Forward and Adjoint Modeling Using Green’s Functions: Forward modeling of the wave equation is defined as computing the propagating wavefields for a given source-receiver distribution, the source wavelet, and a velocity-density model. This chapter presents the forward-modeling approach with the Lippmann-Schwinger (LS) equation, a summation of weighted Green’s functions over the model coordinates, in which the weights are the reflection-like coeficients in the model. Another name for this is diffraction-stack modeling under the weak scattering approximation, otherwise known as the Born approximation.
Reverse Time Migration: In this chapter, we derive the equations for the reverse time migration (RTM) algorithm. This algorithm is used heavily by the oil industry for subsalt imaging of reflectors. It also is used to migrate residuals iteratively for both LSM and FWI. Compared to other migration methods such as diffraction-stack migration discussed in Chapter 10, RTM accounts for all the arrivals in the wavefield, including both primaries and multiples if the velocity model is suficiently accurate. This can lead to much better resolution in the image, but it is at the cost of being more sensitive to errors in the migration velocity model. For frequencies less than 20 Hz, RTM is the migration method of choice for imaging below complex geology such as salt bodies.