Phase-encoded Wave-equation Migration

The theory for least-squares generalized diffraction-stack migration (LSGDM) was presented in Chapter . Now I test the performance of LSGDM using the phase-encoded multisource technology. The key idea is, for an assumed velocity model, the receiver-side Green's function and the source-side Green's function are computed by a numerical solution of the wave equation. The multisource migration operator is formed by convolution of these two Green's functions followed by phase-encoding. Recorded shot gathers are phase-encoded together with the same phase-encoding function to form a supergather. Then the GDM image is obtained by an $x-t$ domain dot product between the supergather and the multisource migration operator for every trial image point. The dot product of unrelated migration operators and shot gathers inevitably brings cross-talk noise into the migration image. To deal with such noise, the least-squares algorithm is adopted. Numerical results show that the LSGDM method combined with the phase-encoded multisource technology can lead to an efficient computation of wave equation least-squares migration (LSM) images in almost the same time as that of conventional reverse-time migration (RTM). It is especially suited to efficient target oriented migration.