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One-way wave equation

A one-way wave equation is a first-order partial differential equation describing one wave traveling in a direction defined by the vector wave velocity. It contrasts with the second-order two-way wave equation describing a standing wavefield resulting from superposition of two waves in opposite directions (using the squared scalar wave velocity).[1][2][3] In the one-dimensional case it is also known as a transport equation,[4] and it allows wave propagation to be calculated without the mathematical complication of solving a 2nd order differential equation. Due to the fact that in the last decades no general solution to the 3D one-way wave equation could be found, numerous approximation methods based on the 1D one-way wave equation are used for 3D seismic and other geophysical calculations, see also the section § Three-dimensional case.[5][6][1][7]

  1. ^ a b Angus, D. A. (2014-03-01). "The One-Way Wave Equation: A Full-Waveform Tool for Modeling Seismic Body Wave Phenomena" (PDF). Surveys in Geophysics. 35 (2): 359–393. Bibcode:2014SGeo...35..359A. doi:10.1007/s10712-013-9250-2. ISSN 1573-0956. S2CID 121469325.
  2. ^ Trefethen, L N. "19. One-way wave equations" (PDF).
  3. ^ Bschorr, Oskar; Raida, Hans-Joachim (March 2020). "One-Way Wave Equation Derived from Impedance Theorem". Acoustics. 2 (1): 164–170. doi:10.3390/acoustics2010012.
  4. ^ Olver, Peter. Introduction to Partial Differential Equations. Springer. pp. 19–29. ISBN 978-3-319-02098-3.
  5. ^ Qiqiang, Yang (2012-01-01). "Forward Modeling of the One-Way Acoustic Wave Equation by the Hartley Method". Procedia Environmental Sciences. 2011 International Conference of Environmental Science and Engineering. 12: 1116–1121. doi:10.1016/j.proenv.2012.01.396. ISSN 1878-0296.
  6. ^ Zhang, Yu; Zhang, Guanquan; Bleistein, Norman (September 2003). "True amplitude wave equation migration arising from true amplitude one-way wave equations". Inverse Problems. 19 (5): 1113–1138. Bibcode:2003InvPr..19.1113Z. doi:10.1088/0266-5611/19/5/307. ISSN 0266-5611. S2CID 250860035.
  7. ^ Cite error: The named reference br2 was invoked but never defined (see the help page).

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