The constant-coefficient inhomogeneous wave equation reads
, where t is the time; x, z are Cartesian coordinates; c is the sound speed; and δ(.) is the Dirac delta source function located at the origin. The solution to the wave equation could be synthesized in terms of plane waves traveling in all directions. In several applications it is desirable to replace equation (1) by a one-way wave equation, an equation that allows wave processes in a 180-degree range of angles only. This idea has become a standard tool in geophysics (Berkhout, 1981; Claerbout, 1985). A “wide-angle” one-way wave equation is designed to be accurate over nearly the whole 180-degree range of permitted angles. Such formulas can be systematically constructed by drawing upon the connection with the mathematical field of approximation theory (Halpern and Trefethen, 1988).
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