Lowrank one-step wave extrapolation for reverse-time migration |
In this paper, we adopt the one-step scheme due to its superior stability and ability to handle complex-valued phase functions. Because the two-step scheme depends on a real-valued phase function, it cannot include higher-order terms from the expansion (equation 20) and implement more accurate phase functions. By switching to a one-step scheme, we can easily incorporate the second-order term (
) in equation 20 to achieve a more accurate wave extrapolation operator. As defined in equation 22,
involves the gradient of the velocity model, and can become significant when either the time step size is large or the velocity model changes rapidly. Substituting the first three terms from the Taylor series (equation 20) into equation 17, the second-order operator takes the form
Lowrank one-step wave extrapolation for reverse-time migration |