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


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.


Sensitivity kernel coda waves velocity change single scattering 



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”.


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

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

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