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 wave]]field resulting from superposition of two waves in opposite directions (using the squared scalar wave velocity).<ref name="An">{{Cite journal| last=Angus|first=D. A.|date=2014-03-01|title=The One-Way Wave Equation: A Full-Waveform Tool for Modeling Seismic Body Wave Phenomena| journal=Surveys in Geophysics|language=en|volume=35|issue=2|pages=359–393|doi=10.1007/s10712-013-9250-2| bibcode=2014SGeo...35..359A| s2cid=121469325|issn=1573-0956|url=http://eprints.whiterose.ac.uk/77377/8/SIG_2013_with_coversheet.pdf}}</ref><ref>{{Cite web|url=https://people.maths.ox.ac.uk/trefethen/pdectb/oneway2.pdf|title=19. One-way wave equations|last=Trefethen|first=L N}}</ref><ref name="br1">{{Cite journal |last1=Bschorr |first1=Oskar| last2=Raida|first2=Hans-Joachim|date=March 2020|title=One-Way Wave Equation Derived from Impedance Theorem |journal=Acoustics|language=en| volume=2|issue=1| pages=164–170| doi=10.3390/acoustics2010012 |doi-access=free}}</ref> In the one-dimensional case,theit one-wayis wavealso known as a '''transport equation'''<ref name="Olver">{{cite book |last1=Olver |first1=Peter |title=Introduction to Partial Differential Equations |publisher=Springer |isbn=978-3-319-02098-3 |pages=19-29}}</ref>, 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 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 {{Section link|2=Three-dimensional case |nopage=y}}.<ref>{{Cite journal|last=Qiqiang|first=Yang|date=2012-01-01|title=Forward Modeling of the One-Way Acoustic Wave Equation by the Hartley Method|journal=Procedia Environmental Sciences|series=2011 International Conference of Environmental Science and Engineering|language=en|volume=12|pages=1116–1121|doi=10.1016/j.proenv.2012.01.396|issn=1878-0296|doi-access=free}}</ref><ref>{{Cite journal|last1=Zhang|first1=Yu|last2=Zhang|first2=Guanquan|last3=Bleistein|first3=Norman|date=September 2003| title=True amplitude wave equation migration arising from true amplitude one-way wave equations|journal=Inverse Problems| language=en|volume=19|issue=5|pages=1113–1138|doi=10.1088/0266-5611/19/5/307|bibcode=2003InvPr..19.1113Z|s2cid=250860035 |issn=0266-5611}}</ref><ref name="An" /><ref name="br2" />