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Magnitude-constrained spatio-temporal hierarchical clustering method for acoustic emission events

Hongyu Zhai1,2 ,  Rui Li1 ,  Ya Zhou3 ,  Wei Zhu4* ,  Changsheng Jiang1,2 ,  Xiangchun Wang3 ,  Yajing Song5 ,  Xiaying Li6,7
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1 Division of Seismology Non-natural Earthquake Research, Institute of Geophysics, China Earthquake Administration, Beijing, China
2 Beijing Baijiatuan Earth Sciences National Observation and Research Station, Beijing, China
3 School of Geophysics and Information Technology, China University of Geosciences, Beijing, China
4 Institute for Deep Earth Science, Chinese Institute of Coal Science, Beijing, China
5 Yaxia National Hydropower Technology Innovation Center Co., Ltd., Chengdu, Sichuan, China
6 State Key Laboratory of Geomechanics and Geotechnical Engineering Safety, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, Hubei, China
7 University of Chinese Academy of Sciences, Beijing, China
JSE, 026250108 https://doi.org/10.36922/JSE026250108
Received: 15 June 2026 | Revised: 20 July 2026 | Accepted: 22 July 2026 | Published online: 12 August 2026
© 2026 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License ( https://creativecommons.org/licenses/by/4.0/ )
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Abstract

Acoustic emission (AE) monitoring is an effective means of investigating the characteristics of fracture surfaces in rocks, and accurate clustering analysis is essential for reliable extraction of fracture-surface information. Rock AE events cluster strongly in space and time, but physically distinct event populations—such as a main fracture and its co-located microcracking—often overlap spatially and differ chiefly in magnitude, so conventional clustering methods constrained only by space and time cannot separate them. In this study, a magnitude-constrained spatio-temporal hierarchical clustering algorithm (MSTC) is proposed. The algorithm introduces a magnitude weighting factor into the spatio-temporal distance metric of an agglomerative hierarchical clustering procedure, so that events close in space and time and similar in magnitude are preferentially grouped, and a minimum-cluster-size filter suppresses background noise. Validation on synthetic data shows that MSTC recovers the correct clusters with an adjusted Rand index of 0.97 over a broad, stable parameter range, whereas the magnitude-free algorithm and the established spatio-temporal density-based spatial clustering of applications with noise and nearest-neighbor methods achieved an adjusted Rand index of 0.82 and fail to separate spatially interleaved, magnitude-distinct populations. Applied to AE data from a triaxial-compression experiment on a partly water-saturated tight sandstone, the algorithm resolves the main fracture, its secondary branch, the terminal fracture network, and off-fault damage; the extracted clusters agree well with the fracture morphology revealed by X-ray computed tomography (CT) scanning, and the strike of the fracture surface fitted from the main-fracture cluster shows only a small deviation from the CT-derived measurement. This study provides a new method for laboratory-scale rock-fracture analysis, and because the algorithm operates on a standard time–location–magnitude event catalog, the workflow extends directly to microseismic monitoring of hydraulic fracturing in unconventional reservoirs—supporting fracture-plane identification, fracture network delineation, and noise rejection—and to rock-mass stability monitoring in underground engineering.

Keywords
Acoustic emission
Magnitude-constrained clustering
Spatio-temporal hierarchical clustering
Fracture identification
Microseismic monitoring
Funding
This work was supported by the National Natural Science Foundation of China (Grant Nos. 42574170 and 42274150).
Conflict of interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
References
  1. Li R, Zhai H, Jiang C, et al. A review of laboratory hydraulic fracturing experiments on shales. Geoenergy Sci Eng. 2025;254:214028. doi: 10.1016/j.geoen.2025.214028
  2. Holditch SA. Tight gas sands. J Pet Technol. 2006;58(06):86-93. doi: 10.2118/103356-JPT
  3. Pang M, Ba J, Carcione JM, Balcewicz M, Yue W, Saenger EH. Acoustic and Electrical Properties of Tight Rocks: A Comparative Study Between Experiment and Theory. Surv Geophys. 2022;43(6):1761-1791. doi: 10.1007/s10712-022-09730-3
  4. Hu D, Li Z, Wei Z, et al. Major advancement in oil and gas exploration of Jurassic channel sandstone in Well Bazhong 1HF in northern Sichuan Basin and its significance. Nat Gas Ind B. 2023;10(3):270-282. doi: 10.1016/j.ngib.2023.05.004
  5. Yang Y, Yang Y, Wen L, et al. New progress and prospect of Middle Permian natural gas exploration in the Sichuan Basin. Nat Gas Ind B. 2021;8(1):35-47. doi: 10.1016/j.ngib.2020.07.002
  6. Zou C, Zhu R, Liu K, et al. Tight gas sandstone reservoirs in China: characteristics and recognition criteria. J Pet Sci Eng. 2012;88-89:82-91. doi: 10.1016/j.petrol.2012.02.001
  7. Ji B, Fang J. An overview of efficient development practices at low permeability sandstone reservoirs in China. Energy Geosci. 2023;4(3):100179. doi: 10.1016/j.engeos.2023.100179
  8. Lufeng Z, Fujian Z, Shicheng Z, Zhun L, Jin W, Yuechun W. Evaluation of permeability damage caused by drilling and fracturing fluids in tight low permeability sandstone reservoirs. J Pet Sci Eng. 2019;175:1122-1135. doi: 10.1016/j.petrol.2019.01.031
  9. Li S, Zhang S, Ma X, et al. Hydraulic Fractures Induced by Water-/Carbon Dioxide-Based Fluids in Tight Sandstones. Rock Mech Rock Eng. 2019;52(9):3323-3340. doi: 10.1007/s00603-019-01777-w
  10. Wu S, Gao K, Wang X, Ge H, Zou Y, Zhang X. Investigating the Propagation of Multiple Hydraulic Fractures in Shale Oil Rocks Using Acoustic Emission. Rock Mech Rock Eng. 2022;55(10):6015-6032. doi: 10.1007/s00603-022-02960-2
  11. Lin C, Jia X, Deng S, et al. The Roles of Micro Pores and Minerals in Shale during Hydraulic Fracturing. Rock Mech Rock Eng. 2024;57(11):10177-10186. doi: 10.1007/s00603-024-04063-6
  12. Zhai H, Chang X, Wang Y, Lei X, Xue Z. Analysis of acoustic emission events induced during stress unloading of a hydraulic fractured Longmaxi shale sample. J Pet Sci Eng. 2020;189:106990. doi: 10.1016/j.petrol.2020.106990
  13. He JC, Zhang KS, Liu HB, Tang MR, Zheng XL, Zhang GQ. Laboratory investigation on hydraulic fracture propagation in sandstone-mudstone-shale layers. Pet Sci. 2022;19(4):1664-1673. doi: 10.1016/j.petsci.2022.03.018
  14. Guo P, Li X, Li S, Mao T. Combined Effect of In Situ Stress Level and Bedding Anisotropy on Hydraulic Fracture Vertical Growth in Deep Marine Shale Revealed via CT Scans and Acoustic Emission. Energies. 2023;16(21):7270. doi: 10.3390/en16217270
  15. Josh M, Delle Piane C, Esteban L, et al. Advanced laboratory techniques characterising solids, fluids and pores in shales. J Pet Sci Eng. 2019;180:932-949. doi: 10.1016/j.petrol.2019.06.002
  16. Wang H. Hydraulic fracture propagation in naturally fractured reservoirs: Complex fracture or fracture networks. J Nat Gas Sci Eng. 2019;68:102911. doi: 10.1016/j.jngse.2019.102911
  17. Zhao N, McLennan J, Deo M. Morphology and Growth of Fractures in Unconventional Reservoirs. In: Canadian Unconventional Resources Conference. Richardson, TX: Society of Petroleum Engineers; 2011. doi: 10.2118/147509-ms
  18. Khoshouei M, Bagherpour R. Application of acoustic emission (AE) in mining and earth sciences: A review. Rud Geol Naft Zb. 2019;34(4):19-31. doi: 10.17794/rgn.2019.4.3
  19. Grosse CU, Ohtsu M, Aggelis DG, Shiotani T, eds. Acoustic Emission Testing. Cham, Switzerland: Springer International Publishing; 2022. doi: 10.1007/978-3-030-67936-1
  20. Lockner DA, Byerlee JD, Kuksenko V, Ponomarev A, Sidorin A. Quasi-static fault growth and shear fracture energy in granite. Nature. 1991;350(6313):39-42. doi: 10.1038/350039a0
  21. Zhang S, Wang C, Zhu G, Gao G, Zhou H. Experimental investigation on fracturing effects in hydraulic sand fracturing with acoustic emission and 3D laser scanning. Sci Rep. 2023;13(1). doi: 10.1038/s41598-023-38775-6
  22. Xue Q, Wang Y, Zhai H, Chang X. Automatic Identification of Fractures Using a Density-Based Clustering Algorithm with Time-Spatial Constraints. Energies. 2018;11(3):563. doi: 10.3390/en11030563
  23. Niemz P, Cesca S, Heimann S, et al. Full-waveform-based characterization of acoustic emission activity in a mine-scale experiment: a comparison of conventional and advanced hydraulic fracturing schemes. Geophys J Int. 2020;222(1):189-206. doi: 10.1093/gji/ggaa127
  24. Zhang Y, Wu W, Yao X, Liang P, Sun L, Liu X. Study on spectrum characteristics and clustering of acoustic emission signals from rock fracture. Circuits Syst Signal Process. 2020;39(2):1133-1145. doi: 10.1007/s00034-019-01168-0
  25. Zhang Z, Hu L, Liu T, Zheng H, Tang C. Cluster and information entropy analysis of acoustic emission during rock failure process. Geomech Eng. 2021;25(2):135-142. doi: 10.12989/gae.2021.25.2.135
  26. Hohl A, Griffith AD, Eppes MC, Delmelle E. Computationally enabled 4D visualizations facilitate the detection of rock fracture patterns from acoustic emissions. Rock Mech Rock Eng. 2018;51(9):2733-2746. doi: 10.1007/s00603-018-1488-z
  27. Khan M, He X, Song D, Li Z, Tian X. Predicting deformation kinetics and fractures propagation in coal-rock masses using acoustic emission testing. Int J Coal Sci Technol. 2025;12(1):28. doi: 10.1007/s40789-025-00768-3
  28. Xue D, Zhang Z, Chen C, et al. Spatial correlation-based characterization of acoustic emission signal-cloud in a granite sample by a cube clustering approach. Int J Min Sci Technol. 2021;31(4):535-551. doi: 10.1016/j.ijmst.2021.05.008
  29. Wu S, Zhao Q, Yang H, Ge H. Combining acoustic emission and unsupervised machine learning to investigate microscopic fracturing in tight reservoir rock. Eng Geol. 2025;347:107939. doi: 10.1016/j.enggeo.2025.107939
  30. Yang J, Mu ZL, Yang SQ, Tian WL. Experimental investigation of microscopic crack development and damage characteristics of sandstone based on acoustic emission characteristic parameters. Geomech Geophys Geo-Energy Geo-Resour. 2022;8(2):51. doi: 10.1007/s40948-022-00361-x
  31. Kamran M, Ullah B, Ahmad M, Sabri MMS. Application of KNN-based isometric mapping and fuzzy c-means algorithm to predict short-term rockburst risk in deep underground projects. Front Public Health. 2022;10. doi: 10.3389/fpubh.2022.1023890
  32. Cesca S, Şen AT, Dahm T. Seismicity monitoring by cluster analysis of moment tensors. Geophys J Int. 2014;196(3):1813-1826. doi: 10.1093/gji/ggt492
  33. Wang C, Hou X, Liu Y. Three-dimensional crack recognition by unsupervised machine learning. Rock Mech Rock Eng. 2021;54(2):893-903. doi: 10.1007/s00603-020-02287-w
  34. Su G, Huang J, Xu H, Qin Y. Extracting acoustic emission features that precede hard rock instability with unsupervised learning. Eng Geol. 2022;306:106761. doi: 10.1016/j.enggeo.2022.106761
  35. Prabhakaran R, Bertotti G, Urai J, Smeulders D. Investigating spatial heterogeneity within fracture networks using hierarchical clustering and graph distance metrics. Solid Earth. 2021;12(10):2159-2209. doi: 10.5194/se-12-2159-2021
  36. Karimpouli S, Kwiatek G, Martínez-Garzón P, Dresen G, Bohnhoff M. Unsupervised clustering of catalogue-driven features for characterizing temporal evolution of labquake stress. Geophys J Int. 2024;237(2):755-771. doi: 10.1093/gji/ggae071
  37. Coléou T, Poupon M, Azbel K. Unsupervised seismic facies classification: A review and comparison of techniques and implementation. Leading Edge. 2003;22(10):942-953. doi: 10.1190/1.1623635
  38. Georgoulas G, Konstantaras A, Katsifarakis E, Stylios CD, Maravelakis E, Vachtsevanos GJ. "Seismic-mass" density-based algorithm for spatio-temporal clustering. Expert Syst Appl. 2013;40(10):4183-4189. doi: 10.1016/j.eswa.2013.01.028
  39. Zaliapin I, Ben-Zion Y. A global classification and characterization of earthquake clusters. Geophys J Int. 2016;207(1):608-634. doi: 10.1093/gji/ggw300
  40. Zaliapin I, Ben-Zion Y. Earthquake Declustering Using the Nearest-Neighbor Approach in Space-Time-Magnitude Domain. J Geophys Res Solid Earth. 2020;125(4):e2018JB017120. doi: 10.1029/2018JB017120
  41. Zaliapin I, Ben-Zion Y. Earthquake clusters in southern California I: Identification and stability. J Geophys Res Solid Earth. 2013;118(6):2847-2864. doi: 10.1002/jgrb.50179
  42. Yamagishi Y, Saito K, Hirahara K, Ueda N. Spatio-temporal clustering of earthquakes based on distribution of magnitudes. Appl Netw Sci. 2021;6(1). doi: 10.1007/s41109-021-00413-3
  43. Bien J, Tibshirani R. Hierarchical Clustering With Prototypes via Minimax Linkage. J Am Stat Assoc. 2011;106(495):1075-1084. doi: 10.1198/jasa.2011.tm10183
  44. Murtagh F, Contreras P. Algorithms for hierarchical clustering: an overview. Wiley Interdiscip Rev Data Min Knowl Discov. 2012;2(1):86-97. doi: 10.1002/widm.53
  45. Fernández A, Gómez S. mdendro: An R Package for Extended Agglomerative Hierarchical Clustering. J Stat Softw. 2025;114(2):1-26. doi: 10.18637/jss.v114.i02
  46. Shang X, Li X, Morales-Esteban A, Asencio-Cortés G, Wang Z. Data Field-Based K-Means Clustering for Spatio-Temporal Seismicity Analysis and Hazard Assessment. Remote Sens. 2018;10(3):461. doi: 10.3390/rs10030461
  47. Steinley D. Properties of the hubert-arable adjusted rand index. Psychol Methods. 2004;9(3):386-396. doi: 10.1037/1082-989X.9.3.386
  48. Scholz CH. On the stress dependence of the earthquake b value. Geophys Res Lett. 2015;42(5):1399-1402. doi: 10.1002/2014GL062863
  49. Utsu T, Ogata Y. The centenary of the Omori formula for a decay law of aftershock activity. J Phys Earth. 1995;43(1):1-33. doi: 10.4294/jpe1952.43.1
  50. Baiesi M, Paczuski M. Scale-free networks of earthquakes and aftershocks. Phys Rev E. 2004;69(6):066106. doi: 10.1103/PhysRevE.69.066106
  51. Li X, Lei X, Shen H, Li Q. Fracturing Around Dry/Wet Boundary in Tight Sandstones Monitored by Micro-seismicity in Laboratory. Rock Mech Rock Eng. 2023;56(5):3693-3708. doi: 10.1007/s00603-023-03241-2
  52. Lei X, Kusunose K, Rao MVMS, Nishizawa O, Satoh T. Quasi-static fault growth and cracking in homogeneous brittle rock under triaxial compression using acoustic emission monitoring. J Geophys Res Solid Earth. 2000;105(B3):6127-6139. doi: 10.1029/1999JB900385
  53. Lei X. Evolution of b-value and fractal dimension of acoustic emission events during shear rupture of an immature fault in granite. Appl Sci. 2019;9(12):2498. doi: 10.3390/app9122498
  54. Lei X, Ohuchi T, Kitamura M, Li X, Li Q. An effective method for laboratory acoustic emission detection and location using template matching. J Rock Mech Geotech Eng. 2022;14(5):1642-1651. doi: 10.1016/j.jrmge.2022.03.010
  55. Lei X, Ma S. Laboratory acoustic emission study for earthquake generation process. Earthq Sci. 2014;27(6):627-646. doi: 10.1007/s11589-014-0103-y
  56. Thapa N, Dresen G, Goebel TH. Does b-Value Increase With Pore-Pressure? Insights From Laboratory Experiments and Induced Seismicity. Geophys Res Lett. 2025;52(11):e2025GL115740. doi: 10.1029/2025GL115740
  57. Rivière J, Lv Z, Johnson PA, Marone C. Evolution of b-value during the seismic cycle: Insights from laboratory experiments on simulated faults. Earth Planet Sci Lett. 2018;482:407-413. doi: 10.1016/j.epsl.2017.11.036
  58. Goebel THW, Kwiatek G, Becker TW, Brodsky EE, Dresen G. What allows seismic events to grow big? Insights from b-value and fault roughness analysis in laboratory stick-slip experiments. Geology. 2017;45(9):815-818. doi: 10.1130/G39147.1
  59. Jones R, Stewart R. A method for determining significant structures in a cloud of earthquakes. J Geophys Res Solid Earth. 1997;102(B4):8245-8254. doi: 10.1029/96JB03739
  60. Williams-Stroud S, Ozgen C, Billingsley RL. Microseismicity-constrained discrete fracture network models for stimulated reservoir simulation. Geophysics. 2013;78(1):B37-B47. doi: 10.1190/geo2011-0061.1
  61. Mayerhofer MJ, Lolon EP, Warpinski NR, Cipolla CL, Walser D, Rightmire CM. What is stimulated reservoir volume? SPE Prod Oper. 2010;25(01):89-98. doi: 10.2118/119890-PA
  62. Cipolla C, Wallace J. Stimulated reservoir volume: A misapplied concept? In: SPE Hydraulic Fracturing Technology Conference. Richardson, TX: Society of Petroleum Engineers; 2014. doi: 10.2118/168596-ms
  63. Jones GA, Kendall JM, Bastow ID, Raymer DG. Locating microseismic events using borehole data. Geophys Prospect. 2014;62(1):34-49. doi: 10.1111/1365-2478.12076
  64. Fuggi A, Re S, Tango G, Del Gaudio S, Brovelli A, Cassiani G. Assessment of earthquake location uncertainties for the design of local seismic networks. Earthq Sci. 2024;37(5):415-433. doi: 10.1016/j.eqs.2024.06.006
  65. Langet N, Goertz-Allmann B, Oye V, et al. Joint focal mechanism inversion using downhole and surface monitoring at the Decatur, Illinois, CO2 injection site. Bull Seismol Soc Am. 2020;110(5):2168-2187. doi: 10.1785/0120200075
  66. Mignan A, Werner MJ, Wiemer S, Chen CC, Wu YM. Bayesian estimation of the spatially varying completeness magnitude of earthquake catalogs. Bull Seismol Soc Am. 2011;101(3):1371-1385. doi: 10.1785/0120100223
  67. von Luxburg U. Clustering stability: an overview. Found Trends Mach Learn. 2010;2(3):235-274. doi: 10.1561/2200000008
  68. Cesca S. Seiscloud, a tool for density-based seismicity clustering and visualization. J Seismol. 2020;24(3):443-457. doi: 10.1007/s10950-020-09921-8
  69. Gibbons SJ, Ringdal F. The detection of low magnitude seismic events using array-based waveform correlation. Geophys J Int. 2006;165(1):149-166. doi: 10.1111/j.1365-246X.2006.02865.x
  70. Zhu W, Beroza GC. PhaseNet: a deep-neural-network-based seismic arrival-time picking method. Geophys J Int. 2018. doi: 10.1093/gji/ggy423
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