Chapter 6
Prestack Time and Depth Migration

Prestack migration algorithms are relatively simple variants of the poststack methodologies. The primary difference lies not in the mathematical theory but in the way in which any given algorithm is structured and applied to recorded multi-fold data. The basic differences arise because the prestack method must handle non-coincident sources and receivers. This means that it must handle the traveltime issues and amplitude correction factors associated with the source and similar issues for each and every receiver.

To resolve this issue, it is normal to split the imaging problem into two independent pieces. One piece handles the traveltime and amplitude from the source to the image point, while the other handles the traveltime and amplitude from the image point to the receiver. When both pieces are based on the same modeling approach, the names of the prestack algorithms are frequently identical to those given to the poststack methods from which they arose. When the two pieces are based on technically different methods, the resulting algorithm is assigned a hybrid combination of the two names. Figure  1 details these methodologies and becomes the framework for the discussion on zero offset technologies.

  Wavefield and Wave-Motion Hierarchies
  Shot Profile Prestack Migration
   Performing Shot Profile Migration
   Shot Profile Migration Example
  Partial Prestack Migratio–Azimuth Moveout (AMO)
  Velocity Independent Prestack Time Imaging
  Double Downward Continuation—Common Azimuth Migration
  Common Offset Kirchhoff Ray-Based Methods
   Straight Ray Kirchhoff Prestack Time Migration
   Curved Ray Kirchhoff Prestack Time Migration
   Single Arrival Kirchhoff Depth Migration
   Multiple Arrival Kirchhoff Migration
   Kirchhoff Elastic Depth Migration
   Single Arrival Kirchhoff Depth Migration Summary
  Beam and Plane Wave Migrations
   Pure Plane Wave Migration
   Beam Stack Migration
   Delayed Shot Migration
   Gaussian Beam Migration
  Algorithmic Differences
 
Introduction
Seismic Modeling
History
Zero Offset Migration Algorithms
Exploding Reflector Examples
Prestack Migration
Prestack Migration Examples
Data Acquisition
Migration Summary
Isotropic Velocity Analysis
Anisotropic Velocity Analysis
Case Studies
Course Summary