Citation: | KONG Yue, LI Min, CHEN Weiminet al. Sensor arrangement in moment-tensor inversion for cracks[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(7): 1380-1387. doi: 10.13700/j.bh.1001-5965.2018.0705(in Chinese) |
The moment-tensor inversion method utilizes acoustic-emission signal to obtain cracking information and is regarded as an effective tool to monitor the dynamic growth of cracks. However, in engineering practices, the signal, got by sensors, is always contaminated by noise. The noise will reduce moment-tensor accuracy, and even cause completely wrong results. Sensor arrangements are studied to suppress the effect of noise on moment-tensor accuracy. Based on the first-arrival polarity method, the theory of choosing sensor locations is analyzed. The sensitivity of moment-tensor inversion accuracy to noise is investigated with different sensor arrangements by the use of synthetical acoustic-emission signal. The results show that the pentagonal arrangement of sensors is a superior form, where five sensors locate on a circle, the azimuthal angle between adjacent sensors is 72°, and the sixth sensor locates at the center of the circle. Then the condition number of the equation set achieves a relative small value. When the wave amplitude is changed by noise, the moment-tensor result is quite stable and achieves high accuracy. For the determination of sensor arrangement in moment-tensor inversion, the guidelines and theoretical basis of engineering practices are provided in the study.
[1] |
BAIG A, URBANCIC T.Microseismic moment tensors:A path to understanding FRAC growth[J].The Leading Edge, 2010, 29(3):320-324. doi: 10.1190/1.3353729
|
[2] |
BAIG A, URBANCIC T, PRINCE M.Microseismic moment tensors: A path to understanding growth of hydraulic fractures[C]//Canadian Unconventional Resources and International Petroleum Conference.Richardson, Texas: Society of Petroleum Engineers, 2010.
|
[3] |
BURRIDGE R, KNOPOFF L.Body force equivalents for seismic dislocations[J].Bulletin of the Seismological Society of America, 1964, 54(6A):1875-1888.
|
[4] |
KNOPOFF L, RANDALL M J.The compensated linear-vector dipole:A possible mechanism for deep earthquakes[J].Journal of Geophysical Research, 1970, 75(26):4957-4963. doi: 10.1029/JB075i026p04957
|
[5] |
AKI K, PATTON H.Determination of seismic moment tensor using surface waves[J].Tectonophysics, 1978, 49(3-4):213- 222. doi: 10.1016/0040-1951(78)90180-4
|
[6] |
KANAMORI H, GIVEN J W.Use of long-period surface waves for rapid determination of earthquake-source parameters[J].Physics of the Earth and Planetary Interiors, 1981, 27(1):8-31. doi: 10.1016/0031-9201(81)90083-2
|
[7] |
KANAMORI H, GIVEN J W.Use of long-period surface waves for rapid determination of earthquake source parameters 2.Preliminary determination of source mechanisms of large earthquakes(MS ≥ 6.5)in 1980[J].Physics of the Earth and Planetary Interiors, 1982, 30(2-3):260-268. doi: 10.1016/0031-9201(82)90112-1
|
[8] |
SIPKIN S A. Interpretation of non-double-couple earthquake mechanisms derived from moment tensor inversion[J].Journal of Geophysical Research, 1986, 91(B1):531-547. doi: 10.1029/JB091iB01p00531
|
[9] |
JULIAN B R, MILLER A D, FOULGER G R.Non-double-couple earthquakes 1.Theory[J].Reviews of Geophysics, 1998, 36(4): 525-549.
|
[10] |
AKI K, RICHARDS P G.Quantitative seismology[M].San Francisco, CA: W.H.Freeman & Co., 1980.
|
[11] |
OHTSU M.Source inversion of acoustic emission waveform[J].Doboku Gakkai Ronbunshu, 1988, 1988(398):71-79.
|
[12] |
HUDSON J A, PEARCE R G, ROGERS R M.Source type plot for inversion of the moment tensor[J].Journal of Geophysical Research, 1989, 94(B1):765-774. doi: 10.1029/JB094iB01p00765
|
[13] |
DAHM T.Relative moment tensor inversion based on ray theory:Theory and synthetic tests[J].Geophysical Journal International, 1996, 124(1):245-257. doi: 10.1111/gji.1996.124.issue-1
|
[14] |
CHAPMAN C H, LEANEY W S.A new moment-tensor decomposition for seismic events in anisotropic media[J].Geophysical Journal International, 2012, 188(1):343-370. doi: 10.1111/gji.2012.188.issue-1
|
[15] |
GU C, MARZOUK Y M, TOKSÖKZ M.Bayesian moment tensor inversion and uncertainty quantification for induced seismicity:Uncertainties from both the location and velocity model[M]//SEG Technical Program Expanded Abstracts 2017.Tulsa, OK:Society of Exploration Geophysicists, 2017:2784-2790.
|
[16] |
STANCHITS S, VINCIGUERRA S, DRESEN G.Ultrasonic velocities, acoustic emission characteristics and crack damage of basalt and granite[J].Pure and Applied Geophysics, 2006, 163(5):975-994. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=9410fd699cf83866b67a031d9a26f58e
|
[17] |
HAMIEL Y, LYAKHOVSKY V, STANCHITS S, et al.Brittle deformation and damage-induced seismic wave anisotropy in rocks[J].Geophysical Journal International, 2009, 178(2):901-909. doi: 10.1111/gji.2009.178.issue-2
|
[18] |
HUDSON J A.Overall properties of a cracked solid[J].Mathematical Proceedings of the Cambridge Philosophical Society, 2008, 88(2):371. doi: 10.1017-S0305004100057674/
|
[19] |
刘宁, 李敏, 陈伟民.基于EMT采用FEM研究含裂纹介质中弹性波传播机制[J].北京航空航天大学学报, 2015, 41(9):1686-1692. https://bhxb.buaa.edu.cn/CN/abstract/abstract13430.shtml
LIU N, LI M, CHEN W M.Wave propagation in cracked elastic media based on EMT using FEM[J].Journal of Beijing University of Aeronautics and Astronautics, 2015, 41(9):1689-1692(in Chinese). https://bhxb.buaa.edu.cn/CN/abstract/abstract13430.shtml
|
[20] |
FORD S R, DREGER D S, WALTER W R.Identifying isotropic events using a regional moment tensor inversion[J].Journal of Geophysical Research:Solid Earth, 2009, 114(B1):593-602. http://d.old.wanfangdata.com.cn/NSTLQK/NSTL_QKJJ0221070796/
|
[21] |
MUSTAC M, TKALCIC H.On the use of data noise as a site-specific weight parameter in a hierarchical bayesian moment tensor inversion:The case study of the geysers and long valley caldera earthquakes[J].Bulletin of the Seismological Society of America, 2017, 107(4):1914-1922.
|
[22] |
傅一钦.页岩气水力压裂微地震波的时域-频域二维瞬时谱全波形分析[D].北京: 中国科学院大学, 2017.
FU Y Q.Full-waveform analysis in time-frequency domain of micro-seismic wave during shale hydraulic fracturing[D].Beijing: University of Chinese Academy of Sciences, 2017(in Chinese).
|
[23] |
ABDEL-AAL A A K, YAGI Y.Earthquake source characterization, moment tensor solutions, and stress field of small-moderate earthquakes occurred in the northern Red Sea Triple Junction[J].Geosciences Journal, 2017, 21(2):235-251. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=891c9c209213ca2df5c2fe4437d57234
|
[24] |
CESCA S, HEIMANN S, KRIEGEROWSKI M, et al.Moment tensor inversion for nuclear explosions:What can we learn from the 6 January and 9 September 2016 nuclear tests, North Korea[J].Seismological Research Letters, 2017, 88(2):300-310. http://cn.bing.com/academic/profile?id=2620d6f22b812029ee2fea3824f92796&encoded=0&v=paper_preview&mkt=zh-cn
|
[25] |
DAVI R, VAVRYČUK V, CHARALAMPIDOU E-M, et al.Network sensor calibration for retrieving accurate moment tensors of acoustic emissions[J].International Journal of Rock Mechanics and Mining Sciences, 2013, 62:59-67. doi: 10.1016/j.ijrmms.2013.04.004
|
[26] |
KWIATEK G, CHARALAMPIDOU E-M, DRESEN G, et al.An improved method for seismic moment tensor inversion of acoustic emissions through assessment of sensor coupling and sensitivity to incidence angle[J].International Journal of Rock Mechanics and Mining Sciences, 2014, 65:153-161. doi: 10.1016/j.ijrmms.2013.11.005
|
[27] |
STIERLE E, VAVRYCUK V, KWIATEK G, et al.Seismic moment tensors of acoustic emissions recorded during laboratory rock deformation experiments:Sensitivity to attenuation and anisotropy[J].Geophysical Journal International, 2016, 205(1):38-50. doi: 10.1093/gji/ggw009
|
[28] |
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. http://d.old.wanfangdata.com.cn/Conference/7958657
LIU P X, CHEN S Y, GUO Y S, et al.Moment tensor inversion of acoustic emission[J].Chinese Journal of Geophysics, 2014, 57(3):858-866(in Chinese). http://d.old.wanfangdata.com.cn/Conference/7958657
|
[29] |
OHTSU M.Acoustic emission theory for moment tensor analysis[J].Research in Nondestructive Evaluation, 1995, 6(3):169-184. doi: 10.1080/09349849509409555
|