Surveys in Geophysics

, Volume 35, Issue 2, pp 359–393 | Cite as

The One-Way Wave Equation: A Full-Waveform Tool for Modeling Seismic Body Wave Phenomena

  • D. A. Angus


The study of seismic body waves is an integral aspect in global, exploration and engineering scale seismology, where the forward modeling of waves is an essential component in seismic interpretation. Forward modeling represents the kernel of both migration and inversion algorithms as the Green’s function for wavefield propagation and is also an important diagnostic tool that provides insight into the physics of wave propagation and a means of testing hypotheses inferred from observational data. This paper introduces the one-way wave equation method for modeling seismic wave phenomena and specifically focuses on the so-called operator-root one-way wave equations. To provide some motivation for this approach, this review first summarizes the various approaches in deriving one-way approximations and subsequently discusses several alternative matrix narrow-angle and wide-angle formulations. To demonstrate the key strengths of the one-way approach, results from waveform simulation for global scale shear-wave splitting modeling, reservoir-scale frequency-dependent shear-wave splitting modeling and acoustic waveform modeling in random heterogeneous media are shown. These results highlight the main feature of the one-way wave equation approach in terms of its ability to model gradual vector (for the elastic case) and scalar (for the acoustic case) waveform evolution along the underlying wavefront. Although not strictly an exact solution, the one-way wave equation shows significant advantages (e.g., computational efficiency) for a range of transmitted wave three-dimensional global, exploration and engineering scale applications.


Forward modeling One-way wave equation Seismic anisotropy Wave phenomena 



I would like to thank James Hammond for providing the SKS synthetic seismograms for the Ethiopian rift model, Alan Baird for providing the algorithm to compute the frequency-dependent fracture-induced elastic tensors and Tobias Müller for providing the stochastic heterogeneous acoustic model.


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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.School of Earth and EnvironmentUniversity of LeedsLeedsUK

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