Wave‐field extrapolation by the linearly transformed wave equation

Many approximations to different order of the one‐way scalar wave equation have been suggested in seismic imaging or modeling. Of these approximations, the first‐order approximation, usually called the 15‐degree equation, is most commonly used in industry because of its high efficiency. However, one common constraint of all these approximations is that they cannot handle large‐angle events exactly. Through a linear transformation of the wave equation, the LInearly Transformed Wave EQuation (LITWEQ) is obtainable, without approximation. The LITWEQ has the form of the 15‐degree equation. The solution to the LITWEQ is still a two‐way wave solution. By imposing the boundary condition for upcoming (or downgoing) waves, the LITWEQ can be applied to seismic imaging (or modeling). Implementing the LITWEQ with a finite‐differencing algorithm gives a 180‐degree, or all‐dip, finite‐difference wave‐extrapolation operator, which solves the angle limitation problem of conventional finite‐difference methods.