PRESTACK MIGRATION

Prestack migration creates an image of the earth's reflectivity directly from prestack data. It is an alternative to the ``exploding reflector'' concept that proved so useful in zero-offset migration. In prestack migration,

we consider both downgoing and upcoming waves.

A good starting point for discussing prestack migration is a reflecting point within the earth. A wave incident on the point from any direction reflects waves in all directions. This geometry is particularly important because any model is a superposition of such point scatterers. The point-scatterer geometry for a point located at (x,z) is shown in Figure 1.

 

pgeometry Figure 1 Geometry of a point scatterer.

The equation for travel time t is the sum of the two travel paths is  

$$t\,v\ \eq \ \sqrt { z^2\ +\ {( s \ -\ x ) }^2} \ +\ \sqrt { z^2 \ +\ {( g \ -\ x )}^2}$$ (1)

We could model field data with equation (1) by copying reflections from any point in (x,z)-space into (s,g,t)-space. The adjoint program would form an image stacked over all offsets. This process would be called prestack migration. The problem here is that the real problem is estimating velocity. In this chapter we will see that it is not satisfactory to use a horizontal layer approximation to estimate velocity, and then use equation (1) to do migration. Migration becomes sensitive to velocity when wide angles are involved. Errors in the velocity would spoil whatever benefit could accrue from prestack (instead of poststack) migration.