Wave Field Extrapolation by the Linearly Transformed Wave Equation Operator
, by Zhiming Li
Many approximations of different orders of the one-way wave equation have been suggested in seismic imaging or modeling. Of these approximations, the second-order approximation, usually called the 15 degree equation, is most commonly used in industry because of its high efficiency. However, all of these approximations have in common the constraints of not being able to handle the large angle events exactly.
Trough a linear transformation of the wave equation, one can obtain, without approximation, the Linearly Transformed Wave Equation (LTWE) which exactly resembles in form a 15 degree wave equation. The solution to the LTWE is still a two-way wave solution. By imposing the upcoming (or downgoing) wave boundary condition, the LTWE can be applied to seismic imaging (or modeling). Implementing the LTWE with finite difference algorithm gives an one-hundred-and-eighty-degree, or all-dip, finite difference wave extrapolation operator, which solves the angle limitation problem in the conventional finite difference methods.
STANFORD