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地球与行星物理

ISSN  2096-3955

CN  10-1502/P

Citation: XinYan Zhang, ZhiMing Bai, Tao Xu, Rui Gao, QiuSheng Li, Jue Hou, José Badal, 2018: Joint tomographic inversion of first-arrival and reflection traveltimes for recovering 2-D seismic velocity structure with an irregular free surface, Earth and Planetary Physics, 2, 220-230. doi: 10.26464/epp2018021

2018, 2(3): 220-230. doi: 10.26464/epp2018021

SOLID EARTH: SEISMOLOGY

Joint tomographic inversion of first-arrival and reflection traveltimes for recovering 2-D seismic velocity structure with an irregular free surface

1. 

Key Laboratory of Deep-Earth Dynamics of Ministry of Land and Resources, Institute of Geology, Chinese Academy of Geological Sciences, Beijing 100037, China

2. 

State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China

3. 

CAS Center for Excellence in Tibetan Plateau Earth Sciences, Beijing 100101, China

4. 

School of Earth Science and Engineering, Sun Yat-sen University, Guangzhou 510275, China

5. 

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

6. 

Physics of the Earth, Sciences B, University of Zaragoza, Spain

Corresponding author: XinYan Zhang, zhangxinyana@163.comZhiMing Bai, bbzzmm@mail.iggcas.ac.cn

Received Date: 2018-03-02
Web Publishing Date: 2018-05-01

Irregular surface flattening, which is based on a boundary conforming grid and the transformation between curvilinear and Cartesian coordinate systems, is a mathematical method that can elegantly handle irregular surfaces, but has been limited to obtaining first arrivals only. By combining a multistage scheme with the fast-sweeping method (FSM, the method to obtain first-arrival traveltime in curvilinear coordinates), the reflected waves from a crustal interface can be traced in a topographic model, in which the reflected wave-front is obtained by reinitializing traveltimes in the interface for upwind branches. A local triangulation is applied to make a connection between velocity and interface nodes. Then a joint inversion of first-arrival and reflection traveltimes for imaging seismic velocity structures in complex terrains is presented. Numerical examples all perform well with different seismic velocity models. The increasing topographic complexity and even use of a high curvature reflector in these models demonstrate the reliability, accuracy and robustness of the new working scheme; checkerboard testing illustrates the method’s high resolution. Noise tolerance testing indicates the method’s ability to yield practical traveltime tomography. Further development of the multistage scheme will allow other later arrivals to be traced and used in the traveltime inversion.

Key words: irregular surface flattening, boundary conforming grid, multistage scheme, traveltime tomography

Afnimar, and Koketsu, K. (2000). Finite difference traveltime calculation for head waves travelling along an irregular interface. Geophys. J. Int., 143(3), 729–734. https://doi.org/10.1046/j.1365-246X.2000.00269.x

Appelö, D., and Petersson, N. A. (2009). A stable finite difference method for the elastic wave equation on complex geometries with free surfaces. Commun. Comput. Phys., 5(1), 84–107.

Artemieva, I. M. (2003). Lithospheric structure, composition, and thermal regime of the East European Craton: implications for the subsidence of the Russian platform. Earth Planet. Sci. Lett., 213(3-4), 431–446. https://doi.org/10.1016/S0012-821X(03)00327-3

Bai, C. Y., Huang, G. J., and Zhao, R. (2009). 2-D/3-D irregular shortest-path ray tracing for multiple arrivals and its applications. Geophys. J. Int., 183(3), 1596–1612.

Bai, C. Y., Tang, X. P., and Zhao, R. (2009). 2-D/3-D multiply transmitted, converted and reflected arrivals in complex layered media with the modified shortest path method. Geophys. J. Int., 179(1), 201–214.

Bai, Z. M., Zhang, Z. J., and Wang, Y. H. (2007). Crustal Structure across the Dabie-Sulu orogenic belt revealed by seismic velocity profiles. J. Geophys. Eng., 4(4), 436–442. https://doi.org/10.1088/1742-2132/4/4/009

Benamou, J. D. (1996). Big ray tracing: Multivalued travel time field computation using viscosity solutions of the Eikonal equation. J. Comput. Phys., 128(2), 463–474. https://doi.org/10.1006/jcph.1996.0224

Cao, S. H., and Greenhalgh, S. (1994). Finite-difference solution of the eikonal equation using an efficient, first-arrival, wavefront tracking scheme. Geophysics, 59(4), 632–643. http://dx.doi.org/10.1190/1.1443623

Carbonell, R., Simancas, F., Juhlin, C., Pous, J., Pérez-Estaún, A., Gonzalez-Lodeiro, F., Muñoz, G., Heise, W., and Ayarza, P. (2004). Geophysical evidence of a mantle derived intrusion in SW Iberia. Geophys. Res. Lett., 31(11), L11601. https://doi.org/10.1029/2004GL019684

Cassell, B. R. (1982). A method for calculating synthetic seismograms in laterally varying media. Geophys. J. R. Astron. Soc., 69(2), 339–354. https://doi.org/10.1111/j.1365-246X.1982.tb04953.x

Fornberg, B. (1988). The pseudospectral method: Accurate representation of interfaces in elastic wave calculations. Geophysics, 53(5), 625–637. http://dx.doi.org/10.1190/1.1442497

Gao, R., Lu, Z. W., Li, Q. S., Guan, Y., Zhang, J. S., He, R. Z., and Hang, L. Y. (2005). Geophysical survey and geodynamic study of crust and upper mantle in the Qinghai-Tibet Plateau. Episodes, 28(4), 263–273.

Haines, A. J. (1988). Multi-source, multi-receiver synthetic seismograms for laterally heterogeneous media using F-K domain propagators. Geophys. J. Int., 95(2), 237–260. https://doi.org/10.1111/j.1365-246X.1988.tb00465.x

Hole, J. (1992). Nonlinear high‐resolution three‐dimensional seismic travel time tomography. J. Geophys. Res., 97(B5), 6553–6562. https://doi.org/10.1029/92JB00235

Huang G. J., Bai C. Y., Zhu D. I., and Greenhalgh S. (2012). 2D/3D seismic simultaneous inversion for the velocity and interface geometry using multiple classes of arrivals. Bull. Seismol. Soc. Am., 102(2), 790–801. https://doi.org/10.1785/0120110155

Hvid, S. (1994). Three Dimensional Algebraic Grid Generation. Copenhagen, Denmark: Technical University of Denmark.222

Julian, B. R., and Gubbins, D. (1977). Three-dimensional seismic ray tracing. J. Geophys. Res., 43, 95–113.

Kaila, K. L., and Krishna, V. G. (1992). Deep seismic sounding studies in India and major discoveries. Curr. Sci., 62(1-2), 117–154.

Kao, C. Y., Osher, S., and Qian, J. L. (2008). Legendre-transform-based fast sweeping methods for static Hamilton–Jacobi equations on triangulated meshes. J. Comput. Phys., 227(24), 10209–10225. https://doi.org/10.1016/j.jcp.2008.08.016

Kim, S., and Cook, R. (1999). 3-D traveltime computation using second-order ENO scheme. Geophysics, 64(6), 1867–1876. http://dx.doi.org/10.1190/1.1444693

Kimmel, R., and Sethian, J. A. (1998). Computing geodesic paths on manifolds. Proc. Natl. Acad. Sci. USA, 95(15), 8431–8435. https://doi.org/10.1073/pnas.95.15.8431

Knapp, C. C., Knapp, J. H., and Connor, J. A. (2004). Crustal-scale structure of the South Caspian Basin revealed by deep seismic reflection profiling. Mar. Pet. Geol., 21(8), 1073–1081. https://doi.org/10.1016/j.marpetgeo.2003.04.002

Koketsu, K., and Sekine, S. (1998). Pseudo-bending method for three-dimensional seismic ray tracing in a spherical earth with discontinuities. Geophys. J. Int., 132(2), 339–346. https://doi.org/10.1046/j.1365-246x.1998.00427.x

Lan, H. Q., and Zhang, Z. J. (2011a). Comparative study of the free-surface boundary condition in two-dimensional finite-difference elastic wave field simulation. J. Geophys. Eng., 8(2), 275–286. https://doi.org/10.1088/1742-2132/8/2/012

Lan, H. Q., and Zhang, Z. J. (2011b). Three-dimensional wave-field simulation in heterogeneous transversely isotropic medium with irregular free surface. Bull. Seismol. Soc. Am., 101(3), 1354–1370. http://dx.doi.org/10.1785/0120100194

Lan, H. Q., Zhang, Z., Xu, T., and Bai, Z. M. (2012). Influences of anisotropic stretching of boundary conforming grid on traveltime computation by topography-dependent eikonal equation. Chin. J. Geophys., 55(5), 564–579. https://doi.org/10.1002/cjg2.1750

Lan, H. Q., and Zhang, Z. J. (2013a). Topography-dependent eikonal equation and its solver for calculating first-arrival traveltimes with an irregular surface. Geophys. J. Int., 193(2), 1010–1026. https://doi.org/10.1093/gji/ggt036

Lan, H. Q, and Zhang, Z. J. (2013b). A high-order fast-sweeping scheme for calculating first-arrival travel times with an irregular surface. Bull. Seismol. Soc. Am., 103(3), 2070–2082. https://doi.org/10.1785/0120120199

Lelièvre, P. G., Farquharson, C. G., and Hurich, C. A. (2011). Computing first-arrival seismic traveltimes on unstructured 3-D tetrahedral grids using the fast marching method. Geophys. J. Int., 184(2), 885–896. https://doi.org/10.1111/j.1365-246X.2010.04880.x

Li, S. L., and Mooney, W. D. (1998). Crustal structure of China from deep seismic sounding profiles. Tectonophysics, 288(1-4), 105–113. https://doi.org/10.1016/S0040-1951(97)00287-4

Ma, T., and Zhang, Z. J. (2014a). Calculating ray paths for first-arrival travel times using a topography-dependent eikonal equation solver. Bull. Seismol. Soc. Am., 104(3), 1501–1517. https://doi.org/10.1785/0120130172

Ma, T., and Zhang, Z. J. (2014b). A model expansion criterion for treating surface topography in ray path calculations using the eikonal equation. J. Geophys. Eng., 11(2), 025007. https://doi.org/10.1088/1742-2132/11/2/025007

Ma, T., and Zhang, Z. J. (2015). Topography-dependent eikonal traveltime tomography for upper crustal structure beneath an irregular surface. Pure Appl. Geophys., 172(6), 1511–1529. https://doi.org/10.1007/s00024-014-0984-7

Podvin, P., and Lecomte, I. (1991). Finite difference computation of traveltimes in very contrasted velocity models: a massively parallel approach and its associated tools. Geophys. J. Int., 105(1), 271–284. https://doi.org/10.1111/j.1365-246X.1991.tb03461.x

Qian, J. L., and Symes, W. W. (2002). An adaptive finite-difference method for traveltimes and amplitudes. Geophysics, 67(1), 167–176. http://dx.doi.org/10.1190/1.1451472

Qian, J. L., Zhang, Y. T., and Zhao, H. K. (2007a). A fast sweeping method for static convex Hamilton-Jacobi equations. J. Sci. Comput., 31(1-2), 237–271. https://doi.org/10.1007/s10915-006-9124-6

Qian, J. L., Zhang, Y. T., and Zhao, H. K. (2007b). Fast sweeping methods for Eikonal equations on triangular meshes. SIAM J. Numer. Anal., 45(1), 83–107. https://doi.org/10.1137/050627083

Qin, F. H., Luo, Y., Olsen, K. B., Cai, W. Y., and Schuster, G. T. (1992). Finite-difference solution of the eikonal equation along expanding wavefronts. Geophysics, 57(3), 478–487. http://dx.doi.org/10.1190/1.1443263

Rawlinson, N., and Sambridge, M. (2004a). Multiple reflection and transmission phases in complex layered media using a multistage fast marching method. Geophysics, 69(5), 1338–1350. http://dx.doi.org/10.1190/1.1801950

Rawlinson, N., and Sambridge, M. (2004b). Wave front evolution in strongly heterogeneous layered media using the fast marching method. Geophys. J. Int., 156(3), 631–647. https://doi.org/10.1111/j.1365-246X.2004.02153.x

Rawlinson, N., and Goleby, B. R. (2012). Seismic imaging of continents and their margins: New research at the confluence of active and passive seismology. Tectonophysics, 572-573, 1–6. https://doi.org/10.1016/j.tecto.2012.07.021

Reshef, M. (1991). Depth migration from irregular surfaces with depth extrapolation methods. Geophysics, 56(1), 119–122. http://dx.doi.org/10.1190/1.1442947

Riahi, M. A., and Juhlin, C. (1994). 3-D interpretation of reflected arrival times by finite-difference techniques. Geophysics, 59(5), 844–849. http://dx.doi.org/10.1190/1.1443642

Sambridge, M. S. (1990). Non-linear arrival time inversion: Constraining velocity anomalies by seeking smooth models in 3-D. Geophys. J. Int., 102(3), 653–677. https://doi.org/10.1111/j.1365-246X.1990.tb04588.x

Scarascia, S., and Cassinis, R. (1997). Crustal structures in the central-eastern Alpine sector: a revision of the available DSS data. Tectonophysics, 271(1-2), 157–188. https://doi.org/10.1016/S0040-1951(96)00206-5

Sethian, J. A. (1999). Fast marching methods. SIAM Rev., 41(2), 199–235. https://doi.org/10.1137/S0036144598347059

Sethian, J. A., and Vladimirsky, A. (2000). Fast methods for the Eikonal and related Hamilton–Jacobi equations on unstructured meshes. Proc. Natl. Acad. Sci. USA, 97(11), 5699–5703. https://doi.org/10.1073/pnas.090060097

Symes, W. W., and Qian, J. L. (2003). A slowness matching eulerian method for multivalued solutions of eikonal equations. J. Sci. Comput., 19(1-3), 501–526. https://doi.org/10.1023/A:1025380731197

Teng, J. W., Wei, S. Y., Sun, K. Z., and Xue, C. S. (1987). The characteristics of the seismic activity in the Qinghai-Xizang (Tibet) Plateau of China. Tectonophysics, 134(1-3), 129–144. https://doi.org/10.1016/0040-1951(87)90253-8

Teng, J. W., Zeng, R. S., Yan, Y. F., and Zhang, H. (2003). Depth distribution of Moho and tectonic framework in eastern Asian continent and its adjacent ocean areas. Sci. China Ser. D Earth Sci., 46(5), 428–446. https://doi.org/10.1360/03yd9038

Thompson, J. F., Warsi, Z. U. A., and Mastin, C. W. (1985). Numerical Grid Generation: Foundations and Applications. Amsterdam: North-Holland.222

Tian, X. B., Teng, J. W., Zhang, H. S., Zhang, Z. J., Zhang, Y. Q., Yang, H., and Zhang K. K. (2011). Structure of crust and upper mantle beneath the Ordos Block and the Yinshan Mountains revealed by receiver function analysis. Phys. Earth Planet. Inter., 184(3-4), 186–193. https://doi.org/10.1016/j.pepi.2010.11.007

Um, J., and Thurber, C. (1987). A fast algorithm for two-point seismic ray tracing. Bull. Seismol. Soc. Am., 77(3), 972–986.

van Trier, J., and Symes, W. W. (1991). Upwind finite-difference calculation of traveltimes. Geophysics, 56(6), 812–821. http://dx.doi.org/10.1190/1.1443099

Vidale, J. (1988). Finite-difference calculation of travel times. Bull. Seismol. Soc. Am., 78(6), 2062–2076.

Wang, C. Y., Zeng, R. S., Mooney, W. D., and Hacker, B. R. (2000). A crustal model of the ultrahigh-pressure Dabie Shan orogenic belt, China, derived from deep seismic refraction profiling. J. Geophys. Res., 105(B5), 10857–10869. https://doi.org/10.1029/1999JB900415

Wang, C. Y., Han, W. B., Wu, J. P., Lou, H., and Chan, W. W. (2007). Crustal structure beneath the eastern margin of the Tibetan Plateau and its tectonic implications. J. Geophys. Res., 112(B7), B07307. https://doi.org/10.1029/2005JB003873

Wu, C. L., Harris, J. M., Nihei, K. T., and Nakagawa, S. (2005). Two-dimensional finite-difference seismic modeling of an open fluid-filled fracture: Comparison of thin-layer and linear-slip models. Geophysics, 70(4), T57-T62. http://dx.doi.org/10.1190/1.1988187

Xu, T., Xu, G. M., Gao, E. G., Li, Y. C., Jiang, X. Y., and Luo, K. Y. (2006). Block modeling and segmentally iterative ray tracing in complex 3D media. Geophysics, 71(3), T41-T51. https://doi.org/10.1190/1.2192948

Xu, T., Zhang, Z. J., Gao, E. G., Xu, G. M., and Sun, L. (2010). Segmentally iterative ray tracing in complex 2D and 3D heterogeneous block models. Bull. Seismol. Soc. Am., 100(2), 841–850. https://doi.org/10.1785/0120090155

Xu, T., Li, F., Wu, Z. B., Wu, C. L., Gao, E. G., Zhou, B., Zhang, Z. J., and Xu, G. M. (2014). A successive three-point perturbation method for fast ray tracing in complex 2D and 3D geological models. Tectonophysics, 627, 72–81. https://doi.org/10.1016/j.tecto.2014.02.012

Zelt, C. A., and Smith, R. B. (1992). Seismic traveltime inversion for 2-D crustal velocity structure. Geophys. J. Int., 108(1), 16–34. https://doi.org/10.1111/j.1365-246X.1992.tb00836.x

Zeng, R. S., Ding, Z. F., and Wu, Q. J. (1995). A review on the lithospheric structures in the Tibetan Plateau and constraints for dynamics. Pure Appl. Geophys., 145(3-4), 425–443. https://doi.org/10.1007/BF00879582

Zhang, W., and Chen, X. F. (2006). Traction image method for irregular free surface boundaries in finite difference seismic wave simulation. Geophys. J. Int., 167(1), 337–353. https://doi.org/10.1111/j.1365-246X.2006.03113.x

Zhang, Z. J., and Klemperer, S. L. (2005). West-east variation in crustal thickness in northern Lhasa block, central Tibet, from deep seismic sounding data. J. Geophys. Res., 110(B9), B09403. https://doi.org/10.1029/2004JB003139

Zhang, Z. J., and Klemperer, S. (2010). Crustal structure of the Tethyan Himalaya, southern Tibet: New constraints from old wide-angle seismic data. Geophys. J. Int., 181(3), 1247–1260. https://doi.org/10.1111/j.1365-246X.2010.04578.x

Zhang, Z. J., Deng, Y. F., Teng, J. W., Wang, C. Y., Gao, R., Chen, Y., and Fan, W. M. (2011). An overview of the crustal structure of the Tibetan plateau after 35 years of deep seismic soundings. J. Earth Sci., 40(4), 977–989. https://doi.org/10.1016/j.jseaes.2010.03.010

Zhou, B., Greenhalgh, S. A., and Sinadlnovskl, C. (1992). Iterative algorithm for the damped minimum norm, least-squares and constrained problem in seismic tomography. Explor. Geophys., 23(3), 497–505. https://doi.org/10.1071/EG992497

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Joint tomographic inversion of first-arrival and reflection traveltimes for recovering 2-D seismic velocity structure with an irregular free surface

XinYan Zhang, ZhiMing Bai, Tao Xu, Rui Gao, QiuSheng Li, Jue Hou, José Badal