Recent advances in computer power make it practical to use prestack depth migration as an imaging operator. This operator directly transforms our data, which is in data-midpoint position, data-offset, and time coordinates [(m_{D},h_{D},t)], into an image that is in image-midpoint location, image-offset, and depth coordinates [()].
Prestack depth migration can be achieved using Kirchhoff migration methods, which are based on a high-frequency approximation of the wave-equation. Kirchhoff methods require the summation of the data over complex multivalued surfaces, and cannot correctly handle complex subsurfaces. The high-frequency approximation breaks down for very complex subsurface structures.
Wave-equation-based methods
provide a solution to the wave-equation along the
entire range of frequencies, wave-equation-based
methods can handle complex subsurface structures
such as overthrusts, salt bodies, and others.
There are several
ways to implement wave-equation migration, which
differ mainly in propagation of the wavefield
and the imaging condition.
The next section describes the basics of prestack wave-equation imaging,
Its main purpose is to describe the
algorithm I use to transform the prestack data into the prestack
image space, and describe the elements of this space.