Insights into the statistical relationship between focal mechanisms and stress from synthetic experiments

LI Zhenyue; WAN Yongge

doi:10.12090/j.issn.1006-6616.2025082

Volume 31 Issue 6

Dec. 2025

Turn off MathJax

Article Contents

Article Navigation > Journal of Geomechanics > 2025 > 31(6): 1159-1167

LI Z Y，WAN Y G，2025. Insights into the statistical relationship between focal mechanisms and stress from synthetic experiments[J]. Journal of Geomechanics，31（6）：1159−1167 doi: 10.12090/j.issn.1006-6616.2025082

Citation:

PDF( 17540 KB)

Insights into the statistical relationship between focal mechanisms and stress from synthetic experiments

doi: 10.12090/j.issn.1006-6616.2025082

LI Zhenyue^1
,,
WAN Yongge^{1, 2
,
,}

1.
Institute of Disaster Prevention, Sanhe 065201, Hebei, China
2.
Hebei Key Laboratory of Earthquake Dynamics, Sanhe 065201, Heibei, China

Funds: This research was financially supported by the National Natural Science Foundation of China (Grant No. 42174074).

More Information

Received: 2025-07-08
Revised: 2025-09-28
Accepted: 2025-09-30

Available Online: 2025-11-27

Published: 2025-12-28

Abstract

Abstract

Objective The extent to which the spatial distribution patterns (particularly the clustering characteristics) of fault nodal planes or the P, B, and T axes of a set of focal mechanism data can provide information about background stress causing earthquakes has long been a controversial academic topic. Methods This study systematically investigates this issue through synthetic experiments designed on the basis of the stress–fault slip relationship, with stress parameters including the orientations of the three principal stresses and the stress shape ratio (R). Results The experimental results demonstrate that the spatial distribution patterns of both fault nodal planes and PBT axes are jointly controlled by the stress shape ratio and the fault failure conditions. In most cases, the two nodal planes exhibit widely scattered spatial distributions. Only when the shape ratio is close to 0.5 and the contact area between the Mohr-Coulomb failure envelope and Mohr’s circle is minimized do the distributions of both the actual and the auxiliary planes become relatively concentrated. Under these specific conditions, the fault nodal planes (their normals) gain statistical significance for estimating stress orientations. Identifying the actual fault plane among the two nodal planes in focal mechanisms would enhance the determination of principal stress directions. Notably, the spatial distribution of PBT axes effectively captures both the principal stress orientations and the shape ratio. Key findings include: (1) Due to the influence of fault failure conditions and the shape ratio, the P, B, and T axes may not cluster or disperse simultaneously. However, when clustering occurs, they converge near the $ {\sigma }_{1} $, $ {\sigma }_{2} $, or $ {\sigma }_{3} $ axes, respectively. (2) A ring-shaped (toroidal) distribution of T axes indicates a high R-value. (3) P and T axes never exhibit fully random scattering; if such disorder is observed in real data, it suggests that the focal mechanisms may not share a common stress regime. Conclusion This study provides critical constraints for evaluating whether focal mechanism data used in stress inversion belong to a unified stress regime and for predicting stress parameters from the distribution of PBT axes. [ Significance ] These results offer significant implications for developing and applying stress inversion methodology using focal mechanisms.
- focal mechanism,
- fault nodal planes,
- PBT axes,
- stress tensor

Full-text Translaiton by iFLYTEK

The full translation of the current issue may be delayed. If you encounter a 404 page, please try again later.

FullText(HTML)

References(45)

References

[1]	BEAUCÉ E, VAN DER HILST R D, CAMPILLO M, 2022. An iterative linear method with variable shear stress magnitudes for estimating the stress tensor from earthquake focal mechanism data: method and examples[J]. Bulletin of the Seismological Society of America, 112(3): 1224-1239. doi: 10.1785/0120210319
[2]	BEELER N M, SIMPSON R W, HICKMAN S H, et al., 2000. Pore fluid pressure, apparent friction, and Coulomb failure[J]. Journal of Geophysical Research: Solid Earth, 105(B11): 25533-25542. doi: 10.1029/2000JB900119
[3]	BOTT M H P, 1959. The mechanics of oblique slip faulting[J]. Geological Magazine, 96(2): 109-117. doi: 10.1017/S0016756800059987
[4]	CHEN J, LI J, XIN C J, et al., 2023. Analysis of focal mechanism and regional characteristics of medium and small earthquakes in Yunnan region[J]. Journal of Yunnan University: Natural Sciences Edition, 45(S1): 316-323. (in Chinese with English abstract)
[5]	CHEN Y T, GU H D, 2023. Fundamentals of the theory of seismic sources[M]. Beijing: Science Press. (in Chinese)
[6]	CUI H W, WAN Y G, HUANG J C, et al., 2019. Inversion for the tectonic stress field and the characteristic of the stress shape factor of the detachment slab in the Pamir-Hindu Kush area[J]. Chinese Journal of Geophysics, 62(5): 1633-1649. (in Chinese with English abstract)
[7]	DONG C L, GUO W F, DING D Y, et al., 2025. Analysis of stress field characteristics in Changzhi area of Shanxi Province based on focal mechanism solutions[J]. Journal of Geodesy and Geodynamics, 45(5): 456-463. (in Chinese with English abstract)
[8]	GAO Y, WU J, FUKAO Y, et al., 2011. Shear wave splitting in the crust in North China: stress, faults and tectonic implications[J]. Geophysical Journal International, 187(2): 642-654. doi: 10.1111/j.1365-246X.2011.05200.x
[9]	GEPHART J W, 1990. FMSI: a Fortran program for inverting fault/slickenside and earthquake focal mechanism data to obtain the regional stress tensor[J]. Computers & Geosciences, 16(7): 953-989.
[10]	GEPHART J W, FORSYTH D W, 1984. An improved method for determining the regional stress tensor using earthquake focal mechanism data: application to the San Fernando Earthquake Sequence[J]. Journal of Geophysical Research: Solid Earth, 89(B11): 9305-9320. doi: 10.1029/JB089iB11p09305
[11]	GUAN L N, JIANG G M, 2023. High-precision earthquake locations and deep fault characteristics beneath Xianyou area, Fujian Province[J]. Geoscience, 37(1): 40-47, doi: 10.19657/j.geoscience.1000-8527.2022.071
[12]	JAEGER J C, COOK N G W, ZIMMERMAN R W, 2007. Fundamentals of rock mechanics[M]. 4th ed. Malden: Blackwell Publishing.
[13]	JIA S Q, EATON D W, WONG R C K, 2018. Stress inversion of shear-tensile focal mechanisms with application to hydraulic fracture monitoring[J]. Geophysical Journal International, 215(1): 546-563. doi: 10.1093/gji/ggy290
[14]	LEI X L, SU J R, WANG Z W, 2020. Growing seismicity in the Sichuan Basin and its association with industrial activities[J]. Science China Earth Sciences, 63(11): 1633-1660. doi: 10.1007/s11430-020-9646-x
[15]	LI Z Y, WAN Y G, HU X H, et al., 2020. A genetic algorithm for stress tensor inversion and its application to the northeast margin of the Tibetan Plateau[J]. Chinese Journal of Geophysics, 63(2): 562-572. (in Chinese with English abstract)
[16]	LI Z Y, WAN Y G, LIU R F, et al., 2023. Fault stability analysis and its application in stress inversion quality assessment[J]. Environmental Earth Sciences, 82(24): 609. doi: 10.1007/s12665-023-11304-4
[17]	LI Z Y, WAN Y G, GUO X Y, et al., 2024. Significance of accurate selection of the seismogenic faults from the earthquake focal mechanisms for stress field reconstruction[J]. Chinese Journal of Geophysics, 67(7): 2612-2624. (in Chinese with English abstract)
[18]	LI Z Y, WAN Y G, LIU R F, et al., 2025. Can the azimuth of the horizontal principal stress indicate the azimuth of the three-dimensional principal stress?[J]. Pure and Applied Geophysics, 182(5): 2039-2053. doi: 10.1007/s00024-025-03704-3
[19]	MENG J, ZHANG P, WANG J M, et al., 2024. Study on regional stress background and prevention of the rock burst accident on October 20th, 2018 in the Longyun Coal Industry area, Shandong, China[J]. Journal of Geomechanics, 30(3): 473-486. (in Chinese with English abstract)
[20]	MICHAEL A J, 1987. Use of focal mechanisms to determine stress: a control study[J]. Journal of Geophysical Research: Solid Earth, 92(B1): 357-368. doi: 10.1029/JB092iB01p00357
[21]	SIBSON R H, 1982. Fault zone models, heat flow, and the depth distribution of earthquakes in the continental crust of the United States[J]. Bulletin of the Seismological Society of America, 72(1): 151-163.
[22]	STEIN S, WYSESSION M, 2003. An introduction to seismology, earthquakes, and earth structure[M]. Malden: Blackwell Publishing.
[23]	VAVRYČUK V, 2014. Iterative joint inversion for stress and fault orientations from focal mechanisms[J]. Geophysical Journal International, 199(1): 69-77. doi: 10.1093/gji/ggu224
[24]	VAVRYČUK V, 2015. Earthquake mechanisms and stress field[M]//BEER M, KOUGIOUMTZOGLOU I A, PATELLI E, et al. Encyclopedia of earthquake engineering. Berlin Heidelberg: Springer: 1-21.
[25]	WALLACE R E, 1951. Geometry of shearing stress and relation to faulting[J]. The Journal of Geology, 59(2): 118-130. doi: 10.1086/625831
[26]	WAN Y G, 2016. Introduction to seismology[M]. Beijing: Science Press. (in Chinese)
[27]	WAN Y G, SHENG S Z, HUANG J C, et al., 2016. The grid search algorithm of tectonic stress tensor based on focal mechanism data and its application in the boundary zone of China, Vietnam and Laos[J]. Journal of Earth Science, 27(5): 777-785. doi: 10.1007/s12583-015-0649-1
[28]	XU Z H, WANG S Y, HUANG Y R, et al., 1992. Tectonic stress field of China inferred from a large number of small earthquakes[J]. Journal of Geophysical Research: Solid Earth, 97(B8): 11867-11877. doi: 10.1029/91JB00355
[29]	XUE L, YAO D X, LU H F, et al. , 2018. Focal mechanism solution inversion regional tectonic stress field features in Huainan and Huaibei mining areas[J]. Coal Geology of China, 30(2): 14-17, 79. (in Chinese with English abstract)
[30]	ZHANG B, SUN Y, MA X M, et al., 2023. Analysis of in-situ stress field characteristics and tectonic stability in the Motuo key area of the eastern Himalayan syntaxis[J]. Journal of Geomechanics, 29(3): 388-401. (in Chinese with English abstract)
[31]	ZHAO Y F, SHI W, ZHANG Y, 2023. Study on the reconstruction of the paleo-tectonic stress field and its evolution in the Jinchuan mining district, Gansu Province, China[J]. Journal of Geomechanics, 29(6): 770-785. (in Chinese with English abstract)
[32]	ZOBACK M D, HEALY J H, 1992. In situ stress measurements to 3.5 km depth in the Cajon Pass Scientific Research Borehole: implications for the mechanics of crustal faulting[J]. Journal of Geophysical Research: Solid Earth, 97(B4): 5039-5057. doi: 10.1029/91JB02175
[33]	ZOBACK M L, 1992. First- and second-order patterns of stress in the lithosphere: the World Stress Map Project[J]. Journal of Geophysical Research: Solid Earth, 97(B8): 11703-11728. doi: 10.1029/92JB00132
[34]	陈佳, 李见, 辛灿锦, 等, 2023. 云南地区中小地震震源机制解及分区特征分析[J]. 云南大学学报(自然科学版), 45(S1): 316-323.
[35]	陈运泰, 顾浩鼎, 2023. 震源理论基础[M]. 北京: 科学出版社.
[36]	崔华伟, 万永革, 黄骥超, 等, 2019. 帕米尔—兴都库什地区构造应力场反演及拆离板片应力形因子特征研究[J]. 地球物理学报, 62(5): 1633-1649. doi: 10.6038/cjg2019M0202
[37]	董春丽, 郭文峰, 丁大业, 等, 2025. 基于震源机制解分析山西长治地区应力场特征[J]. 大地测量与地球动力学, 45(5): 456-463. doi: 10.14075/j.jgg.2024.06.267
[38]	关露凝, 江国明, 2023. 福建仙游地区高精度地震震源定位及深部断裂特征[J]. 现代地质, 37(1): 40-47, doi: 10.19657/j.geoscience.1000-8527.2022.071.
[39]	李振月, 万永革, 胡晓辉, 等, 2020. 应力张量反演的遗传算法及其在青藏高原东北缘的应用[J]. 地球物理学报, 63(2): 562-572. doi: 10.6038/cjg2020N0047
[40]	李振月, 万永革, 郭祥云, 等, 2024. 从震源机制中准确识别发震断层面对重构应力场的意义[J]. 地球物理学报, 67(7): 2612-2624. doi: 10.6038/cjg2023R0193
[41]	孟静, 张鹏, 王继明, 等, 2024. 山东龙郓煤业10·20冲击地压事故区域应力背景与防控研究[J]. 地质力学学报, 30(3): 473-486.
[42]	万永革, 2016. 地震学导论[M]. 北京: 科学出版社.
[43]	薛凉, 姚多喜, 鲁海峰, 等, 2018. 两淮矿区震源机制解反演区域构造应力场特征[J]. 中国煤炭地质, 30(2): 14-17, 79. doi: 10.3969/j.issn.1674-1803.2018.02.03
[44]	张斌, 孙尧, 马秀敏, 等, 2023. 东构造结墨脱关键区域地应力场特征及其构造稳定性分析[J]. 地质力学学报, 29(3): 388-401. doi: 10.12090/j.issn.1006-6616.20232908
[45]	赵远方, 施炜, 张宇, 2023. 甘肃金川矿区古构造应力场恢复及演化研究[J]. 地质力学学报, 29(6): 770-785. doi: 10.12090/j.issn.1006-6616.2023161

Relative Articles

Supplements(0)

Cited By

Proportional views

Proportional views

Figures(6)

Get Citation

PDF

XML

Article Metrics

Article views (132) PDF downloads(34)