(1. CCTEG Coal Mining Research Institute, Beijing 100013, China；
2. State Key Laboratory of Intelligent Coal Mining and Strata Control, Beijing 100013, China)
Abstract：High-frequency acoustic emission (AE) signals generated during rock microcracking contain essential source parameters—such as moment magnitude, source radius, and stress drop—that characterize the underlying rupture process. To facilitate their quantitative inversion, this study develops and calibrates a broadband, high-fidelity AE sensor, AcouSeek, which exhibits a flat displacement response across the frequency range of 10 to 1000 kHz. Two standard sources—steel ball impact and capillary glass rupture—are employed to establish an absolute calibration methodology, grounded in Hertzian contact theory and a step-loading model, respectively. In a three-point bending test with controlled crack opening, 24 AcouSeek sensors are utilized to record AE signals. A total of 561 microcracking events are analyzed through displacement-based spectral fitting and physical source models, resulting in moment magnitudes ranging from –8.6 to –7.2, source radii between 1.6 and 2.9 mm, and stress drops between 30 and 82 kPa. The obtained parameters are consistent with those reported for mining-induced and natural earthquakes, demonstrating cross-scale compatibility. This study establishes a comprehensive workflow—from broadband sensing to absolute calibration and source parameter inversion—providing a standardized and extensible approach for integrating laboratory AE studies into the framework of quantitative seismology.
[1] 谢和平，彭瑞东，鞠 杨，等. 岩石破坏的能量分析初探[J]. 岩石力学与工程学报，2005，24(15)：2 603–2 608.(XIE Heping，PENG Ruidong，JU Yang，et al. On energy analysis of rock failure[J]. Chinese Journal of Rock Mechanics and Engineering，2005，24(15)：2 603–2 608.(in Chinese))
[2] 吴顺川，郭 超，高永涛，等. 岩体破裂震源定位问题探讨与展望[J]. 岩石力学与工程学报，2021，40(5)：874–891.(WU Shunchuan，GUO Chao，GAO Yongtao，et al. Discussion and prospect of source location of rock fracture[J]. Chinese Journal of Rock Mechanics and Engineering，2021，40(5)：874–891.(in Chinese))
[3] ISHIDA T，LABUZ J F，MANTHEI G，et al. ISRM suggested method for laboratory acoustic emission monitoring[J]. Rock Mechanics and Rock Engineering，2017，50(3)：665–674.
[4] LEI X，MA S. Laboratory acoustic emission study for earthquake generation process[J]. Earthquake Science，2014，27(6)：627–646.
[5] KWIATEK G，PLENKERS K，DRESEN G，et al. Source parameters of picoseismicity recorded at Mponeng Deep Gold Mine，South Africa：implications for scaling relations[J]. Bulletin of the Seismological Society of America，2011，101(6)：2 592–2 608.
[6] GROSSE C U，OHTSU M. Acoustic emission testing[M]. [S. l.]：[s. n.]，2008：203–310.
[7] 董陇军，张义涵，孙道元，等. 花岗岩破裂的声发射阶段特征及裂纹不稳定扩展状态识别[J]. 岩石力学与工程学报，2022，41(1)：120–131.(DONG Longjun，ZHANG Yihan，SUN Daoyuan，et al. Stage characteristics of acoustic emission and identification of unstable crack state for granite fractures[J]. Chinese Journal of Rock Mechanics and Engineering，2022，41(1)：120–131.(in Chinese))
[8] 杨永杰，王德超，郭明福，等. 基于三轴压缩声发射试验的岩石损伤特征研究[J]. 岩石力学与工程学报，2014，33(1)：98–104.(YANG Yongjie，WANG Dechao，GUO Mingfu，et al. Study of rock damage characteristics based on acoustic emission tests under triaxial compression[J]. Chinese Journal of Rock Mechanics and Engineering，2014，33(1)：98–104.(in Chinese))
[9] DONG L，CHEN Y，SUN D，et al. Implications for rock instability precursors and principal stress direction from rock acoustic experiments[J]. International Journal of Mining Science and Technology，2021，31(5)：789–798.
[10] 刘建坡，刘召胜，王少泉，等. 岩石张拉及剪切破裂声发射震源机制分析[J]. 东北大学学报：自然科学版，2015，36(11)：1 624– 1 628.(LIU Jianpo，LIU Zhaosheng，WANG Shaoquan，et al. Analysis of acoustic emission source mechanisms for tensile and shear cracks of rock fractures[J]. Journal of Northeastern University：Natural Science，2015，36(11)：1 624–1 628.(in Chinese))
[11] 刘培洵，陈顺云，郭彦双，等. 声发射矩张量反演[J]. 地球物理学报，2014，57(3)：858–866.(LIU Peixun，CHEN Shunyun，GUO Yanshuang，et al. Moment tensor inversion of acoustic emission [J]. Chinese Journal of Geophysics，2014，57(3)：858–866.(in Chinese))
[12] 吴顺川，黄小庆，陈 钒，等. 岩体破裂矩张量反演方法及其应用[J]. 岩土力学，2016，37(增1)：1–18.(WU Shunchuan，HUANG Xiaoqing，CHEN Fan，et al. Moment tensor inversion of rock failure and its application[J]. Rock and Soil Mechanics，2016，37(Supp.1)：1–18.(in Chinese))
[13] 王恩元，王笑然，刘晓斐，等. 煤岩张剪破裂震源模型与动裂隙参数定量反演及应用[J]. 中国矿业大学学报，2023，52(6)：1 058–1 074.(WANG Enyuan，WANG Xiaoran，LIU Xiaofei，et al. Generalized tensile-shear fracturing representation and cracking source parameters quantitative inversion in loaded coal/rock and its application[J]. Journal of China University of Mining and Technology，2023，52(6)：1 058–1 074.(in Chinese))
[14] SAVAGE J C. Relation of corner frequency to fault dimensions[J]. Journal of Geophysical Research(1896–1977)，1972，77(20)：3 788– 3 795.
[15] WU R，SELVADURAI P A，CHEN C，et al. Revisiting piezoelectric sensor calibration methods using elastodynamic body waves[J]. Journal of Nondestructive Evaluation，2021，40(3)：68.
[16] BRUNE J N. Tectonic stress and the spectra of seismic shear waves from earthquakes[J]. Journal of Geophysical Research，1970，75(26)：4 997–5 009.
[17] WALTER W R，BRUNE J N. Spectra of seismic radiation from a tensile crack[J]. Journal of Geophysical Research，1993，98(B3)：4 449–4 459.
[18] MAIN I. Statistical physics，seismogenesis，and seismic hazard[J]. Reviews of Geophysics，1996，34(4)：433–462.
[19] 刘希灵，潘梦成，李夕兵，等. 动静加载条件下花岗岩声发射 b 值特征的研究[J]. 岩石力学与工程学报，2017，36(增1)：3 148–3 155. (LIU Xiling，PAN Mengcheng，LI Xibing，et al. Acoustic emission b-value characteristics of granite under dynamic loading and static loading[J]. Chinese Journal of Rock Mechanics and Engineering，2017，36(Supp.1)：3 148–3 155.(in Chinese))
[20] 张黎明，马绍琼，任明远，等. 不同围压下岩石破坏过程的声发射频率及b值特征[J]. 岩石力学与工程学报，2015，24(10)：2 057–2 063. (ZHANG Liming，MA Shaoqiong，REN Mingyuan，et al. Acoustic emission frequency and b value characteristics in rock failure process under various confining pressures[J]. Chinese Journal of Rock Mechanics and Engineering，2015，24(10)：2 057–2 063.(in Chinese))
[21] 李浩然，徐 壮，魏 群，等. 盐岩高温三轴蠕变损伤破裂机制试验研究[J]. 岩石力学与工程学报，2023，42(12)：2 945–2 956.(LI Haoran，XU Zhuang，WEI Qun，et al. Experimental study on salt rock creep damage rupture mechanism in high temperature triaxial conditions[J]. Chinese Journal of Rock Mechanics and Engineering，2023，42(12)：2 945–2 956.(in Chinese))
[22] 任 义，吴顺川，高永涛，等. 传感器校准对花岗岩单轴压缩矩张量分析的影响[J]. 岩土力学，2021，42(2)：451–461.(REN Yi，WU Shunchuan，GAO Yongtao，et al. Effect of sensor calibration on moment tensor analysis of granite uniaxial compression[J]. Rock and Soil Mechanics，2021，42(2)：451–461.(in Chinese))
[23] 吴坤波，邹俊鹏，焦玉勇，等. 深部煤矿强矿震震源参数分析及震源机制研究[J]. 岩石力学与工程学报，2023，42(10)：2 540–2 551. (WU Kunbo，ZOU Junpeng，JIAO Yuyong，et al. Study on the internal relationship of source parameters and focal mechanism of strong mine tremors in deep coal mines[J]. Chinese Journal of Rock Mechanics and Engineering，2023，42(10)：2 540–2 551.(in Chinese))
[24] 陈 栋，王恩元，李 楠. 千秋煤矿微震震源参数特征以及震源机制分析[J]. 煤炭学报，2019，44(7)：2 011–2 019.(CHEN Dong，WANG Enyuan，LI Nan. Analysis of microseismic source parameters and focal mechanism in Qianqiu Coal Mine[J]. Journal of China Coal Society，2019，44(7)：2 011–2 019.(in Chinese))
[25] MCLASKEY G C，LOCKNER D A. Calibrated acoustic emission system records M −3.5 to M −8 events generated on a saw-cut granite sample[J]. Rock Mechanics Rock Engineering，2016，49(11)：4 527–4 536.
[26] SELVADURAI P A. Laboratory insight into seismic estimates of energy partitioning during dynamic rupture：An observable scaling breakdown[J]. Journal of Geophysical Research：Solid Earth，2019，124：11 350–11 379.
[27] LI B Q，EINSTEIN H H. Comparison of visual and acoustic emission observations in a four point bending experiment on Barre Granite[J]. Rock Mechanics and Rock Engineering，2017，50(9)：2 277–2 296.
[28] LI B Q，EINSTEIN H H. Normalized Radiated seismic energy from laboratory fracture experiments on Opalinus Clayshale and Barre Granite[J]. Journal of Geophysical Research：Solid Earth，2020，125(3)：e2019JB018544.
[29] MATTIAT O E. Ultrasonic transducer materials[M]. [S. l.]：Springer Science and Business Media，2013：167–270.
[30] REED J. Energy losses due to elastic wave propagation during an elastic impact[J]. Journal of Physics D：Applied Physics，1985，18(12)：2 329–2 337.
[31] 中华人民共和国国家标准编写组. GB/T 19800－2005 无损检测 声发射检测换能器的一级校准[S]. 北京：中国标准出版社，2005.(The National Standards Compilation Group of People?s Republic of China GB/T 19801—2005 Non-destructive testing-acoustic emission inspection-primary calibration of transducers[S]. Beijing：Standards Press of China，2005.(in Chinese))
[32] ASTM. ASTM D5045-14 Standard test methods for plane-strain fracture toughness and strain energy release rate of plastic materials[S]. West Conshohocken：ASTM International，2007.
[33] HANKS T C. b values and ω-γ seismic source models：Implications for tectonic stress variations along active crustal fault zones and the estimation of high-frequency strong ground motion[J]. Journal of Geophysical Research：Solid Earth，1979，84(B5)：2 235–2 242.
[34] OHTSU M. Simplified moment tensor analysis and unified decomposition of acoustic emission source：application to in situ hydrofracturing test[J]. Journal of Geophysical Research：Solid Earth，1991，96(B4)：6 211–6 221.
[35] 任会兰，宁建国，宋水舟，等. 基于声发射矩张量分析混凝土破坏的裂纹运动[J]. 力学学报，2019，51(6)：1 830–1 840.(REN Huilan，NING Jianguo，SONG Shuizhou，et al. Investigation on crack growth in concrete by moment tensor analysis of acoustic emission[J]. Chinese Journal of Theoretical and Applied Mechanics，2019，51(6)：1 830–1 840.(in Chinese))
[36] 徐世达，李元辉，刘建坡，等. 基于矩张量分析的花岗岩破裂声发射特征试验[J]. 东北大学学报：自然科学版， 2014，35(3)：433–437.(XU Shida，LI Yuanhui，LIU Jianpo，et al. Experiment of characteristics of acoustic emission during granite fracture based on moment tensor analysis[J]. Journal of Northeastern University：Natural Science，2014，35(3)：433–437.(in Chinese))
[37] OHNO K，UJI K，UENO A，et al. Fracture process zone in notched concrete beam under three-point bending by acoustic emission[J]. Construction and Building Materials，2014，67(PART B)：139–145.
[38] WU R，GAO F，PENG X，et al. Size effect of accelerated seismic release from failures under compression in naturally fractured media[J]. Physical Review E，2024，110(4)：044146.
2026, Vol. 45 
