基于Langston分解和Hilbert变换约束的区域偏量矩张量反演方法及其应用
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摘要
本文基于Langston的震源机制分解方法以及Minson和Dreger修正后的近场位移的解析解表达式,给出了一种区域纯偏量矩张量的求解方法,方法使用基于Hilbert变换的波形包络作为增强约束.对该方法进行了数值试验.试验结果表明,定位准确且速度结构已知的情况下,背景高斯噪声水平达30%时,该方法仍可以得到较稳定的解;使用0.01—0.1Hz的中长周期频段进行反演,在随机震相到时误差最大±3s的情况下,近90%的情况可以得到相对准确的解.速度结构模型的干扰试验表明,平均模型接近真实地壳结构时,可以得到接近真实的解;模型与真实的地壳结构的误差在10%以内时,得到的解与真实解比较接近;误差接近20%时,矩张量解会出现很大的偏差;地震的定位误差主要影响震源深度的判定,从而导致最终解中出现虚假的非双力偶成分,但在约束为偏量矩张量的情况下,反演得到的断层面参数与真实解偏差不大;在台站方位角覆盖较差(<60°)的情况下,使用平均模型仍可以得到较为准确的解.使用该方法研究了2010年10月24日河南周口太康MW4.7地震的震源机制,结果显示矩张量解与初动符号解较为一致.
Based on Langston's decomposition theory and Minson and Dreger's near-field displacement formula,this paper proposes a deviatoric moment tensor inversion method.Waveform's envelop function calculated from Hilbert transform is introduced to stabilize the inversion.The method is successfully tested with synthetic data.Numerical experiment result shows that the method has decent robustness and stabilization.Specific results are as follows.(1) While the velocity structure and earthquake location are exactly known,the solution will be accurate and stable(Kagan angle<5°,the error of double couple component percent,noted as DC%,within ±5%),despite of high noise level even reaching to 30% of original signals.(2) While random disturbances on wave arrival time are limited within ±3 s,the moment tensor solutions inverted in 0.01—0.1 Hz frequency range are still entirely stable.About two-thirds of solutions can be considered to be very close to the true solution(Kagan angle<15°,DC% within ±5%),and about 90% of solutions have a small deviation to the true ones(Kagan angle<30°,DC% within ±10%).It shows that the method has good compatibility with crustal anisotropy and lateral heterogeneity.(3) The test results under various crust models show that the velocity model has important effect on inversion result.If a 1D model being close to the mean model of true crust structure is used,the inversion can retrieve near-real solution.If the model is a little different from the true model(no more than 10% error),the solution would be close to the real one;if the error exceeds 10%,even reaching to 20%,of original signals,the solution will have notable bias.(4) Earthquake location error mainly affects focal depth determination,accordingly cause spurious non-DC component in final solution.But,with the constraint of pure deviatoric moment tensor,the fault parameters retrieved from inversion have little bias from the real one.(5) In case of sparse data(3 stations at least) and worse station coverage(less than 60°),we can still get relatively correct solution from the method under mean crust model.The method is applied to 24 Oct.2010 Zhoukou--Taikang MW4.7 event in Henan province,China.The optimized solution retrieved by this method is consistent with that estimated from P wave polarity data.
Based on Langston's decomposition theory and Minson and Dreger's near-field displacement formula,this paper proposes a deviatoric moment tensor inversion method.Waveform's envelop function calculated from Hilbert transform is introduced to stabilize the inversion.The method is successfully tested with synthetic data.Numerical experiment result shows that the method has decent robustness and stabilization.Specific results are as follows.(1) While the velocity structure and earthquake location are exactly known,the solution will be accurate and stable(Kagan angle<5°,the error of double couple component percent,noted as DC%,within ±5%),despite of high noise level even reaching to 30% of original signals.(2) While random disturbances on wave arrival time are limited within ±3 s,the moment tensor solutions inverted in 0.01—0.1 Hz frequency range are still entirely stable.About two-thirds of solutions can be considered to be very close to the true solution(Kagan angle<15°,DC% within ±5%),and about 90% of solutions have a small deviation to the true ones(Kagan angle<30°,DC% within ±10%).It shows that the method has good compatibility with crustal anisotropy and lateral heterogeneity.(3) The test results under various crust models show that the velocity model has important effect on inversion result.If a 1D model being close to the mean model of true crust structure is used,the inversion can retrieve near-real solution.If the model is a little different from the true model(no more than 10% error),the solution would be close to the real one;if the error exceeds 10%,even reaching to 20%,of original signals,the solution will have notable bias.(4) Earthquake location error mainly affects focal depth determination,accordingly cause spurious non-DC component in final solution.But,with the constraint of pure deviatoric moment tensor,the fault parameters retrieved from inversion have little bias from the real one.(5) In case of sparse data(3 stations at least) and worse station coverage(less than 60°),we can still get relatively correct solution from the method under mean crust model.The method is applied to 24 Oct.2010 Zhoukou--Taikang MW4.7 event in Henan province,China.The optimized solution retrieved by this method is consistent with that estimated from P wave polarity data.
引文
李旭,陈运泰.1996.用长周期地震波波形资料反演1990年青海共和地震的震源过程[J].地震学报,18(3):279-286.
倪江川,陈运泰,陈祥熊.1991.地震矩张量的及其反演[J].地震地磁观测与研究,12(5):1-17.
许力生,陈运泰.1997.震源深度误差对矩张量反演的影响[J].地震学报,19(5):462-470.
许力生,陈运泰.2004.从全球长周期波形资料反演2001年11月14日昆仑山口地震时空破裂过程[J].中国科学:D辑,34(3):256-264.
许力生,蒋长胜,陈运泰,李春来,张天中.2007.2004年首都圈地区中小地震的矩张量反演[J].地震学报,29(3):229-239.
姚振兴,郑天愉.1994.用P波波形资料反演中强地震地震矩张量的方法[J].地球物理学报,37(1):37-44.
张勇,冯万鹏,许力生,周成虎,陈运泰.2008.2008年汶川大地震的时空破裂过程[J].中国科学:D辑,38(10):1186-1194.
Ammon C J,Herrmann R B,Langston C A,Benz H.1998.Faulting parameters of the January16,1994WyomissingHills,Pennsylvania earthquakes[J].Seism Res Lett,69(3):261-269.
Braunmiller J,Kradolfer U,Baer M,Giardini D.2002.Regional moment tensor determination in the European-Mediter-ranean area—initial results[J].Tectonophysics,356(1-3):5-22.
Cesca S,Buforn E,Dahm T.2006.Amplitude spectra moment tensor inversion of shallow earthquakes in Spain[J].Geo-phys J Int,166(2):839-854.
Chen Y T,Xu L S,Li X,Zhao M.1996.Source process of the1990Gonghe,China,earthquake and tectonic stress fieldin the northeastern Qinghai-Xizang(Tibetan)plateau[J].Pure Appl Geophys,146(3-4):697-715.
Dahm T.1996.Relative moment tensor inversion based on ray theory:Theory and synthetic tests[J].Geophys J Int,124(1):245-257.
Dreger D S,Helmberger D V.1993.Determination of source parameters at regional distances with single station orsparse network data[J].J Geophys Res,98(5):8107-8125.
Dziewonski A M,Chou T A,Woodhouse J H.1981.Determination of earthquake source parameters from waveform datafor studies of global and regional seismicity[J].J Geophys Res,86(B4):2825-2852.
Dziewonski A,Woodhouse J.1983.An experiment in systematic study of global seismicity:Centroid moment tensor so-lutions for201moderate and large earthquakes of1981[J].J Geophys Res,84(B4):3247-3271.
Gilbert F.1970.Excitation of the normal modes of the earth by earthquake sources[J].Geophys J R astr Soc,22(2):223-226.
Godano M,Regnier M,Deschamps A,Bardainne T,Gaucher E.2009.Focal mechanisms from sparse observations bynonlinear inversion of amplitude:Method and tests on synthetic and real data[J].Bull Seism Soc Amer,99(4):2243-2264.
He Y M,Wang W M,Yao Z X.2002.A procedure for modeling shallow dislocation sources with tensional component[J].Chin Phys Lett,19(3):441-444.
Helmberger D V.1974.Generalized ray theory for shear dislocations[J].Bull Seism Soc Amer,64(1):45-64.
Helmberger D V.1983.Theory and application of synthetic seismograms[G]∥Kanamori H,Boschi E eds.Earthquakes:Observation,Theory and Interpretation.Amsterdam:North-Holland:174-222.
Ichinose A G,Anderson J G,Smith K D,Zeng Y.2003.Source parameters of Eastern California and Western Nevadaearthquakes from regional moment tensor inversion[J].Bull Seism Soc Amer,93(1):61-84.
Jiang C S,Wu Z L.2006.Location accuracy of the China National Seismograph Network estimated by repeating events[J].Earthquake Research in China,20(1):67-74.
Jost M L,Herrmann R B.1989.A student’s guide to and review of moment tensors[J].Seism Res Lett,60(2):37-57.
Julian B R.1983.Evidence for dyke intrusion earthquake mechanisms near Long Valley caldera,California[J].Nature,303(5915):323-325.
Kagan Y Y.1991.3-D rotation of double-couple earthquake sources[J].Geophys J Int,106(3):709-716.
Kawakatsu H.1995.Automated near-realtime CMT inversion[J].Geophys Res Lett,22(19):2569-2572.
Kennett B.1983.Seismic Wave Propagation in Stratified Media[M].Cambridge:Cambridge University Press:1-339.
Kravanja S,Panza G F,ílenJ.1999.Robust retrieval of a seismic point-source time function[J].Geophys J Int,136(2):385-394.
Kubo A,Fukuyama E,Kawai H,Nonomura K.2002.NIED seismic moment tensor catalogue for regional earthquakesaround Japan:Quality test and application[J].Tectonophysics,356(1-3):23-48.
Langston C A.1979.Structure under Mount Rainier,Washington,inferred from teleseismic body waves[J].J GeophysRes,84(B9):4749-4762.
Langston C A.1981.Source inversion of seismic waveforms:The Koyna,India,earthquakes of13September1967[J].Bull Seism Soc Amer,71(1):1-24.
Langston C A,Helmberger D V.1975.A procedure for modeling shallow dislocation sources[J].Geophys J R astr Soc,42(1):117-130.
Langston C A,Nyblade A A,Owens T J.2002.Regional wave propagation in Tanzania,East Africa[J].J GeophysRes,107(B1):1-18.
Lienert B R.1997.Assessment of earthquake location accuracy and confidence region estimates using known nuclear tests[J].Bull Seism Soc Amer,87(5):1150-1157.
Liu Q,Polet J,Komatitsch D,Tromp J.2004.Spectral-element moment tensor inversions for earthquakes in SouthernCalifornia[J].Bull Seism Soc Amer,94(5):1748-1761.
Miller A D,Foulger G R,Julian B R.1998.Non-double-couple earthquakes2:Observations[J].Reviews of Geophys-ics,36(4):551-568.
Minson S E,Dreger D S.2008.Stable inversions for complete moment tensors[J].Geophys J Int,174(2):585-592.
Pasyanos M E,Dreger D S,Romanowicz B.1996.Toward real-time estimation of regional moment tensors[J].BullSeism Soc Amer,86(5):1255-1269.
Randall G E,Ammon C J,Owens T J.1995.Moment tensor estimation using regional seismograms from a Tibetan plat-eau portable network deployment[J].Geophys Res Lett,22(13):1665-1668.
Roumelioti Z,Kiratzi A,Benetatos C.2010.Time-domain moment tensors for shallow(h≤40km)earthquakes in thebroader Aegean Sea for the years2006and2007:The database of the Aristotle University of Thessaloniki[J].Jour-nal of Geodynamics,51(2-3):179-189.
Scognamiglio L,Tinti E,Michelini A.2009.Real-time determination of seismic moment tensor for the Italian region[J].Bull Seism Soc Amer,99(4):2223-2242.
Sipkin S A.1982.Estimation of earthquake source parameters by the inversion of waveform data:Synthetic waveforms[J].Phys Earth Planet Inter,30(2-3):242-259.
Sipkin S A.1986.Interpretation of non-double-couple earthquake mechanisms derived from moment tensor inversion[J].J Geophys Res,91(B1):531-547.
ílenJ,Panza G F,Campus P.1992.Waveform inversion for point source moment tensor retrieval with variable hypo-central depth and structural model[J].Geophys J Int,109(2):259-274.
Zahradnik J,Jansky J,Plicka V.2008.Detailed waveform inversion for moment tensors of M～4events:Examples fromthe Corinth Gulf,Greece[J].Bull Seism Soc Amer,98(6):2756-2771.
Zhao L,Helmberger D V.1994.Source estimation from broadband regional seismograms[J].Bull Seism Soc Amer,84(1):91-104.
倪江川,陈运泰,陈祥熊.1991.地震矩张量的及其反演[J].地震地磁观测与研究,12(5):1-17.
许力生,陈运泰.1997.震源深度误差对矩张量反演的影响[J].地震学报,19(5):462-470.
许力生,陈运泰.2004.从全球长周期波形资料反演2001年11月14日昆仑山口地震时空破裂过程[J].中国科学:D辑,34(3):256-264.
许力生,蒋长胜,陈运泰,李春来,张天中.2007.2004年首都圈地区中小地震的矩张量反演[J].地震学报,29(3):229-239.
姚振兴,郑天愉.1994.用P波波形资料反演中强地震地震矩张量的方法[J].地球物理学报,37(1):37-44.
张勇,冯万鹏,许力生,周成虎,陈运泰.2008.2008年汶川大地震的时空破裂过程[J].中国科学:D辑,38(10):1186-1194.
Ammon C J,Herrmann R B,Langston C A,Benz H.1998.Faulting parameters of the January16,1994WyomissingHills,Pennsylvania earthquakes[J].Seism Res Lett,69(3):261-269.
Braunmiller J,Kradolfer U,Baer M,Giardini D.2002.Regional moment tensor determination in the European-Mediter-ranean area—initial results[J].Tectonophysics,356(1-3):5-22.
Cesca S,Buforn E,Dahm T.2006.Amplitude spectra moment tensor inversion of shallow earthquakes in Spain[J].Geo-phys J Int,166(2):839-854.
Chen Y T,Xu L S,Li X,Zhao M.1996.Source process of the1990Gonghe,China,earthquake and tectonic stress fieldin the northeastern Qinghai-Xizang(Tibetan)plateau[J].Pure Appl Geophys,146(3-4):697-715.
Dahm T.1996.Relative moment tensor inversion based on ray theory:Theory and synthetic tests[J].Geophys J Int,124(1):245-257.
Dreger D S,Helmberger D V.1993.Determination of source parameters at regional distances with single station orsparse network data[J].J Geophys Res,98(5):8107-8125.
Dziewonski A M,Chou T A,Woodhouse J H.1981.Determination of earthquake source parameters from waveform datafor studies of global and regional seismicity[J].J Geophys Res,86(B4):2825-2852.
Dziewonski A,Woodhouse J.1983.An experiment in systematic study of global seismicity:Centroid moment tensor so-lutions for201moderate and large earthquakes of1981[J].J Geophys Res,84(B4):3247-3271.
Gilbert F.1970.Excitation of the normal modes of the earth by earthquake sources[J].Geophys J R astr Soc,22(2):223-226.
Godano M,Regnier M,Deschamps A,Bardainne T,Gaucher E.2009.Focal mechanisms from sparse observations bynonlinear inversion of amplitude:Method and tests on synthetic and real data[J].Bull Seism Soc Amer,99(4):2243-2264.
He Y M,Wang W M,Yao Z X.2002.A procedure for modeling shallow dislocation sources with tensional component[J].Chin Phys Lett,19(3):441-444.
Helmberger D V.1974.Generalized ray theory for shear dislocations[J].Bull Seism Soc Amer,64(1):45-64.
Helmberger D V.1983.Theory and application of synthetic seismograms[G]∥Kanamori H,Boschi E eds.Earthquakes:Observation,Theory and Interpretation.Amsterdam:North-Holland:174-222.
Ichinose A G,Anderson J G,Smith K D,Zeng Y.2003.Source parameters of Eastern California and Western Nevadaearthquakes from regional moment tensor inversion[J].Bull Seism Soc Amer,93(1):61-84.
Jiang C S,Wu Z L.2006.Location accuracy of the China National Seismograph Network estimated by repeating events[J].Earthquake Research in China,20(1):67-74.
Jost M L,Herrmann R B.1989.A student’s guide to and review of moment tensors[J].Seism Res Lett,60(2):37-57.
Julian B R.1983.Evidence for dyke intrusion earthquake mechanisms near Long Valley caldera,California[J].Nature,303(5915):323-325.
Kagan Y Y.1991.3-D rotation of double-couple earthquake sources[J].Geophys J Int,106(3):709-716.
Kawakatsu H.1995.Automated near-realtime CMT inversion[J].Geophys Res Lett,22(19):2569-2572.
Kennett B.1983.Seismic Wave Propagation in Stratified Media[M].Cambridge:Cambridge University Press:1-339.
Kravanja S,Panza G F,ílenJ.1999.Robust retrieval of a seismic point-source time function[J].Geophys J Int,136(2):385-394.
Kubo A,Fukuyama E,Kawai H,Nonomura K.2002.NIED seismic moment tensor catalogue for regional earthquakesaround Japan:Quality test and application[J].Tectonophysics,356(1-3):23-48.
Langston C A.1979.Structure under Mount Rainier,Washington,inferred from teleseismic body waves[J].J GeophysRes,84(B9):4749-4762.
Langston C A.1981.Source inversion of seismic waveforms:The Koyna,India,earthquakes of13September1967[J].Bull Seism Soc Amer,71(1):1-24.
Langston C A,Helmberger D V.1975.A procedure for modeling shallow dislocation sources[J].Geophys J R astr Soc,42(1):117-130.
Langston C A,Nyblade A A,Owens T J.2002.Regional wave propagation in Tanzania,East Africa[J].J GeophysRes,107(B1):1-18.
Lienert B R.1997.Assessment of earthquake location accuracy and confidence region estimates using known nuclear tests[J].Bull Seism Soc Amer,87(5):1150-1157.
Liu Q,Polet J,Komatitsch D,Tromp J.2004.Spectral-element moment tensor inversions for earthquakes in SouthernCalifornia[J].Bull Seism Soc Amer,94(5):1748-1761.
Miller A D,Foulger G R,Julian B R.1998.Non-double-couple earthquakes2:Observations[J].Reviews of Geophys-ics,36(4):551-568.
Minson S E,Dreger D S.2008.Stable inversions for complete moment tensors[J].Geophys J Int,174(2):585-592.
Pasyanos M E,Dreger D S,Romanowicz B.1996.Toward real-time estimation of regional moment tensors[J].BullSeism Soc Amer,86(5):1255-1269.
Randall G E,Ammon C J,Owens T J.1995.Moment tensor estimation using regional seismograms from a Tibetan plat-eau portable network deployment[J].Geophys Res Lett,22(13):1665-1668.
Roumelioti Z,Kiratzi A,Benetatos C.2010.Time-domain moment tensors for shallow(h≤40km)earthquakes in thebroader Aegean Sea for the years2006and2007:The database of the Aristotle University of Thessaloniki[J].Jour-nal of Geodynamics,51(2-3):179-189.
Scognamiglio L,Tinti E,Michelini A.2009.Real-time determination of seismic moment tensor for the Italian region[J].Bull Seism Soc Amer,99(4):2223-2242.
Sipkin S A.1982.Estimation of earthquake source parameters by the inversion of waveform data:Synthetic waveforms[J].Phys Earth Planet Inter,30(2-3):242-259.
Sipkin S A.1986.Interpretation of non-double-couple earthquake mechanisms derived from moment tensor inversion[J].J Geophys Res,91(B1):531-547.
ílenJ,Panza G F,Campus P.1992.Waveform inversion for point source moment tensor retrieval with variable hypo-central depth and structural model[J].Geophys J Int,109(2):259-274.
Zahradnik J,Jansky J,Plicka V.2008.Detailed waveform inversion for moment tensors of M～4events:Examples fromthe Corinth Gulf,Greece[J].Bull Seism Soc Amer,98(6):2756-2771.
Zhao L,Helmberger D V.1994.Source estimation from broadband regional seismograms[J].Bull Seism Soc Amer,84(1):91-104.
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