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). In the one-dimensional case, the one-way wave equation 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 § Three-dimensional case.