Accuracy Estimation of Earthquake Source Geometry Parameters by the Sterling Interpolation Method in Nonlinear Inversion
Publication: Journal of Surveying Engineering
Volume 147, Issue 1
Abstract
Estimating the accuracy of source geometry parameters is helpful for understanding error propagation in a nonlinear inversion. To date, no studies have estimated the nonlinear inversion accuracy of source geometry parameters. Multipeak particle swarm optimization (MPSO) is used to invert source geometry parameters, providing them good reliability as is shown by Monte Carlo analysis. Also, Sterling interpolation is introduced to estimate the accuracy of nonlinear inversion of parameters in earthquakes. The square roots of variance in the source geometry parameters are obtained by the displacements and the corresponding errors. A simulation experiment illustrates that changing the number of observation points does not affect the accuracy of the seven source geometry parameters. When the number of observation points is constant, the square roots of variance in the source geometry parameters increase with an increase in noise in the observations. Finally, Sterling interpolation accuracy estimation as proposed is applied to the Lushan and L’Aquila earthquakes. We find that the random noise in the observation data affects the inversion results. The applicability and feasibility of the proposed method are verified.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request. (The raw data of the simulated earthquake, the Lushan and L’Aquila earthquakes, and Figs. 1–9 are provided as .mat files.)
Acknowledgments
This research is supported by the National Natural Science Foundation of China, Grant Nos. 41874001 and 41664001, and the Innovation Found Designated for Graduate Students of ECUT, Grant No. DHYC-201924.
References
Aki, K., and P. G. Richards. 2002. Quantitative seismology. San Francisco: Freeman.
Alkhatib, H., and W. D. Schuh. 2006. “Integration of the Monte Carlo covariance estimation strategy into tailored solution procedures for large scale least squares problems.” J. Geod. 81 (1): 53–66. https://doi.org/10.1007/s00190-006-0034-z.
Anzidei, M., et al. 2009. “Coseismic deformation of the destructive April 6, 2009 L’Aquila earthquake (central Italy) from GPS data.” Geophys. Res. Lett. 36 (17): L17307. https://doi.org/10.1029/2009GL039145.
Cheloni, D., et al. 2010. “Coseismic and initial post-seismic slip of the 2009 Mw 6.3 L’Aquila earthquake, Italy, from GPS measurements.” Geophys. J. Int. 181 (3): 1539–1546. https://doi.org/10.1111/j.1365-246X.2010.04584.x.
Dahlquist, G., and Å. Björck. 1974. Numerical methods. Englewood Cliffs, NJ: Prentice-Hall.
Feng, W. P., and Z. H. Li. 2010. “A novel hybrid PSO/simplex algorithm for determining earthquake source parameters.” [In Chinese.] Process Geophys. 25 (4): 1189–1196.
Fröberg, C. 1970. Introduction to numerical analysis. Boston: Addison Wesley.
Hanks, T., and H. Kanamori. 1979. “A moment magnitude scale.” J. Geophys. Res. 84 (5): 2348–2349. https://doi.org/10.1029/JB084iB05p02348.
Huang, M. H., H. Tung, E. J. Fielding, H. H. Huang, C. Liang, C. Huang, and J. Hu. 2016. “Multiple fault slip triggered above the 2016 Mw 6.4 MeiNong earthquake in Taiwan.” Geophys. Res. Lett. 43 (14): 7459–7467. https://doi.org/10.1002/2016GL069351.
Jiang, Z. S., et al. 2014. “GPS constrained coseismic source and slip distribution of the 2013 Mw 6.6 Lushan, China, earthquake and its tectonic implications.” Geophys. Res. Lett. 41 (2): 407–413. https://doi.org/10.1002/2013GL058812.
Jonsson, S. 2002. “Fault slip distribution of the 1999 Mw 7.1 Hector Mine, California, earthquake, estimated from satellite radar and GPS measurements.” B. Seismol. Soc. Am. 92 (4): 1377–1389. https://doi.org/10.1785/0120000922.
Julier, S., and J. Uhlmann. 1996. A general method for approximating nonlinear transformations of probability distributions. Oxford, UK: Oxford University Press.
Kennedy, J., and R. Eberhart. 1995. “Particle swarm optimization.” In Proc., 1995 IEEE Int. Conf. on Neural Networks, 1942–1948. New York: IEEE.
Li, Z. H., W. P. Feng, Z. H. Xu, P. Cross, and J. F. Zhang. 2013. “The 1998 Mw 5.7 Zhangbei-Shangyi (China) earthquake revisited: A buried thrust fault revealed with interferometric synthetic aperture radar.” Geochem. Geophys. Geosyst. 9 (4): Q04026. https://doi.org/10.1029/2007GC001910.
Merwe, R. V. D. 2004. Sigma point Kalman filters for probabilistic inference in dynamic state space models. Portland, OR: Oregon Health & Science Univ.
Migliaccio, F., M. Reguzzoni, F. Sansö, and N. Tselfes. 2009. “An error model for the GOCE space-wise solution by Monte Carlo methods.” In Observing our changing earth, 337–344. Berlin: Springer.
Nunnari, G., G. Puglisi, and F. Guglielmino. 2005. “Inversion of SAR data in active volcanic areas by optimization techniques.” Nonlinear Processes Geophys. 12: 863–870.
Okada, Y. 1985. “Surface deformation due to shear and tensile faults in a half-space.” Bull. Seismol. Soc. Am. 75 (4): 1135–1154.
Okada, Y. 1992. “Internal deformation due to shear and tensile faults in a half-space.” Bull. Seismol. Soc. Am. 82 (2): 1018–1040.
Paziewski, J., R. Sieradzki, and R. Baryla. 2018. “Multi-GNSS high-rate RTK, PPP and novel direct phase observation processing method: Application to precise dynamic displacement detection.” Meas. Sci. Technol. 29 (3): 035002. https://doi.org/10.1088/1361-6501/aa9ec2.
Paziewski, J., R. Sieradzki, and R. Baryla. 2019. “Detection of structural vibration with high-rate precise point positioning: Case study results based on 100 Hz Multi-GNSS observables and shake-table simulation.” Sensors 19 (22): 4832. https://doi.org/10.3390/s19224832.
Pedersen, R., S. Jonsson, T. Arnadottir, F. Sigmundsson, and K. L. Feigl. 2003. “Fault slip distribution of two June 2000 Mw 6.5 earthquakes in South Iceland estimated from joint inversion of InSAR and GPS measurements.” Earth Planet. Sci. Lett. 213 (3–4): 487–502. https://doi.org/10.1016/S0012-821X(03)00302-9.
Shen, Y. Z., B. F. Li, and Y. Chen. 2011. “An iterative solution of weighted total least squares adjustment.” J. Geod. 85 (4): 229–238. https://doi.org/10.1007/s00190-010-0431-1.
Théa, R., S. Anthony, and S. Mark. 2018. “Accounting for uncertain fault geometry in earthquake source inversions—I: Theory and simplified application.” Geophys. J. Int. 241 (2): 1174–1190. https://doi.org/10.1093/gji/ggy187.
USGS. 2018. Earthquake catalog released by U.S. Geological Survey. Accessed March 13, 2018. https://earthquake.usgs.gov/earthquakes/search/.
Wang, L. Y., and R. Ding. 2020. “Inversion and precision estimation of earthquake fault parameters based on scaled unscented transformation and hybrid PSO/Simplex algorithm with GPS measurement data.” Measurement 153 (Mar): 107422. https://doi.org/10.1016/j.measurement.2019.107422.
Wang, L. Y., F. B. Yu, Z. Q. Li, and C. Y. Zou. 2020. “Jackknife method for variance components estimation of partial EIV model.” J. Surv. Eng. 146 (4): 04020016. https://doi.org/10.1061/(ASCE)SU.1943-5428.0000327.
Wang, L. Y., X. Zhao, W. B. Xu, L. Xie, and N. Fang. 2019. “Co-seismic slip distribution inversion with unequal weighted Laplacian smoothness constraints.” Geophys. J. Int. 218 (1): 145–162. https://doi.org/10.1093/gji/ggz125.
Wang, L. Y., and Y. W. Zhao. 2017. “Unscented transformation with scaled symmetric sampling strategy for precision estimation of total least-squares.” Stud. Geophys. Geod. 61 (3): 385–411. https://doi.org/10.1007/s11200-016-1113-0.
Wang, L. Y., and Y. W. Zhao. 2018. “Scaled unscented transformation of nonlinear error propagation: Accuracy, sensitivity, and applications.” J. Surv. Eng. 144 (1): 04017022. https://doi.org/10.1061/(ASCE)SU.1943-5428.0000243.
Wang, L. Y., and Y. W. Zhao. 2019. “Second order approximating function method for precision estimation of total least squares.” J. Surv. Eng. 145 (1): 04018011. https://doi.org/10.1061/(ASCE)SU.1943-5428.0000266.
Wang, L. Y., and C. Y. Zou. 2019. “Accuracy analysis and applications of the Sterling interpolation method for nonlinear function error propagation.” Measurement 146 (Nov): 55–64. https://doi.org/10.1016/j.measurement.2019.06.017.
Wen, Y. M., P. He, C. J. Xu, and Y. Liu. 2012. “Source parameters of the 2009 L’Aquila earthquake, Italy, from Envisat and ALOS satellite SAR images.” [In Chinese.] Chin. J. Geophys. 55 (1): 53–65.
Xiong, L. Y., C. J. Xu, Y. Liu, Y. M. Wen, and J. Fang. 2020. “3D displacement field of Wenchuan Earthquake based on iterative least squares for virtual observation and GPS/InSAR observations.” Remote Sens. 12 (6): 977. https://doi.org/10.3390/rs12060977.
Xu, P. L., Y. M. Shu, J. N. Liu, T. Nishimura, Y. Shi, and J. T. Freymueller. 2019. “A large scale of apparent sudden movements in Japan detected by high-rate GPS after the 2011 Tohoku Mw 9.0 earthquake: Physical signals or unidentified artifacts?” Earth Planets Space 71 (1): 1–16. https://doi.org/10.1186/s40623-019-1023-9.
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Journal of Surveying Engineering
Volume 147 • Issue 1 • February 2021
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© 2020 American Society of Civil Engineers.
History
Received: Dec 24, 2019
Accepted: Jun 1, 2020
Published online: Sep 16, 2020
Published in print: Feb 1, 2021
Discussion open until: Feb 16, 2021
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