Advanced Search
Hu Y S，Chen Y L，Liu R F，Liu W. 2022. Quantitative evaluation of modeling error in Lg-wave attenuation model. Acta Seismologica Sinica，44（6）：1019−1034. DOI: 10.11939/jass.20210083
Citation: Hu Y S，Chen Y L，Liu R F，Liu W. 2022. Quantitative evaluation of modeling error in Lg-wave attenuation model. Acta Seismologica Sinica，44（6）：1019−1034. DOI: 10.11939/jass.20210083
shu

Quantitative evaluation of modeling error in Lg-wave attenuation model

  • 1.

    Institute of Geophysics，China Earthquake Administration，Beijing 100081，China

  • 2 .

    Advanced Technology Division，Array Information Technology，Inc.，Greenbelt，Maryland 20770，USA

  • 3.

    The Second Monitoring and Application Center，China Earthquake Administration，Xi'an 710054，China

More Information
  • Received Date: May 18, 2021
  • Revised Date: June 22, 2021
  • Available Online: December 11, 2022
  • Published Date: December 12, 2022
    Graphical Abstract
    • Abstract
  • In this study, we performed comprehensive statistical studies for the characteristics of the modeling error in Lg-wave attenuation model and obtained a two-dimensional crustal Lg-wave attenuation model. The amplitudes of Lg-wave can be strongly influenced by the geometrical spreading function and it is essential to reasonably evaluate the error of the inversion process if we use the inverted method under the meaning of least squares. Based on the modeling error samples collected in the Sichuan-Yunnan region and its adjacent areas, we use three statistical test methods, namely the K-S test, the Q-Q plot, and the normal distribution plot, to analyze the distribution characteristics of modeling errors in the input data of Lg- wave attenuation tomography inversion. We used both the SVD-based tomographic method and the back-projection method to invert for the Lg Q model of the Sichuan-Yunnan region and its adjacent area respectively. Then, we calculated the covariance matrix and the resolution matrix of the model and evaluated the resolution and error of each grid point in the Lg Q model quantitatively. Our results indicate that the modeling errors in the input data obeyed a normal distribution under first-order approximation. By using the data screening technique, we generated a new dataset with nearly perfect normally distributed for Q tomography. Compared with the result of back-projection, the SVD-based method could allow for obtaining a finer resolution of crustal Q value in the areas with dense ray path coverages, where the model resolution can be resolved within a range of 100 km with a relative error of less than 3%.
    • FullText(HTML)
    • References (56)
  • 邓起东,张培震,冉勇康,杨晓平,闵伟,楚全芝. 2002. 中国活动构造基本特征[J]. 中国科学:D辑,32(12):1020–1030.
    Deng Q D,Zhang P Z,Ran Y K,Yang X P,Min W,Chu Q Z. 2003. Basic characteristics of active tectonics of China[J]. Science in China:Series D,46(4):356–372.
    盛骤, 谢式千, 潘承毅. 2008. 概率论与数理统计[M]. 北京: 高等教育出版社: 119–126.
    Sheng Z, Xie S Q, Pan C Y. 2008. Probability Theory and Mathematical Statistics[M]. Beijing: Higher Education Press: 119–126 （in Chinese）.
    郑秀芬,欧阳飚,张东宁,姚志祥,梁建宏,郑洁. 2009. “国家数字测震台网数据备份中心”技术系统建设及其对汶川大地震研究的数据支撑[J]. 地球物理学报,52(5):1412–1417.
    Zheng X F,Ouyang B,Zhang D N,Yao Z X,Liang J H,Zheng J. 2009. Technical system construction of Data Backup Centre for China Seismograph Network and the data support to researches on the Wenchuan earthquake[J]. Chinese Journal of Geophysics,52(5):1412–1417 (in Chinese).
    周连庆,赵翠萍,修济刚,陈章立. 2008. 川滇地区Lg波Q值层析成像[J]. 地球物理学报,51(6):1745–1752. doi: 10.3321/j.issn:0001-5733.2008.06.015
    Zhou L Q,Zhao C P,Xiu J G,Chen Z L. 2008. Tomography of QLg in Sichuan-Yunnan zone[J]. Chinese Journal of Geophysics,51(6):1745–1752 (in Chinese).
    Akinci A,Del Pezzo E,Ibáñez J M. 1995. Separation of scattering and intrinsic attenuation in southern Spain and western Anatolia (Turkey)[J]. Geophys J Int,121(2):337–353. doi: 10.1111/j.1365-246X.1995.tb05715.x
    Backus G,Gilbert F. 1970. Uniqueness in the inversion of inaccurate gross Earth data[J]. Philosophical Transactions of the Royal Society of London. Series A:Mathematical and Physical Sciences,266(1173):123–192.
    Bostock M G,Kennett B L N. 1990. The effect of 3-D structure on Lg propagation patterns[J]. Geophys J Int,101(2):355–364. doi: 10.1111/j.1365-246X.1990.tb06574.x
    Chen Y L,Xie J K. 2017. Resolution,uncertainty and data predictability of tomographic Lg attenuation models:Application to southeastern China[J]. Geophys J Int,210(1):166–183. doi: 10.1093/gji/ggx147
    Chun K Y,West G F,Kokoski R J,Samson C. 1987. A novel technique for measuring Lg attenuation-results from eastern Canada between 1 to 10 Hz[J]. Bull Seismol Soc Am,77(2):398–419. doi: 10.1785/BSSA0770020398
    Dai A,Tang C C,Liu L,Xu R. 2020. Seismic attenuation tomography in southwestern China:Insight into the evolution of crustal flow in the Tibetan Plateau[J]. Tectonophysics,792:228589. doi: 10.1016/j.tecto.2020.228589
    Gallegos A,Ranasinghe N,Ni J,Sandvol E. 2014. Lg attenuation in the central and eastern United States as revealed by the Earth Scope Transportable Array[J]. Earth Planet Sci Lett,402:187–196. doi: 10.1016/j.jpgl.2014.01.049
    Gibbons S J,Kværna T,Ringdal F. 2010. Considerations in phase estimation and event location using small-aperture regional seismic arrays[J]. Pure Appl Geophys,167(4/5):381–399.
    Gök R,Sandvol E,Türkelli N,Seber D,Barazangi M. 2003. Sn attenuation in the Anatolian and Iranian plateau and surrounding regions[J]. Geophys Res Lett,30(24):8042.
    Gung Y,Romanowicz B. 2004. Q tomography of the upper mantle using three-component long-period waveforms[J]. Geophys J Int,157(2):813–830. doi: 10.1111/j.1365-246X.2004.02265.x
    Hearn T M,Wang S Y,Pei S P,Xu Z H,Ni J F,Yu Y X. 2008. Seismic amplitude tomography for crustal attenuation beneath China[J]. Geophys J Int,174(1):223–234. doi: 10.1111/j.1365-246X.2008.03776.x
    Ji C,Tsuboi S,Komatitsch D,Tromp J. 2005. Rayleigh-wave multipathing along the West coast of North America[J]. Bull Seismol Soc Am,95(6):2115–2124. doi: 10.1785/0120040180
    Kennett B L N. 1986. Lg waves and structural boundaries[J]. Bull Seismol Soc Am,76(4):1133–1141.
    Larsen R M, 1998. Lanczos Bidiagonalization With Partial Reorthogonalization[D]. Jutland: Aarhus University: 8–87.
    Liang X F,Sandvol E,Kay S,Heit B,Yuan X H,Mulcahy P,Chen C,Brown L,Comte D,Alvarado P. 2014. Delamination of southern Puna lithosphere revealed by body wave attenuation tomography[J]. J Geophys Res:Solid Earth,119(1):549–566. doi: 10.1002/2013JB010309
    Marden J I. 2004. Positions and QQ plots[J]. Statist Sci,19(4):606–614.
    Massey F J. 1951. The Kolmogorov-Smirnov test for goodness of fit[J]. J Am Statist Associat,46(253):68–78. doi: 10.1080/01621459.1951.10500769
    McNamara D E,Owens T J,Walter W R. 1996. Propagation characteristics of L g across the Tibetan Plateau[J]. Bull Seismol Soc Am,86(2):457–469. doi: 10.1785/BSSA0860020457
    Menke W,Holmes R C,Xie J K. 2006. On the nonuniqueness of the coupled origin time-velocity tomography problem[J]. Bull Seismol Soc Am,96(3):1131–1139. doi: 10.1785/0120050192
    Mitchell B J. 1995. Anelastic structure and evolution of the continental crust and upper mantle from seismic surface wave attenuation[J]. Rev Geophys,33(4):441–462. doi: 10.1029/95RG02074
    Mitchell B J,Hwang H J. 1987. Effect of low Q sediments and crustal Q on L g attenuation in the United States[J]. Bull Seismol Soc Am,77(4):1197–1210. doi: 10.1785/BSSA0770041197
    Mitchell B J,Pan Y,Xie J K,Cong L L. 1997. L g coda Q variation across Eurasia and its relation to crustal evolution[J]. J Geophys Res:Solid Earth,102(B10):22767–22779. doi: 10.1029/97JB01894
    Nolet G. 1987. Seismic Tomography: With Applications in Global Seismology and Exploration Geophysics[M]. Dordrecht: Springer: 1–24.
    Nuttli O W. 1980. The excitation and attenuation of seismic crustal phases in Iran[J]. Bull Seismol Soc Am,70(2):469–485. doi: 10.1785/BSSA0700020469
    Pasyanos M E,Matzel E M,Walter W R,Rodgers A J. 2009. Broad-band L g attenuation modelling in the Middle East[J]. Geophys J Int,177(3):1166–1176. doi: 10.1111/j.1365-246X.2009.04128.x
    Pei S P,Zhao J M,Rowe C A,Wang S Y,Hearn T M,Xu Z H,Liu H B,Sun Y S. 2006. ML amplitude tomography in North China[J]. Bull Seismol Soc Am,96(4A):1560–1566. doi: 10.1785/0120060021
    Pukelsheim F. 1994. The three sigma rule[J]. Am Statist,48(2):88–91.
    Rietbrock A. 2001. P wave attenuation structure in the fault area of the 1995 Kobe earthquake[J]. J Geophys Res:Solid Earth,106(B3):4141–4154. doi: 10.1029/2000JB900234
    Rodgers A J,Ni J F,Hearn T M. 1997. Propagation characteristics of short-period Sn and Lg in the Middle East[J]. Bull Seismol Soc Am,87(2):396–413.
    Romanowicz B. 1998. Attenuation tomography of the earth’s mantle:A review of current status[J]. Pure Appl Geophys,153(2):257–272.
    Schurr B,Asch G,Rietbrock A,Trumbull R,Haberland C. 2003. Complex patterns of fluid and melt transport in the central Andean subduction zone revealed by attenuation tomography[J]. Earth Planet Sci Lett,215(1/2):105–119.
    Sereno T J Jr,Bratt S R,Bache T C. 1988. Simultaneous inversion of regional wave spectra for attenuation and seismic moment in Scandinavia[J]. J Geophys Res:Solid Earth,93(B3):2019–2035. doi: 10.1029/JB093iB03p02019
    Street R L,Herrmann R B,Nuttli O W. 1975. Spectral characteristics of the L g wave generated by central United States earthquakes[J]. Geophys J Int,41(1):51–63. doi: 10.1111/j.1365-246X.1975.tb05484.x
    Tian H Y,He C S,Santosh M. 2021. S-wave velocity structure of the Sichuan-Yunnan region,China:Implications for extrusion of Tibet Plateau and seismic activities[J]. Earth Space Sci,8(7):e2021EA001640.
    Vrbik J. 2020. Deriving CDF of Kolmogorov-Smirnov test statistic[J]. Appl Math,11(3):227–246. doi: 10.4236/am.2020.113018
    Wei Z,Zhao L. 2019. Lg Q model and its implication on high-frequency ground motion for earthquakes in the Sichuan and Yunnan region[J]. Earth Planet Phys,3(6):526–536.
    Wheelan C. 2013. Naked Statistics[M]. London: W W Norton & Company: 19–292.
    Xie J K. 1993. Simultaneous inversion for source spectrum and path Q using L g with application to three semipalatinsk explosions[J]. Bull Seismol Soc Am,83(5):1547–1562. doi: 10.1785/BSSA0830051547
    Xie J K. 1998. Spectral inversion of Lg from earthquakes:A modified method with applications to the 1995,western Texas earthquake sequence[J]. Bull Seismol Soc Am,88(6):1525–1537.
    Xie J. 2002. Lg Q in the eastern Tibetan Plateau[J]. Bull Seismol Soc Am,92(2):871–876. doi: 10.1785/0120010154
    Xie J,Mitchell B J. 1990. A back-projection method for imaging large-scale lateral variations of L g coda Q with application to continental Africa[J]. Geophys J Int,100(2):161–181. doi: 10.1111/j.1365-246X.1990.tb02477.x
    Xie J,Gok R,Ni J,Aoki Y. 2004. Lateral variations of crustal seismic attenuation along the INDEPTH profiles in Tibet from LgQ inversion[J]. J Geophys Res:Solid Earth,109(B10):B10308.
    Xie J,Wu Z,Liu R,Schaff D,Liu Y,Liang J. 2006. Tomographic regionalization of crustal Lg Q in eastern Eurasia[J]. Geophys Res Lett,33(3):L03315.
    Yang X. 2002. A numerical investigation of Lg geometrical spreading[J]. Bull Seismol Soc Am,92(8):3067–3079. doi: 10.1785/0120020046
    Zhao L F,Xie X B,Wang W M,Zhang J H,Yao Z X. 2010. Seismic Lg-wave Q tomography in and around northeast China[J]. J Geophys Res:Solid Earth,115(B8):B08307.
    Zhao L F,Xie X B,He J K,Tian X B,Yao Z X. 2013. Crustal flow pattern beneath the Tibetan Plateau constrained by regional Lg-wave Q tomography[J]. Earth Planet Sci Lett,383:113–122. doi: 10.1016/j.jpgl.2013.09.038
    Zhao L F,Xie X B. 2016. Strong Lg-wave attenuation in the Middle East continental collision orogenic belt[J]. Tectonophysics,674:135–146. doi: 10.1016/j.tecto.2016.02.025
    Zor E,Sandvol E,Xie J,Türkelli N,Mitchell B,Gasanov A H,Yetirmishli G. 2007. Crustal attenuation within the Turkish Plateau and surrounding regions[J]. Bull Seismol Soc Am,97(1B):151–161. doi: 10.1785/0120050227
    • Related Articles

  • Related Articles

    Zhang Fan, Han Xiaoming, Bao Jinzhe, Yang Xiaozhong. 2025: Bayesian estimation of completeness magnitude in the Capital Circle Region. Acta Seismologica Sinica, 47(1): 107-121. DOI: 10.11939/jass.20230140
    Meng Sibo, Wei Shitao, Liu Zhongxian, Li Wenxuan, Liu Ying. 2024: Ground motion variability of a mountain-canyon site near a strike-slip fault considering uncertainty of source. Acta Seismologica Sinica, 46(6): 1034-1050. DOI: 10.11939/jass.20230029
    Liu Ye, Ren Yefei, Wen Ruizhi, Wang Hongwei. 2022: Uncertainties in probabilistic tsunami hazard assessment. Acta Seismologica Sinica, 44(4): 688-699. DOI: 10.11939/jass.20210044
    Li Zongchao, Gao Mengtan, Sun Jize, Chen Xueliang, Zhang Bo. 2021: Empirical relationship of stochastic uncertainty of source parameters in relative local area. Acta Seismologica Sinica, 43(4): 483-497. DOI: 10.11939/jass.20200153
    Liu Sen, Bian Yinju, Wang Tingting, Lu Zhinan. 2021: Study on Lg wave attenuation imaging in Yunnan. Acta Seismologica Sinica, 43(4): 410-426. DOI: 10.11939/jass.20200101
    Li Honglei, Chen Shi. 2019: Crustal density variation and its relationship with the seismogenic structure of strong earthquakes in Sichuan-Yunnan region. Acta Seismologica Sinica, 41(5): 600-612. DOI: 10.11939/jass.20190029
    Zheng Dingchang, Wang Jun. 2017: Love wave tomography in Sichuan-Yunnan area from ambient noise. Acta Seismologica Sinica, 39(5): 633-647. DOI: 10.11939/jass.2017.05.001
    Guo Xing, Pan Hua. 2016: Parameter uncertainty analysis on probability model of strong earthquake recurrence. Acta Seismologica Sinica, 38(2): 298-306. DOI: 10.11939/jass.2016.02.013
    Zhang Xiaotao, Zhang Yongxian, Xia Caiyun, Wu Yongjia, Yu huaizhong. 2014: Anomalous seismic activities in the Sichuan-Yunnan region and its adjacent areas before the Lushan MS7.0 earthquake by the pattern informatics method. Acta Seismologica Sinica, 36(5): 780-789. DOI: 10.3969/j.issn.0253-3782.2014.05.003
    Wang Yushi, Li Xiaojun, Zhou Zhenghua. 2013: Research on attenuation relationships for horizontal strong ground motions in Sichuan--Yunnan region. Acta Seismologica Sinica, 35(2): 238-248. DOI: 10.3969/j.issn.0253-3782.2013.02.010

  • Cited by

    Periodical cited type(1)

    1. 夏文鹤，谢万洋，唐印东，李皋，韩玉娇. 砂样岩屑图像特征的岩性智能高效识别. 石油地球物理勘探. 2023(03): 495-506 .

    Other cited types(1)

Catalog

    Get Citation
    PDF
    XML
    Article views (475) PDF downloads (62) Cited by(2)
    Turn off MathJax
    Article Contents
    Abstract
    References
    Related Articles

    Supported by: Beijing Renhe Information Technology Co., Ltd.   

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return