete case (blue), without correction terms (green), amplitude data only (orange), and time data only (red).
Figure 9: The update of the inversion analysis requires a change in this figure. Event locations are shifted inward relative to the map centre.
Inversion results under different settings: (a) complete, (b) without corrections (i.e. amplification and delay factors), (c) amplitude data only, and (d) time data only. The pale-blue dots are hypocentres (i.e. median values of the MCMC samples) in the complete case. The red dots are the resultant hypocentres in the other cases. The inverted triangles are seismic stations. The grey line represents the trench.
Figure 10: The update of the inversion analysis requires a change in this figure. Event locations are shifted inward relative to the map centre. Migration speeds shown in (b) are modified due to the shrink of distance.
![Spatiotemporal evolution of tremors. (a) Map view of tremor epicentres with colours corresponding to days of the study period. The grey line represents the trench. (b) Temporal evolution of tremors projected along the X–Y profile [red line in (a)]. The colour notation corresponds to that in (a). The orange inclined lines delineate trench-parallel migration of tremors. Note that only the first 50 d are shown because this study detected few tremors after this period.](https://oup.silverchair-cdn.com/oup/backfile/Content_public/Journal/gji/236/3/10.1093_gji_ggae010/1/m_ggae010fig10.jpeg?Expires=1749268330&Signature=pmJ4F0TuNSkeugGo~1ghgwImWcyjdQtT1nF2V1hsNyDw6mxrtQI3pFdn2moHJtZ7OL0~6QwXBvm3nKfxMWfUWu2ZGc3mAGtj5f6mVhp~HcEZIBIsnJZN4ZRY5R4Iwr6uE3K4OxuzmSiDWTwcZjBkBz2k-2xyBXbNJrBUNBuM7lRZ8k3y-oyRhEEGec9lHxI~vf1-RND6GYyuqeIhPuU9Cq01-cMeO~BrMKqWA8KsqULpBINNEtqktx7gEjQVEK7x7kWJoiBLyzKHOuNQiFarArwVTSR4vJ0satYvI0uCSel6TnfSXTFCJV1A39zbG-vwvbEoco04CCbn8Lz2LxnjeA__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Spatiotemporal evolution of tremors. (a) Map view of tremor epicentres with colours corresponding to days of the study period. The grey line represents the trench. (b) Temporal evolution of tremors projected along the X–Y profile [red line in (a)]. The colour notation corresponds to that in (a). The orange inclined lines delineate trench-parallel migration of tremors. Note that only the first 50 d are shown because this study detected few tremors after this period.
Figure 11: The update of the inversion analysis requires a change in this figure.
Probability of at least one tremor being located within a 1 km|$\ \times $| 1 km cell. (a) The probability calculated for the entire observation period. (b–i) The probability calculated using events within a specific period defined in Fig. 10(b). The green dashed line represents the trench.
8th paragraph in Section 3.2: ‘|${V}_S$|=2.0–4.0 km s−1’ should be ‘|${V}_S$|=1.5–3.5 km s−1’ (applicable to two places); ‘|${Q}_S$| of 130–520’ should be ‘|${Q}_S$| of 150–700’; ‘1296 of the 34 068 events’ should be ‘1460 of the 34 068 events.’
1st paragraph in Section 4.1: ‘the 1296 events’ should be ‘1460 events’; ‘Only ∼10 per cent of chains’ should be ‘Less than half of chains.’
2nd paragraph in Section 4.1: ‘1208 unique events’ should be ‘1362 unique events.’
4th paragraph in Section 4.1: ‘range from −7.0 to 8.0 s and from −8.6 to 4.2 dB’ should be ‘range from −6.5 to 7.0 s and from −8.7 to 4.1 dB.’
5th paragraph in Section 4.1: ‘mean values of 2.72 km s −1 and 263’ should be ‘mean values of 2.33 km s −1 and 272’; ‘The S-wave velocity of 2.72 km s−1’ should be ‘The S-wave velocity of 2.33 km s−1’; ‘an attenuation strength of 2.20 × 10−2 km−1’ should be ‘an attenuation strength of 2.48 × 10−2 km−1.’
1st paragraph in Section 4.3: ‘The Groups A and B are separated by ∼5 km, while the Groups B and C by ∼10 km’ should be ‘The Groups A and B are separated by ∼3 km, while the Groups B and C by ∼5 km.’
2nd paragraph in Section 4.3: ‘at a speed of ∼17 km d−1’ should be ‘at a speed of ∼15 km d−1’; ‘speeds up to ∼13 km d−1’ should be ‘speeds up to ∼10 km d−1.’
4th paragraph in Section 4.3: ‘high-speed migration (> 10 km d−1)’ should be ‘high-speed migration (≥ 10 km d−1).’
Caption of Figure 10: ‘detected no tremor’ should be ‘detected few tremors.’
Figs S2–S7 have been modified. The modified supplementary data is provided as the supplementary data of this correction paper.
Acknowledgement
We thank Dr. Akiko Toh for identifying the issues in the original paper.
