Advertisement

Pure and Applied Geophysics

, Volume 174, Issue 1, pp 327–337 | Cite as

Deriving Sensitivity Kernels of Coda-Wave Travel Times to Velocity Changes Based on the Three-Dimensional Single Isotropic Scattering Model

  • Hisashi Nakahara
  • Kentaro Emoto
Article

Abstract

Recently, coda-wave interferometry has been used to monitor temporal changes in subsurface structures. Seismic velocity changes have been detected by coda-wave interferometry in association with large earthquakes and volcanic eruptions. To constrain the spatial extent of the velocity changes, spatial homogeneity is often assumed. However, it is important to locate the region of the velocity changes correctly to understand physical mechanisms causing them. In this paper, we are concerned with the sensitivity kernels relating travel times of coda waves to velocity changes. In previous studies, sensitivity kernels have been formulated for two-dimensional single scattering and multiple scattering, three-dimensional multiple scattering, and diffusion. In this paper, we formulate and derive analytical expressions of the sensitivity kernels for three-dimensional single-scattering case. These sensitivity kernels show two peaks at both source and receiver locations, which is similar to the previous studies using different scattering models. The two peaks are more pronounced for later lapse time. We validate our formulation by comparing it with finite-difference simulations of acoustic wave propagation. Our formulation enables us to evaluate the sensitivity kernels analytically, which is particularly useful for the analysis of body waves from deeper earthquakes.

Keywords

Sensitivity kernel coda waves velocity change single scattering 

Notes

Acknowledgments

This study was supported by Grant-in-Aid for Scientific Research (C) (16K05528) from Japan Society for the Promotion of Science (JSPS) and the Ministry of Education, Culture, Sports, Science and Technology (MEXT). Computations were conducted on the Earth Simulator at the Japan Agency for Marine-Earth Science and Technology (JAMSTEC) under the support of a joint research project between Earthquake Research Institute, the University of Tokyo, and Center of Earth Information Science and Technology entitled “Numerical simulations of seismic- and tsunami-wave propagation in 3D heterogeneous earth”.

References

  1. Furumura, T., & Chen, L. (2004). Large scale parallel simulation and visualization of 3-D seismic wavefield using Earth simulator. Computer Modeling in Engineering and Sciences, 6, 153–168.Google Scholar
  2. Hobiger, M., Wegler, U., Shiomi, K., & Nakahara, H. (2012). Coseismic and postseismic elastic wave velocity variations caused by the 2008 Iwate-Miyagi Nairiku earthquake, Japan. Journal Geophysical Research, 117, B09313. doi: 10.1029/2012jb009402.CrossRefGoogle Scholar
  3. Kanu, C., & Snieder, R. (2015). Time-lapse imaging of a localized weak change with multiply scattered waves using numerical-based sensitivity kernel. Journal Geophysical Research, 120, 5595–5605. doi: 10.1002/2015JB011871.Google Scholar
  4. Larose, E., Planes, T., Rossetto, V., & Margerin, L. (2010). Locating a small change in a multiple scattering environment. Applied Physics Letters, 96(20), 204101. doi: 10.1063/1.3431269.CrossRefGoogle Scholar
  5. Maeda, T. (2007). Sensitivity kernel of coda envelopes (in Japanese). Paper Presented at the Seismic Scattering Workshop, University of Tokyo, Tokyo, 25–26 September 2007, http://wwweic.eri.u-tokyo.ac.jp/viewdoc/scat2007/14-maeda.pdf.
  6. Margerin, L., Planes, T., Mayol, J., & Calvet, M. (2016). Sensitivity kernels for coda-wave interferometry and scattering tomography: theory and numerical evaluation in two-dimensional anisotropically scattering media. Geophysical Journal International, 204, 650–666.CrossRefGoogle Scholar
  7. Morse, P. M., & Feshbach, H. (1953). Methods of theoretical physics (Vol. I). New York: McGraw-Hill.Google Scholar
  8. Nishimura, T., Uchida, N., Sato, H., Ohtake, M., Tanaka, S., & Hamaguchi, H. (2000). Temporal changes of the crustal structure associated with the M6.1 earthquake on September 3, 1998, and the volcanic activity of Mount Iwate, Japan. Geophysical Research Letters, 27(2), 269–272.CrossRefGoogle Scholar
  9. Obermann, A., Planes, T., Larose, E., & Campillo, M. (2013a). Imaging preeruptive and coeruptive structural and mechanical changes of a volcano with ambient seismic noise. Journal Geophysical Research, 118, 6285–6294.Google Scholar
  10. Obermann, A., Planes, T., Larose, E., Sens-Schonfelder, C., & Campillo, M. (2013b). Depth sensitivity of seismic coda waves to velocity perturbations in an elastic heterogeneous medium. Geophysical Journal International, 194(1), 372–382.CrossRefGoogle Scholar
  11. Pacheco, C., & Snieder, R. (2005). Time-lapse travel time change of multiply scattered acoustic waves. Journal of the Acoustic Society of America, 118(3), 1300–1310.CrossRefGoogle Scholar
  12. Pacheco, C., & Snieder, R. (2006). Time-lapse traveltime change of singly scattered acoustic waves. Geophysical Journal International, 165(2), 485–500.CrossRefGoogle Scholar
  13. Poupinet, G., Ellsworth, W. L., & Frechet, J. (1984). Monitoring velocity variations in the crust using earthquake doublets—An application to the Calaveras fault, California. Journal Geophysical Research, 89, 5719–5731.CrossRefGoogle Scholar
  14. Ratdomopurbo, A., & Poupinet, G. (1995). Monitoring a temporal change of seismic velocity in a volcano—Application to the 1992 eruption of Mt-Merapi (Indonesia). Geophysical Reseach Letters, 22(7), 775–778.CrossRefGoogle Scholar
  15. Rossetto, V., Margerin, L., Planes, T., & Larose, E. (2011). Locating a weak change using diffuse waves: Theoretical approach and inversion procedure. Journal of Applied Physics, 109(3), 034903. doi: 10.1063/1.3544503.CrossRefGoogle Scholar
  16. Sato, H. (1977). Energy propagation including scattering effect: Single isotropic scattering approximation. Journal of Physics of the Earth, 25, 27–41.CrossRefGoogle Scholar
  17. Sato, H., Fehler, M. C., & Maeda, T. (2012). Seismic wave propagation and scattering in the heterogeneous earth (2nd ed.). Berlin: Springer.CrossRefGoogle Scholar
  18. Shapiro, N. M., Campillo, M., Stehly, L., & Ritzwoller, M. H. (2005). High-resolution surface-wave tomography from ambient seismic noise. Science, 307, 1615–1618.CrossRefGoogle Scholar
  19. Snieder, R., Gret, A., Douma, H., & Scales, J. (2002). Coda wave interferometry for estimating nonlinear behavior in seismic velocity. Science, 295(5563), 2253–2255.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Department of Geophysics, Graduate School of ScienceTohoku UniversityAoba-kuJapan

Personalised recommendations