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Mathematical Problems in Engineering
Volume 2015, Article ID 543540, 8 pages
Research Article

Hybrid Kinematic-Dynamic Approach to Seismic Wave-Equation Modeling, Imaging, and Tomography

1Institute of Petroleum Geology and Geophysics SB RAS, Pr. Ac. Koptyuga 3, Novosibirsk 630090, Russia
2Novosibirsk State University, Street Pirogova 2, Novosibirsk 630090, Russia

Received 15 April 2015; Revised 1 July 2015; Accepted 6 July 2015

Academic Editor: Yuming Qin

Copyright © 2015 Alexandr S. Serdyukov and Anton A. Duchkov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Estimation of the structure response to seismic motion is an important part of structural analysis related to mitigation of seismic risk caused by earthquakes. Many methods of computing structure response require knowledge of mechanical properties of the ground which could be derived from near-surface seismic studies. In this paper we address computationally efficient implementation of the wave-equation tomography. This method allows inverting first-arrival seismic waveforms for updating seismic velocity model which can be further used for estimating mechanical properties. We present computationally efficient hybrid kinematic-dynamic method for finite-difference (FD) modeling of the first-arrival seismic waveforms. At every time step the FD computations are performed only in a moving narrowband following the first-arrival wavefront. In terms of computations we get two advantages from this approach: computation speedup and memory savings when storing computed first-arrival waveforms (it is not necessary to make calculations or store the complete numerical grid). Proposed approach appears to be specifically useful for constructing the so-called sensitivity kernels widely used for tomographic velocity update from seismic data. We then apply the proposed approach for efficient implementation of the wave-equation tomography of the first-arrival seismic waveforms.