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From the discussion of kinematics just seen, it is clear that the presence
of artifacts will be diminished by carrying out processing in the
angle domain. Understanding the kinematics allows us to develop methods
to image the subsurface based on the idea of ``reversing'' seismic
wave propagation. Before we can explore imaging methods in the angle domain,
we must first review some basic equations for wave propagation
in the subsurface. For simplicity, I will examine equations relating to the
well-known 2-D acoustic case. A straightforward
derivation of them can be found in ().
The 2-D acoustic wave equation can be written as

where *P* is the pressure wave traveling at time *t* through the subsurface
defined by lateral location *x* and depth *z* with velocity *v*.

We can now obtain the dispersion relation of the 2-D acoustic
wave equation by substituting the trial solution

where 10#10 is frequency, *k*_{x} is lateral wavenumber and *k*_{z}
is vertical wavenumber to give us:

Given this understanding of wave propagation through the subsurface, we
can now explore methods of imaging the subsurface by ``reversing'' the
propagation.

** Next:** Kirchhoff migration methods
** Up:** Migration in complex areas
** Previous:** Subsurface-related domain: reflection angle
Stanford Exploration Project

10/31/2005