I present a new migration algorithm denoted as generalized diffraction-stack migration (GDM). Unlike traditional diffraction-stack migration, it accounts for all arrivals in the wavefield, including two-way primaries and multiple arrivals, and it is not subject to the high-frequency approximation of ray tracing. It is as accurate as reverse-time migration (RTM), but, unlike RTM, filtering and muting can be easily applied to the migration operator to reduce artifacts due to aliasing, and unwanted events such as multiples. Unlike RTM, GDM can be applied to common offset gathers. The main drawback of GDM is that it can be more than an order-of-magnitude more computationally expensive than RTM, and requires much more memory for efficient use. To mitigate some of these disadvantages, I present a multisource least-squares GDM method with phase-encoding.
There are six chapters presented after the introduction. Chapter 2 derives the GDM equation by reformulating the standard RTM equation, and shows how GDM is related to the traditional diffraction-stack migration. Chapter 3 shows how the GDM kernel can be filtered to eliminate coherent noise in the migration image. This precise filtering of the migration operator cannot be done with the standard RTM approach, but it can now be performed with the GDM method. In Chapter 4, I develop an antialiasing filter for GDM. This idea is adapted from the traditional antialiasing strategy for Kirchhoff migration, except GDM antialiasing accounts for both primary and multiple reflection events. This is novel antialiasing filter that can be used for filtering the RTM-like imaging operator. In Chapter 5, I show how to mute or filter the GDM operator to emphasize multiple reflection events. I split the GDM operator into two separate parts, the primary migration operator and the multiple migration operator. By computing the dot-product of the migration operators with the data, followed by an optimal stack of the primary-only image and the multiple-only image, a higher resolution in the migration image can be achieved. An additional benefit is that cross-talk between primary and multiple scattered arrivals, often seen in conventional RTM images, are greatly attenuated. Finally, Chapter 6 presents an efficient implementation of least-squares GDM with supergathers. The supergather consists of a blend of many encoded shot gathers, each one with a unique encoding function that mitigates crosstalk in the migration image. A unique feature of GDM is that the Green's functions (computed by a finite-difference solution to the wave equation) can be reused at each iteration. Unlike conventional least-squares RTM, no new finite-difference simulations are needed to get the updated migration image. This can result in almost two orders-of-magnitude reduction in cost for iterative least-squares migration. Furthermore, when the least-squares GDM is combined with phase-encoded multisource technology, the cost savings are even greater. This is a subject that is discussed in Chapter 7.
The main challenge with GDM is that it demands much more memory and I/O cost than standard RTM algorithm. As a partial remedy, Appendix A describes how to efficiently compute the migration operators either in a target-oriented mode or by using wave equation wavefront modeling. In addition, the intensive I/O and storage costs can be partly, not fully, mitigated by applying a wavelet transform with compression, where a compression ratio of at least an order-of-magnitude can be achieved with a small loss of accuracy. This topic is addressed in Appendix B.