Examining the strength dependency of frequency-magnitude distribution in small Earthquakes: implications for stress state criticality

doi:10.21203/rs.3.rs-3343871/v1

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Examining the strength dependency of frequency-magnitude distribution in small Earthquakes: implications for stress state criticality

https://doi.org/10.21203/rs.3.rs-3343871/v1

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The distribution of earthquake sizes, characterized by the power law decay as “b-value”, exhibits spatiotemporal variations detected by seismic networks. These changes are sometimes evident before a large earthquake. Understanding these variations is key to developing a model for large-earthquake generation. Previous studies have shown that changes in the b-value are caused by the tectonic stress regime. Furthermore, lab experiments have demonstrated b-value dependency of acoustic emissions on the criticality of the failure condition. However, the factors controlling the b-values during natural seismic activity are unclear. In this study, changes in the b-value in small earthquake sequences were investigated, focusing on failure criticality. Based on our high-precision focal mechanism dataset, we conclude that the b-value decreases as it nears a critical failure condition, providing a physical explanation for the reduction in b-value before a major earthquake. Our findings elucidate fault failure models, facilitating improvement in earthquake alerts and disaster mitigation.

Earth and environmental sciences/Solid Earth sciences/Seismology

Earth and environmental sciences/Solid Earth sciences/Tectonics

Earth and environmental sciences/Natural hazards

The Gutenberg–Richter (G–R) relation¹, a well-known power law, characterises the relationship between the frequency of earthquakes and fault size, as determined by magnitude (log₁₀ N(M) = a + bM, where M and N denote earthquake magnitudes and the cumulative number of earthquakes exceeding M, respectively, and a and b are the constants). Numerous studies have reported the b-values for natural earthquake sequences across various regions, revealing spatial variations. Some studies have also demonstrated a correlation between stress conditions and the tectonic regime² and depth range^3–7, suggesting that the b-value is inversely proportional to the inclination of differential stress.

Furthermore, the b-value decreases before a large earthquake and increases after the earthquake^8–10, indicating its potential as an indicator of the stress state in the epicentre of a large earthquake. Owing to the importance of the relationship between the b-value and stress loading, the characteristics of b-values were investigated in laboratory experiments using rock samples. These studies have confirmed that the b-values declined with the build-up of differential stress and proximity to rock failure^11–13. In other words, they suggest that the b-value in a small earthquake sequence decreases according to the state of stress required for large earthquake genesis.

These results highlight the strength of the medium because each earthquake comprising seismic activity for estimating the b-value meets the failure condition between the stress and strength of a medium. Factors such as confining pressure, internal friction, and pore-pressure can lead to a reduction in initial robustness. Based on strength, the following inferences can be made from the above results 1) seismic activity in a relatively strong medium, which is under higher differential stress, yields a relatively low b-value and 2) proximity of the activity to the maximum strength of the medium where is in critical condition to generate large earthquake reduces the b-value. The latter factor has never been investigated in natural earthquake activity despite being implied by b-value decline before a large earthquake. Therefore, we attempted to investigate the relationship between b-value and fault strength by analysing natural earthquake data.

The state of stress on a fault plane can be presented using a “Mohr circle”¹⁴, which depicts the stress state on a fault plane within a medium. Normal and shear stress on any fault plane under stress loaded onto a medium can be plotted inside a circle. According to the Coulomb failure criteria¹⁴, rupture occurs when the shear stress on a fault reaches the strength expressed by the cohesive strength, normal stress, friction coefficient, and pore fluid pressure. All earthquakes are considered that the state satisfied the criteria at the time of failure. Under a uniform stress condition loaded onto a medium, spatial variation in the medium by the earthquake fault plane direction indicates the existence of internal strength variation. The position of differently oriented faults plotted inside the Mohr circle reflects the strength of the fault, suggesting that variations in the b-value across the Mohr circle can provide information on the relationship between the fault strength and b-value.

To determine a point on the Mohr circle defined by the shear and normal stresses, the loaded stress tensor on the medium and the fault orientation of an earthquake have to be determined. The stress field in an area, excluding its absolute value, can be estimated using focal mechanisms or seismic moment tensors^15–18 based on the Wallece-Bott Hypothesis^19,20, suggesting that a fault slips in the maximum shear stress direction on the fault. The principal directions of the stress tensor and stress ratio between the eigenvalues can be estimated using these methods, allowing us to draw a normalised Mohr circle for the area and determine the location of the focal mechanism data on the circle. We can discuss frequency-magnitude relations in different parts of the circle by combining normalised shear and stress data for numerous focal mechanism solutions in various areas on a unit Mohr circle. Here, we present the specific relationship between the b-value derived from frequency-magnitude distribution and parts of the circle, suggesting a unique dependency of the b-value on the fault failure condition.

1000 observation sites for high-precision focal mechanism

To examine the dependency of the b-value on a normalised Mohr circle, we need to accurately obtain focal-mechanism data. We conducted dense seismic observations of over 1000 stations in the hypocentre area (approximately 35 km in diameter) of the 2000 Western Tottori Earthquake (W-Tottori Earthquake (EQ)), which had a magnitude (M) of 7.3. This earthquake is amongst the best-studied intraplate earthquakes, with detailed investigations into aspects such as fault geometry²¹, stress field^22–24 and structure²⁵. Our year-long observations in 2017 allowed us to determine the hypocentres and focal mechanisms of small earthquakes (Fig. 1). Figure 2(a) shows the hypocentre distribution using the present analysis (see Methods) with the automatically detected system. Regardless of previous studies showing a b-value dependence on depth (i.e. on differential stress), the depth-dependent b-value in this region is not clear, as shown in Fig. 2(b). The b-values are estimated for three depth (Z) ranges (i.e. Z ≤ 7.5 km, Z > 7.5km, and all depths) using ZMAP 7 software²⁶ (http://www.seismo.ethz.ch/en/research-and-teaching/products-software/software/ZMAP/). The b-value estimation with a fixed minimum magnitude (Mc = -0.3, as adopted in the subsequent section) did not yield any considerable difference in the b-value. The homogeneous distribution of b-values in this area indicates that the depth dependency of the b-value might be small as the differential stress is expected to increase with depth⁷. According to the empirical relation⁷ between b-value and differential stress, relation between b-value and depth range can be written in the form $\text{b}=1.23-0.0012\bullet 20\bullet \text{Z}$ in strike slip stress regime as seen in the target area. The two focal depth ranges of average 5 and 10 km for Z ≤ 7.5 km and Z > 7.5km creates approximately 0.1 change in the b-value. The dependency on the depth range in the area can be disregarded as long as the difference in b-value exceeds 0.1. Therefore, we considered the b-value change in parts of the unit Mohr circle to reflect its fault-strength dependency related to the criticality of failure of earthquake faults.

To determine relative stress tensors, we employed a stress tensor inversion using focal mechanism data within spatial bins (Figs. A1 and A2), resulting in findings similar to previous studies^22–24. Subsequently, normalised shear and normal stresses for selected individual earthquakes (see Method) were estimated based on the fault plane and the relative stress tensor within the spatial bin containing the earthquake.

b-value map on a normalised Mohr circle

For selected fault planes from the dataset of the observation as described in the Method section, normalised shear and normal stresses are plotted on a unit Mohr circle, as demonstrated in Fig. 3a. We estimated the b-value distribution by segmenting the Mohr circle (Fig. 3b). The lowest b-value was identified to be approximately 90° > θ > 50° clockwise from the horizontal line at the outermost part of the circle. Figure 3c presents the b-value along with the standard error for the segments on the Mohr circle. The b-values for all data and broader segments (r < 0.8, θ = 0–90, 90–180 deg.) are also plotted for reference. The frequency–magnitude plot for the segments is shown in Fig. 3(d). The b-value is significantly small at 90° > θ > 50° with r ≥ 0.8 and appears to be larger outside this range.

To interpret this feature, we introduce a model where the criticality of the Coulomb failure criterion controls the b-value. The b-value reaches a minimum around angle θ at the outer edge of the circle (hereby called the optimal range), indicating that the Mohr circle touches a line defined by the criteria. An angle range, θ > 50, corresponds to a frictional coefficient µ < 0.84. This range falls within the internal friction coefficients of rock²⁷ or smaller. The range of friction coefficients cannot be adequately resolved. However, the results revealed that a larger earthquake occurred in this state. This suggests relatively larger fault slips with minimal action of the fault-strength-weakening mechanism, such as rising fluid pressure. In other words, the optimal fault plane for a stress field rather than unfavourable fault planes can be ruptured by a large-magnitude fault. This is reasonable as the releasable elastic energy on a fault plane is larger at the optimal range in the Mohr circle than out of the range under the same stress conditions. It is natural for a larger elastic energy to generate a larger fault slip. A model¹¹ based on the acoustic emission (AE) magnitude in laboratory experiments proposed that the b-value decline with increasing differential stress, which was equivalent to inclement of strength in a medium, was attributed to the formation and coalescence of microcracks. Fault planes plotted outside the optimal range may generate smaller earthquakes because assistance is required for the entire fault. Our results show that weak faults plotted at out of the optimal range were activated. The activation attributed to pore fluid pressure demonstrates that this area is under a partially high-pressure circumstance that unfavourable oriented fault to the stress field can rupture²⁸.

The absolute b-value was not a concern in this study because it may change in different regions. Generally, the effects of the absolute difference stress on the b-value may overlap with each other. Notably, the b-value was minimal around the outermost part of the Mohr circle with 90° > θ > 50°.

We estimated the b-value dependence of the fault orientation on the state of stress. Generally, the observed seismicity may be composed of events with various fault planes, meaning that the change in the b-value obtained from the seismic catalogue could be smaller than that observed in the present study. Therefore, b-value variation in the present study was not directly related to the b-value change in the seismicity catalogue. However, a lower b-value indicates that the catalogue contains earthquake faults with a critical stress state for the failure criteria rather than those under weak fault rupturing. Laboratory experiments^11–13 showed that the b-value of AE is stress-dependent. In addition, the experiments suggest that the b-value decreases as failure condition approaches. Our results are similar to theirs, although the fault plane orientation of the AE in their studies was unclear.

In the present study, we investigated b-value dependency upon fault strength. Our results show earthquakes with the lowest b-values were under a stress state close to critical failure condition with smallest strength weakening factor among various strengths satisfying Coulomb failure condition. In other words, the b-value decreases toward the end of the seismic cycle. In this study, we found that the change in the b-value was related to the criticality of earthquake generation under Coulomb failure conditions. This reveals the importance of monitoring the b-value for possible earthquakes.

Focal mechanism estimation

We utilized automatic picking and applied focal mechanism determination processes to continuous seismic records after checking the quality of the extracted 100 event data by comparing the manually picked and automated results²⁹.

Similar to a previous study³⁰, we adopted a smoothed, depth-dependent velocity structure for hypocentre determination. Only events within the area covered by the 2017 network were considered. The focal mechanisms of the selected data are determined using the HASH algorithm³¹. The completeness of the detection process reached an M of approximately − 0.5 for 3,641 events within the 2017 network²⁹. High-quality focal mechanism solutions were also obtained. For each event, the optimal solution was derived as the tensor average from all possible focal mechanism tensors. We also generated 1000 focal mechanisms for an event based on the solution distribution using HASH. The datasets are utilized in the subsequent processing. The number of focal mechanism solutions satisfying the criteria was 2,828 for the 2017 observations (Fig. A1). We created 1000 datasets of focal mechanism solutions by random sampling from every 1000 focal mechanism solutions. This dataset is used to calculate the confidence range of the stress field.

Stress field

The normalised deviatoric stress tensors were estimated for the spatial bins dividing the target area. The tensor was derived from the seismic moment tensor data of the aftershocks, utilizing a method¹⁸ based on the equivalent relation between the inelastic strain and the released seismic moment tensor³². To stabilize the solution, we employed the stress field estimation using data in the 2017 observation and seismic observation performed in 2000 as a previous study²². The focal mechanisms of 2,285 events for 2000 observations were obtained using the processing sequence described above (Fig. A1). Subsequently, we created a moment tensor dataset based on the focal mechanism and earthquake magnitude (Ma). The tensor shape and scalar moment (M0) were obtained from the estimated focal mechanism and transformed value from Ma through an empirical relationship used in a previous study²⁴: (log (M0) = 1.15Ma + 10.548). Notably, stress tensor estimation was independent of the fault plane selection, as it utilized moment tensor data. The stress tensor estimated from the seismic data provides a normalised tensor shape that is characterised by the principal directions and ratio among the eigenvalues. The deviatoric stress tensors were estimated in spatial blocks, set at intervals of 3 km horizontally and at 2.5 km depth (Fig. A2). In addition, we performed the same procedure for the block distribution shifted by half a block to the north and east from the origin to smoothen the results. The principal directions and relative values of the eigenvectors that revealed the normalised deviatoric stress tensor were estimated from the events in a spatial bin. The parameters in each spatial bin within a confidence range were estimated (Fig. A3). This result aligns with those of previous studies^22–24. However, the parameters with substantial accuracy were mainly limited to spatial bins around the aftershock area with relatively high seismic activity. Consequently, in the subsequent discussion, we focused solely on the data within the spatial bins exhibiting significant accuracy, as shown in Fig. A2. Finally, we analysed 2,155 (1,412 for Mc = -0.3) focal mechanism data points to investigate the strength dependency of the b-value.

A comparison of the number of focal mechanisms with hypocentres, including spatial bins, is shown in Fig. A4 as the frequency-magnitude distribution. The number of focal-mechanism data points was slightly lower than that of the hypocentre data. This difference can be attributed to a less favourable geometrical condition of the station distribution or a lower signal-to-noise ratio of the seismograms used to determine the focal mechanism. The estimated b-values exhibit a discrepancy of approximately 0.07 due to the larger difference in the small magnitude range. However, no specific focal mechanism was identified in this dataset. Therefore, the relative b-value changes among the parts of the Mohr diagram are discussed.

Shear and normal stress estimation for stress tensor and choice of fault planes

The normalised shear and normal stresses were calculated from the fault geometry and stress tensor ($\sigma$ ). According to previous research¹⁴, normal stress vector ${\sigma }_{N}$ is a product of traction vector T and unit fault normal vector n [${\sigma }_{N}=(T\bullet n)n$], where the traction vector is $\sigma$ applied to n; $T=\sigma n$. The shear stress vector $\tau$ is expressed as $\tau =T-{\sigma }_{N}$. From the seismic data (focal mechanism or moment tensor), we can only determine the normalised deviatoric stress tensor $\widehat{\sigma }$, characterised by the principal directions of the eigenvalues and the ratio between the eigenvalues. This means that the magnitude of $\sigma$ is arbitrary; therefore, the relative relationship between the shear and normal stresses was obtained. In this case, the relationship provides ${\varvec{\sigma }}_{\text{N}}/\left|T\right| \text{a}\text{n}\text{d} \varvec{\tau }/\left|T\right|$ from $\widehat{\sigma }$ and n. Therefore, we can define a Mohr circle with a unit diameter, with its centre point at the coordinates’ origin. For instance, the maximum shear stress under the stress tensor acting on a plane with a normal vector that rotates 45° from the maximum principal direction to the minimum principal direction of the stress tensor is plotted at (normal stress, shear stress) = (0, 1) on the normalised (unit) Mohr circle. In this study, we used coordinates to express the location on the Mohr circle by r (radial length from the centre, i.e., ranging from 0 to 1) and θ (clockwise angle from the horizontal).

To estimate the normal and shear stresses on the unit Mohr circle, a fault-normal vector is required. We have two candidates for the normal vector for each event from the focal mechanism solution owing to the existence of two nodal planes. The following scheme was used to select one of the two planes. Initially, we eliminated the fault plane from the dataset if it had a misfit angle (dθ), which is the discrepancy between the slip vector of the focal mechanism and the maximum shear stress direction expected from the stress field exceeding 30°. We then set two conditions that are used in the plane selection: (1) misfit angle (dθ) and (2) comparison lengths of segments (dp) to the line defined by Coulomb failure function (CFF) for a certain friction coefficient $\left(\mu \right)$ from two points calculated by the normal vectors of the candidates. A schematic of this process is shown in Fig. A5. Shear strength in CFF is expressed as ${{\tau }}_{0}+\mu ({s}_{n}-p)$, where t₀, s_n, and $p\propto \text{d}p$ represent the cohesive strength, normal stress on a plane, and pore fluid pressure proportion to dp. A point touching the CFF line on the unit Mohr circle with angle θ_c can be expressed by ${{\theta }}_{\text{c}}={\text{tan}}^{-1}\left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mu $}\right.\right)$ as shown in Fig. A5b and reported by Jaeger et al.¹⁴. Unfavourable fault planes for the stress field require a high value of p to generate rupture, which is more challenging to achieve naturally than in situations with a low p owing to difficulties sustaining a high p.

The dθ range for each plane was calculated from the stress fields within a 95% confidence interval in the spatial bin containing the event. Initially, we selected a plane with a smaller dθ range than the other plane (condition 1). However, if the dθ ranges overlapped, we chose a plane with a smaller dp (condition 2). This criterion is known as selection based on fault instability, as defined in a previous study³³. To calculate dp, we set µ = 0.6 based on the typical internal friction coefficient²⁷. However, despite assuming µ = 0.2 or 1.0, the result did not change (Fig. A6).

After completing the above process for each event, we compared the selected fault plane for an estimated stress tensor with that for another one. As described in “stress field”, spatial block distribution shifted half the block size horizontally, meaning two candidates of the stress field exist for most events. We used a fault plane and stress field combination to provide a relatively small misfit dθ.

b-value estimation

The b-value, which represents the power-law decay of the frequency-magnitude distribution, has been estimated for various regions and exhibits spatial and temporal variations. We followed the standard method to estimate the b-value^34–36. We set a consistent magnitude range (minimum and maximum magnitudes) for each part of the Mohr circle, as comparing the b-values across different parts of the circle is crucial for this study. We used the magnitude range from − 0.3 to 2, with the lower bound determined using ZMAP software²⁶. The upper bound is the set position at which the segment of the frequency-magnitude relation is slightly deviates from the linear relation between log N and M (i.e. off from the Gutenberg-Richter relation). Additionally, the number of earthquakes above the upper bound was too small for the analysis of the b-value variation within the Mohr circle.

We estimated the b-values for the parts of the Mohr circle that contained over 50 events, excluding events close to the co-seismic fault of the 2000 W-Tottori EQ. The heterogeneity of the stress field may lead to improper estimation of the fault direction relative to the stress field. Based on the co-seismic fault model²¹, we calculated the distance to the fault planes and selected events that were located farther than a certain distance (R). In this study, we set R = 0.5 km. The results for different distance settings are shown in Fig. A7a). Increasing R significantly decreased the number of usable events due to the concentration of hypocentres around the co-seismic fault planes (Fig. A7b). The number of excluded events with larger misfits, as described in the previous section, decreased with increasing R, indicating the influence of the nearby faults on events. We selected R = 0.5 km, which led to the utilization of 65% of events from the initial set, while 8% were excluded..

The unit Mohr circle is divided into parts expressed by range (r minimum, r maximum; θ° minimum, θ° maximum) in the coordinate shown in the inset of Fig. 2(c): those ranges are (0.8, 1: 10, 30), (0.8, 1; 20, 40), (0.8, 1; 40, 60), (0.8, 1; 60, 80), (0.8, 1; 70, 90), (0.8, 1; 80, 100), (0.8, 1; 90, 110), (0.5, 0.8; 22.5, 67.5), (0.5, 0.8; 45, 90), (0.5, 0.8; 67.7, 112.5), (0, 0.8; 0, 90), and (0, 0.8; 90, 180).

Data availability

The focal mechanism data used in this study are available in the Zenodo repository, 10.5281/zenodo.8242561, upon reasonable request to corresponding author. Other datasets used in the current study are accessible from the corresponding author upon reasonable request.

Code availability

The HASH algorithm used to determine the focal mechanism is accessible at https://www.usgs.gov/software/hash-12. The ZMAP program by Wiemer²⁶ is accessible at http://www.seismo.ethz.ch/en/research-and-teaching/products-software/software/ZMAP/). We plotted the figures using GMT5 (http://gmt.soest.hawaii.edu/projects/gmt) and Microsoft Excel 2016. The other customised codes used in this study are accessible from the corresponding author upon request.

Acknowledgments

We thank the staff and students of Kyushu and Kyoto Universities and the University of Tokyo who maintained the seismic stations for their work in obtaining good-quality seismic data. We also used seismic data from the Japan Meteorological Agency and Hi-net.

Author contribution

S.M. performed data processing and analysis of the micro-earthquakes, including relative strength estimation. S.M., Y.I., S.S., and A.K. managed and conducted hyperdense seismic observations. All the authors contributed to the discussion and approved the final manuscript.

Competing Interest

The authors declare no competing interests.

Gutenberg, B. & Richter, C. F. Frequency of earthquakes in California. Bull. Seismol. Soc. Am. 34, 185–188 (1944). 10.1785/BSSA0340040185.
Schorlemmer, D., Wiemer, S. & Wyss, M. Variations in earthquake-size distribution across different stress regimes. Nature 437, 22 September, 539–542 (2005). 10.1038/nature04094, Pubmed:16177788.
Wiemer, S. & Wyss, M. Mapping the frequency–magnitude distribution in asperities: An improved technique to calculate recurrence times? J. Geophys. Res. 102, 15115–15128 (1997). 10.1029/97JB00726.
Mori, J. & Abercrombie, R. E. Depth dependence of earthquake frequency–Magnitude distributions in California: Implications for rupture initiation. J. Geophys. Res. 102, 15081-15090 (1997). 10.1029/97JB01356.
Gerstenberger, M., Wiemer, S. & Giardini, D. A systematic test of the hypothesis that the b value varies with depth in California. Geophys. Res. Lett. 28, 57-60 (2001). 10.1029/2000GL012026.
Spada, M., Tormann, T., Wiemer, S. & Enescu, B. Generic dependence of the frequency–size distribution of earthquakes on depth and its relation to the strength profile of the crust. Geophys. Res. Lett. 40, 709–714 (2013). 10.1029/2012GL054198.
Scholz, C. H. On the stress dependence of the earthquake b value. Geophys. Res. Lett. 42, 1399–1402 (2015). 10.1002/2014GL062863.
Smith, W. D.. The b-value as an earthquake precursor. Nature 289, 136–139 (1981). 10.1038/289136a0.
Schorlemmer, D. & Wiemer, S. Earth science: Microseismicity data forecast rupture area. Nature 434, 1086 (2005). 10.1038/4341086a, Pubmed:15858563.
Nanjo, K. Z., Hirata, N., Obara, K. & Kasahara, K. Decade‐scale decrease in b value prior to the M 9-class 2011 Tohoku and 2004 Sumatra quakes. Geophys. Res. Lett. 39, L20304 (2012). 10.1029/2012GL052997.
Scholz, C. H. The frequency-magnitude relation of microfracturing in rock and its relation to earthquakes. Bull. Seismol. Soc. Am. 58, 399–415 (1968). 10.1785/BSSA0580010399.
Goebel, T. W., Schorlemmer, D., Becker, T. W., Dresen, G. & Sammis, C. G. Acoustic emissions document stress changes over many seismic cycles in stick-slip experiments. Geophys. Res. Lett. 40, 2049–2054 (2013). 10.1002/grl.50507.
Bolton, D. C., Shreedharan, S., Rivière, J. & Marone, C. Frequency-magnitude statistics of laboratory foreshocks vary with shear velocity, fault slip rate, and shear stress. J. Geophys. Res. Solid Earth 126, e2021JB022175, e2021 (2021). 10.1029/2021JB022175, Pubmed:35865108.
Jaeger, J. C. et al. Fundamentals of Rock Mechanics. 4th ed (Blackwell Ltd, Oxford, UK, 2007).
Angelier, J. Tectonic analysis of fault slip data sets. J. Geophys. Res. 89, 5835–5848 (1984). 10.1029/JB089iB07p05835.
Michael, A. J. Determination of stress from slip data: Faults and folds. J. Geophys. Res. 89, 11517–11526 (1984). 10.1029/JB089iB13p11517.
Gephart, J. W. & Forsyth, D. W. An improved method for determining the regional stress tensor using earthquake focal mechanism data: Application to the San Fernando earthquake sequence. J. Geophys. Res. 89, 9305–9320 (1984). 10.1029/JB089iB11p09305.
Matsumoto, S. Method for estimating the stress field from seismic moment tensor data based on the flow rule in plasticity theory. Geophys. Res. Lett. 43, 8928–8935 (2016). 10.1002/2016GL070129.
Wallace, R. E. Geometry of shearing stress and relation to faulting. J. Geol. 59, 118–130 (1951). 10.1086/625831.
Bott, M. H. P. The mechanics of oblique slip faulting. Geol. Mag. 96, 109–117 (1959). 10.1017/S0016756800059987.
Earthquake source model database (SRCMOD). http://equake-rc.info/SRCMOD/searchmodels/viewmodel/s2000TOTTOR01SEKI/.
Yukutake, Y., Iio, Y., Katao, H. & Shibutani, T. Estimation of the stress field in the region of the 2000 Western Tottori Earthquake: Using numerous aftershock focal mechanisms. J. Geophys. Res. 112 (2007). 10.1029/2005JB004250.
Kawanishi, R., Iio, Y., Yukutake, Y., Shibutani, T. & Katao, H. Local stress concentration in the seismic belt along the Japan Sea coast inferred from precise focal mechanisms: Implications for the stress accumulation process on intraplate earthquake faults. J. Geophys. Res. 114, B01309 (2009). 10.1029/2008JB005765.
Matsumoto, S., Iio, Y., Sakai, S. & Kato, A. Inelastic strain in the hypocentral region of the 2000 Western Tottori Earthquake (M 7.3) inferred from aftershock seismic moment tensors. Earth Planets Space 72, 62 (2020). 10.1186/s40623-020-01186-2.
Kato, A., Sakai, S., Matsumoto, S. & Iio, Y. Conjugate faulting and structural complexity on the young fault system associated with the 2000 Tottori earthquake. Commun. Earth Environ. 2, 13 (2021). 10.1038/s43247-020-00086-3.
Wiemer, S. A software package to analyze seismicity: ZMAP. Seismol. Res. Lett. 72, 373-382 (2001). 10.1785/gssrl.72.3.373.
Byerlee, J. Friction of rocks. PAGEOPH 116, 615–626 (1978). 10.1007/BF00876528.
Sibson, R. H. Rupture nucleation on unfavorably oriented faults. Bull. Seismol. Soc. Am. 80, 1580–1604 (1990).
Matsumoto, S., Iio, Y., Sakai, S. & Kato, A. Hyper Dense Seismic Observation for Investigation on Fault Zone Development: Application to hypocentral area of 2000 Western Tottori earthquake. J. Geogr. 129, 511–527 (2020). 10.5026/jgeography.129.511.
Yukutake, Y. & Iio, Y. Why do aftershocks occur? Relationship between mainshock rupture and aftershock sequence based on highly resolved hypocenter and focal mechanism distributions. Earth Planets Space 69, 68 (2017). 10.1186/s40623-017-0650-2.
Hardebeck, J. L. & Shearer, P. M. A new method for determining first-motion focal mechanisms. Bull. Seismol. Soc. Am. 92, 2264–2276 (2002). 10.1785/0120010200.
Kostrov, V. V. Seismic moment and energy of earthquakes, and seismic flow of rock, Izv. Earth Phys. 1, 23-40 (1974).
Vavryčuk, V. Iterative joint inversion for stress and fault orientations from focal mechanisms. Geophys. J. Int. 199, 69–77 (2014). 10.1093/gji/ggu224.
Aki, K. Maximum likelihood estimate of b in the formula log N = a – bM and its confidence limits. Bull. Earthq. Res. Inst. Tokyo Univ. 43, 237–239 (1965).
Bender, B. Maximum likelihood estimation of b values for magnitude grouped data. Bull. Seismol. Soc. Am. 73, 831–851 (1983). 10.1785/BSSA0730030831.
Utsu, T. Representation and analysis of the earthquake size distribution: A historical review and some new approaches. Pure Appl. Geophys.155, 509–535 (1999). 10.1007/s000240050276.

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Examining the strength dependency of frequency-magnitude distribution in small Earthquakes: implications for stress state criticality

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Abstract

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Introduction

Results

1000 observation sites for high-precision focal mechanism

b-value map on a normalised Mohr circle

Methods

Focal mechanism estimation

Stress field

Shear and normal stress estimation for stress tensor and choice of fault planes

b-value estimation

Declarations

References

Additional Declarations

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