Before describing the methodology and performance of reverse-time migration, it should be stated that it is only one of about four accurate depth migration methods. As described by Whitmore et al. (1988), these four methods include phase-shift plus interpolation migration Gazdag, (1978), frequency-space migration Berkhout, (1985), Kirchhoff migration Schneider, (1978), and finite-difference reverse-time migration McMechan, (1983). (The first two of these methods are employed in the frequency domain, while the latter two use the time domain.) Faster, but less general, time migration algorithms include the frequency-wavenumber migration due to Stolt (1978), and the various paraxial approximation codes described by Claerbout (1985). Additionally, the Hale-McClellan algorithm described by Hale (1991) represents an economical method 3-D poststack depth migration.
We focus on finite-difference reverse-time migration for two reasons. First of all, it directly uses the technology described in the first two chapters. Secondly, it is probably the most general of the depth migration codes, albeit the most expensive. However, with the advent of high performance computing and parallel processing, it appears that the computing costs will not be prohibitive – even for three-dimensional problems. The beauty of reverse-time migration is that it can be a very general method for seismic imaging. This method uses the finite-difference wave equation modeling as a means of migrating seismic data. As we will see in this chapter and later chapters, reverse-time migration can be used to image highly complex geological structures.
Migration is the data processing technique which positions seismic reflections in their correct subsurface location. Recorded seismic traces are generally plotted at a horizontal position which is at the mid-point between sources and receivers. For layered media, this common-mid-point (CMP) is generally the correct location for the reflection's common-depth-point (CDP) or common-reflection-point(CRP). In areas where we are dealing with reflections from dipping formations, the CMP is not the correct location for the reflecting point. A correction for the positioning of the reflector can be supplied by migration.
Figures & Tables
Seismic Modeling and Imaging with the Complete Wave Equation
“Seismic modeling and imaging of the earth's subsurface are complex and difficult computational tasks. The authors present general numerical methods based on the complete wave equation for solving these important seismic exploration problems.”