Chapter 2: Description of the Problem
In this chapter, we discuss in more detail and from a mainly geometric point of view the principles on which the two fundamental seismic processes of true-amplitude migration and demigration are based. We show how they form the basis for a unified theory of Kirchhoff-type seismic-reflection imaging. By applying these two operations in sequence (i.e., chaining them), a wide class of seismic-imaging problems can be solved. These include:
1) Transformation of a seismic-data section in the time-trace domain that was recorded with a given measurement configuration into a section that is as if it were recorded with another configuration, except for the reflection and transmission coefficients. This imaging process generally is referred to as a configuration transform (CT). As particular CTs, we can cite dip moveout (DMO), azimuth moveout (AMO), migration-to-zero offset (MZO), shot or offset continuation, etc. In this chapter, we concentrate on the MZO operation, i.e., the transformation of a common-offset (CO) section into a zero-offset (ZO) section.
2) Transformation of a 3D migrated image in the depth domain into another one for a different (improved) macrovelocity model. This imaging process is referred to as remigration.
Other possible image transforms that can be solved by chaining the migration and demigration operations include redatuming, wavemode transformation, transformation of surface data into vertical seismic profiling (VSP) data. This book does not discuss these possible applications in detail. Note that in this context, imaging implies not only going from the time-trace domain to the depth domain or vice versa, but also, in the framework of the unified approach, going from one time-trace domain to another, or from one depth domain to another.
We start by briefly describing the earth and macrovelocity models to be considered and the seismic measurement configurations that commonly are used. Then we summarize the basic (mainly kinematic) aspects of the theory to provide a good geometric understanding of all imaging operations involved.