Multi-image, reverse-time and Kirchhoff migrations with compact Green′s functions

We define a common framework for reverse-time migration (RTM) and Kirchhoff migration based on compact representations of Green’s functions. These compact Green’s functions (CGF) are 3D volumes containing traveltimes and amplitudes for the N most representative events in the upcoming/downgoing decomposed 4D wavefields originating from a point source. Within this framework, we implement an RTM algorithm using a multivalued excitation time/amplitude imaging condition. This new approach produces four complementary imaging volumes (different combinations of source and receiver decomposed wavefields) and angle/azimuth gathers with computational effort less than 15% greater than that of plain (one image, no gathers) RTM algorithms. The advantages of separating the image volume into four complementary volumes are well-established in the literature (low frequency noise separation and turning-wave imaging); however, its use has been limited by the computational cost. Despite using two source propagations to decompose the source wavefield, we reduce the computations to less than 20% of a single source propagation by performing finite-difference propagation with half the frequency limit used in the receiver wavefield propagation. The combination of CGF and an excitation time/amplitude imaging condition allows receiver wavefield decomposition with only one wavefield propagation. Our RTM algorithm constructs angle/azimuth gathers using a post-migration computation of the source and receiver wavefield’s propagation directions. To compute the propagation directions after migration, we use a new concept: the cumulative wavefield volumes, which are 3D, imaging-condition-guided compressions, of the 4D source and receiver wavefields. We also use CGF to implement a Kirchhoff migration algorithm that produces four complementary image volumes with RTM-like quality. Further, we present synthetic and field data examples to clarify the new concepts and illustrate the results obtained using both methods.