Advertisement

Pure and Applied Geophysics

, Volume 167, Issue 12, pp 1525–1536 | Cite as

Finite-Difference Modeling and Dispersion Analysis of High-Frequency Love Waves for Near-Surface Applications

  • Yinhe LuoEmail author
  • Jianghai Xia
  • Yixian Xu
  • Chong Zeng
  • Jiangping Liu
Article

Abstract

Love-wave propagation has been a topic of interest to crustal, earthquake, and engineering seismologists for many years because it is independent of Poisson’s ratio and more sensitive to shear (S)-wave velocity changes and layer thickness changes than are Rayleigh waves. It is well known that Love-wave generation requires the existence of a low S-wave velocity layer in a multilayered earth model. In order to study numerically the propagation of Love waves in a layered earth model and dispersion characteristics for near-surface applications, we simulate high-frequency (>5 Hz) Love waves by the staggered-grid finite-difference (FD) method. The air–earth boundary (the shear stress above the free surface) is treated using the stress-imaging technique. We use a two-layer model to demonstrate the accuracy of the staggered-grid modeling scheme. We also simulate four-layer models including a low-velocity layer (LVL) or a high-velocity layer (HVL) to analyze dispersive energy characteristics for near-surface applications. Results demonstrate that: (1) the staggered-grid FD code and stress-imaging technique are suitable for treating the free-surface boundary conditions for Love-wave modeling, (2) Love-wave inversion should be treated with extra care when a LVL exists because of a lack of LVL information in dispersions aggravating uncertainties in the inversion procedure, and (3) energy of high modes in a low-frequency range is very weak, so that it is difficult to estimate the cutoff frequency accurately, and “mode-crossing” occurs between the second higher and third higher modes when a HVL exists.

Keywords

Finite-difference modeling dispersion analysis Love waves near-surface application 

Notes

Acknowledgments

This work is supported by the National Science Foundation of China (NSFC, #40904031) and the Special Fund for Basic Scientific Research of Central Colleges, China University of Geosciences (Wuhan) (#090106). The first author appreciates the Kansas Geological Survey, University of Kansas, for providing opportunities in surface-wave research and the China University of Geosciences for the financial support to conduct this study. The authors thank Marla Adkins-Heljeson of the Kansas Geological Survey for editing the manuscript.

References

  1. Aki, K. and Richards, P.G., Quantitative Seismology (2nd ed.), (University Science Books 2002).Google Scholar
  2. Alekseev, A. A. (1989), Criteria for existence of Love waves, Vychisl. Seysm. 22, 137–141.Google Scholar
  3. Beaty, K. S., Schmitt, D. R. and Sacchi, M. (2002). Simulated annealing inversion of multimode Rayleigh-wave dispersion curves for geological structure, Geophys. J. Int. 151, 622–631.Google Scholar
  4. Ben-Hador, R. and Buchen, P. (1999), Love and Rayleigh waves in non-uniform media, Geophys. J. Int. 137, 521–534.Google Scholar
  5. Clayton, R. W. and Engquist, B. (1977), Absorbing boundary conditions for acoustic and elastic wave equations, Bull. Seismol. Soc. Am. 67, 1529–1540.Google Scholar
  6. Eslick, R., Tsoflias, G. and Steeples, D. (2008), Field investigation of Love waves in near-surface seismology, Geophysics, 73(3), G1–G6.Google Scholar
  7. Garland, G. D., Introduction to Geophysics: Mantle, Core and Crust (2nd ed.) (Saunders, Toronto 1979).Google Scholar
  8. Graves, R. W. (1996), Simulating seismic wave propagation in 3D elastic media using staggered-grid finite differences, Bull. Seismol. Soc Am. 86(4), 1091–1106.Google Scholar
  9. Guzina, B. and Madyarov, A. (2005), On the spectral analysis of Love waves, Bull. Seismol. Soc. Am. 95(3), 1150–1169.Google Scholar
  10. Ke, L., Wang, Y. and Zhang, Z. (2006), Love waves in an inhomogeneous fluid saturated porous layered half-space with linearly varying properties, Soil Dyn. Earthq. Eng. 26, 574–581.Google Scholar
  11. Kinoshita, S. (1999), A stochastic method for investigating site effects by means of a borehole array SH and Love waves, Bull. Seismol. Soc. Am., 89(2), 484–500.Google Scholar
  12. Lee, H. and McMechan, G. A. (1992), Imaging of Lateral Inhomogeneity Using Love wave Data. Technical Program with Biographies, SEG, 62nd Annual Meeting, 992–994.Google Scholar
  13. Levander, A. R. (1988), Fourth-order finite-difference P-SV seismograms, Geophysics, 53, 1425–1436.Google Scholar
  14. Levshin, A. L., Ritzwoller, M. H. and Shapiro, N. M. (2005), The use of crustal higher modes to constrain crustal structure across Central Asia, Geophys. J. Int. 160, 961–972.Google Scholar
  15. Li, X. (1997), Elimination of higher modes in dispersive in-seam multimode Love waves, Geophys. Prospect. 45, 945–961.Google Scholar
  16. Liang, Q., Chen, C., Zeng, C., Luo, Y. and Xu, Y. (2008), Inversion stability analysis of multimode Rayleigh-wave dispersion curves using low-velocity-layer models, Near Surface Geophys., 6, 157–165.Google Scholar
  17. Luo, Y., Xia, J., Liu, J., Liu, Q. and Xu, S. (2007), Joint inversion of high-frequency surface waves with fundamental and higher modes, J Appl. Geophys. 62, 375–384.Google Scholar
  18. Luo, Y., Xia, J., Miller, R. D., Xu, Y., Liu, J. and Liu, Q. (2008a), Rayleigh-wave dispersive energy imaging by high-resolution linear Radon transform, Pure Appl. Geophys. 165, 902–922.Google Scholar
  19. Luo, Y., Xia, J., Liu, J., Xu, Y. and Liu, Q. (2008b), Generation of a pseudo-2D shear-wave velocity section by inversion of a series of 1D dispersion curves, J. Appl. Geophys. 64(3), 115–124.Google Scholar
  20. Luo, Y., Xia, J., Liu, J., Xu, Y. and Liu, Q. (2009a), Research on the MASW middle-of-the-spread-results assumption, Soil Dyn. Earthq. Eng. 29, 71–79.Google Scholar
  21. Luo, Y., Xia, J., Xu, Y., Zeng, C., Miller, R.D. and Liu, Q. (2009b), Dipping-interface mapping using mode-separated Rayleigh waves, Pure Appl. Geophys. 166(3), 353–374.Google Scholar
  22. Luo, Y., Xia, J., Miller, R. D., Xu, Y., Liu, J. and Liu, Q. (2009c), Rayleigh-wave mode separation by high-resolution linear Radon transform, Geophys. J. Int. 179(1), 254–264.Google Scholar
  23. Narayan, J. P. and Kumar, S. (2008), A fourth order accurate SH-wave staggered grid finite-difference algorithm with variable grid size and VGR-stress imaging technique, Pure Appl. Geophys. 165, 271–294.Google Scholar
  24. O’Neill, A. and Toshifumi, M. (2005), Dominant higher surface-wave modes and possible inversion pitfalls, J. Environ. Eng. Geophys. 10(2), 185–201.Google Scholar
  25. Passier, M. L., Van der Hilst, R. D. and Sneider, R. K. (1997), Surface wave waveform inversions for local shear-wave velocities under eastern Australia, Geophysical Res. Lett. 24(11), 1291–1294.Google Scholar
  26. Robertsson, J. O. A., Levander, A., Symes, W. W. and Holliger, K., (1995), A comparative study of free-surface boundary conditions for finite-difference simulation of elastic/viscoelastic wave propagation, Technical Program with Biographies, SEG, 65th Annual Meeting, 1277–1280.Google Scholar
  27. Safani, J., O’Neill, A., Matsuoka, T. and Yoshinori, S. (2005), Applications of Love wave dispersion for improved shear-wave velocity imaging, J. Environ. Eng. Geophys. 10(2), 135–150.Google Scholar
  28. Safani, J., O’Neill, A. and Matsuoka, T. (2006), Full SH-wavefield modelling and multiple-mode Love wave inversion, Explor. Geophys. 37, 307–321.Google Scholar
  29. Schwab, F. A. and Knopoff, L. (1972), Fast surface wave and free mode computations. In Methods in Computational Physics (ed. B. A. Bolt) (Academic Press, New York, 87–180).Google Scholar
  30. Song, Y. Y., Castagna, J. P., Black, R. A. and Knapp, R. W. (1989), Sensitivity of near-surface shear-wave velocity determination from Rayleigh and Love waves. Technical Program with Biographies, SEG, 59th Annual Meeting, 509–512.Google Scholar
  31. Stoneley, R. (1950), The effect of a low-velocity internal stratum on surface elastic waves, Mon. Notices R. Astronom. Soc. (Geophys. Suppl.) 6, 28–35.Google Scholar
  32. Vidale, J. E. and Clayton, R.W. (1986), A stable free-surface boundary condition for two-dimensional elastic finite-difference wave simulation, Geophysics, 51, 2247–2249.Google Scholar
  33. Virieux, J. (1984), SH wave propagation in heterogeneous media: velocity stress finite-difference method, Geophysics, 49, 1933–1957.Google Scholar
  34. Wait, J. R. (1959), Electromagnetic Radiation from Cylindrical Structures. (Pergamon Press, New York).Google Scholar
  35. Winsborrow, G., Huwsa, D. G. and Muyzertb, E. (2003), Acquisition and inversion of Love wave data to measure the lateral variability of geo-acoustic properties of marine sediments, J. Appl. Geophys. 54, 71–84.Google Scholar
  36. Xia, J., Miller, R.D. and Park, C. B. (1999), Estimation of near-surface shear-wave velocity by inversion of Rayleigh wave, Geophysics, 64, 691–700.Google Scholar
  37. Xia, J., Miller, R. D., Park, C. B., Hunter, J. A., Harris, J. B. and Ivanov, J. (2002), Comparing shear-wave velocity profiles from multichannel analysis of surface wave with borehole measurements, Soil Dyn. Earthq. Eng. 22(3), 181–190.Google Scholar
  38. Xia, J., Miller, R. D., Park, C. B. and Tian, G. (2003), Inversion of high frequency surface waves with fundamental and higher modes, J. Appl. Geophys. 52(1), 45–57.Google Scholar
  39. Xia, J., Chen, C., Li, P. H. and Lewis, M. J. (2004), Delineation of a collapse feature in a noisy environment using a multichannel surface wave technique, Geotechnique, 54(1), 17–27.Google Scholar
  40. Xia, J., Xu, Y., Chen, C., Kaufmann, R. D. and Luo, Y. (2006), Simple equations guide high-frequency surface-wave investigation techniques, Soil Dyn. Earthq. Eng. 26(5), 395–403.Google Scholar
  41. Xia, J., Miller, R. D., Xu, Y., Luo, Y., Chen, C., Liu, J., Ivanov, J. and Zeng, C. (2009), High-frequency Rayleigh-wave method, J. Earth Sci. 20(3), 563–579.Google Scholar
  42. Xu, Y., Xia, J. and Miller, R. D. (2007), Numerical investigation of implementation of air–earth boundary by acoustic–elastic boundary approach, Geophysics, 72(5), SM147–SM153.Google Scholar
  43. Yu, T., Dresen, L. Riiter, D. (1996), The influence of local irregularities on the propagation of Love waves, J. Appl. Geophys. 36, 53–65.Google Scholar
  44. Zahradnfk, J., Moczo, P. and Hron, F. (1993), Testing four elastic finite difference schemes for behavior at discontinuities, Bull. Seismol. Soc. Am. 83, 107–129.Google Scholar
  45. Zeng, C., Liang, Q. and Chen, C. (2007), Comparative analysis on sensitivities of Love and Rayleigh waves, Technical Program with Biographies, SEG, 77th Annual Meeting, 1138–1141.Google Scholar
  46. Zhang, S. and Chan, L. (2003), Possible effects of misidentified mode number on Rayleigh wave inversion, J. Appl. Geophys. 53, 17–29.Google Scholar

Copyright information

© Birkhäuser / Springer Basel AG 2010

Authors and Affiliations

  • Yinhe Luo
    • 1
    Email author
  • Jianghai Xia
    • 2
  • Yixian Xu
    • 3
  • Chong Zeng
    • 2
  • Jiangping Liu
    • 1
  1. 1.Institute of Geophysics and GeomaticsChina University of GeosciencesWuhanChina
  2. 2.Kansas Geological SurveyThe University of KansasLawrenceUSA
  3. 3.State Key Laboratory of Geological Processes and Mineral Resources, Institute of Geophysics and GeomaticsChina University of GeosciencesWuhanChina

Personalised recommendations