Spatiotemporal heterogeneity of b values revealed by a data-driven approach for the 17 June 2019 MS 6.0 Changning earthquake sequence, Sichuan, China

The spatiotemporal heterogeneity of b values has great potential for helping in understanding the seismogenic process and assessing seismic hazard. However, there is still much controversy about whether it exists or not, and an important reason is that the choice of subjective parameters has eroded the foundations of much research. To overcome this problem, we used a recently developed non-parametric method based on a data-driven concept to calculate b values. The major steps of this method include (1) performing a large number of Voronoi tessellations and Bayesian information criterion (BIC) value calculation, selecting the optimal models for the study area, and (2) using the ensemble median (Q2) and median absolute deviation (MAD) value to represent the final b value and its uncertainty. We investigated spatiotemporal variations in b values before and after the 2019 Changning MS = 6.0 earthquake in the Sichuan Basin, China. The results reveal a spatial volume with low pre-mainshock b values near the mainshock source region, and its size corresponds roughly with the rupture area of the mainshock. The anomalously high pre-mainshock b values distributed in the NW direction of the epicenter were interpreted to be related to fluid invasion. The decreases in b values during the aftershock sequence along with the occurrences of several strong aftershocks imply that b values could be an indicator of the stress state. In addition, we found that although the distribution characteristics of b values obtained from different methods of investigation are qualitatively consistent, they differ significantly in terms of their specific values, suggesting that the best way to study the heterogeneous pattern of b values is in the joint dimension of space-time rather than separately in time and space. Overall, our study emphasizes the importance of b-value studies in assessing earthquake hazards.


The Influence of the Uncertainty of Focal Depth on the Distribution of b Values
The uncertainty of the earthquake focal depth calculated by the HypoDD method is statistically about 0.654 km in this paper, but the true uncertainty of the focal depth may exceed the theoretical uncertainty given by the relocation method. Thus, the potential influence of the uncertainty of seismic depth must be considered for the reliability of the distribution characteristics of b values on the depth profile.
In order to study the above problem, we conducted random disturbance tests on the locations of the earthquake sources in Figure 4c. We performed a random disturbance of ±1km on the horizontal position of the earthquakes, and used the uncertainty of ±2km, ±4km and the random distribution in the range of [-22km 0km] to disturb the original depths respectively. Considering the distribution density of seismic stations in the study area, the above-mentioned disturbance scales of 2km and 4km for the focal depth should reach or exceed the uncertainty of the true focal depth.
In the process of generating the random earthquake catalog, in order to prevent the occurrence of "air-quake" with depth ≥0 km, we force the random disturbance to continue until the depth <0 m. The distribution of b values recalculated by using the above three new earthquake catalogues is shown in Figure S1  We used a fixed window of 300 seismic events and a window of gradual cumulative increase with 300 seismic events.
In both methods, the earthquakes are selected and calculated retrospectively from the failure time of the mainshock to the past, and the calculation is stopped when there are less than 300 events in the current window/step. The reason why we use 300 earthquake windows/steps subjectively is to ensure the statistical reliability when fitting the OK1993 model, and to obtain more results of temporal variations of b values at the same time.
The results ( Figure S3

Minimum Completeness Magnitude and its Influence on the Calculation of b Values
The analysis of the minimum completeness magnitude Mc of the earthquake catalog is an important basis for the calculation of b value. In the traditional b value calculation based on the G-R relationship, the accurate calculation of Mc and the reasonable selection of the cut-off magnitude will affect the results of b value (Harte, 2016). Since the OK1993 model in this paper is a model that uses a continuous function to describe the magnitude-frequency distribution, all events including incompletely recorded events are used for model fitting, so there is no need to select the cut-off magnitude. In addition, the Mc and b values are obtained at the same time when fitting the OK1993 model, so the Mc will not affect the result of the b values, which is the inherent advantage of the OK1993 model.
According to the estimation results of Mignan and Woessner (2012) and Iwata (2013), the minimum magnitude of completeness Mc related to OK1993 model can be approximately expressed by using μ+2σ or μ+3σ, which represents the complete record of magnitude at the 95% or 99.9% confidence level. In this paper, we chose μ+2σ as  Figure S4. It can be seen from Figure S3 that the Mc(μ+2σ) in the study area ABCD is mainly distributed between 0.7 and 1.6, and the Mc(μ+2σ) in the East is smaller than that in the West, which is consistent with the distribution characteristics of seismic stations in Figure  which also implies that the minimum completeness magnitude will not significantly affect the results of this paper.