Wave-equation-based travel-time seismic tomography-Part 1: Method

P. Tong, D. Zhao, D. Yang, X. Yang, J. Chen, Q. Liu

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)


In this paper, we propose a wave-equation-based travel-time seismic tomography method with a detailed description of its step-by-step process. First, a linear relationship between the travel-time residual Δ=Tobs-Tsyn and the relative velocity perturbation δc.(x)/c.(x) connected by a finite-frequency travel-time sensitivity kernel K.(x) is theoretically derived using the adjoint method. To accurately calculate the travel-time residual 1t, two automatic arrival-time picking techniques including the envelop energy ratio method and the combined ray and cross-correlation method are then developed to compute the arrival times T syn for synthetic seismograms. The arrival times T obs of observed seismograms are usually determined by manual hand picking in real applications. Travel-time sensitivity kernel K.(x) is constructed by convolving a forward wavefield u.(t;x) with an adjoint wavefield q.(t;x). The calculations of synthetic seismograms and sensitivity kernels rely on forward modeling. To make it computationally feasible for tomographic problems involving a large number of seismic records, the forward problem is solved in the two-dimensional (2-D) vertical plane passing through the source and the receiver by a high-order central difference method. The final model is parameterized on 3-D regular grid (inversion) nodes with variable spacings, while model values on each 2-D forward modeling node are linearly interpolated by the values at its eight surrounding 3-D inversion grid nodes. Finally, the tomographic inverse problem is formulated as a regularized optimization problem, which can be iteratively solved by either the LSQR solver or a nonlinear conjugate-gradient method. To provide some insights into future 3-D tomographic inversions, Fréchet kernels for different seismic phases are also demonstrated in this study.

Original languageEnglish
Pages (from-to)1151-1168
Number of pages18
JournalSolid Earth
Issue number2
Publication statusPublished - 2014 Nov 26

ASJC Scopus subject areas

  • Soil Science
  • Geophysics
  • Geology
  • Geochemistry and Petrology
  • Earth-Surface Processes
  • Stratigraphy
  • Palaeontology


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