Seismic wave propagation

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

 

 8#8 (1)

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  

 9#9 (2)

where 10#10 is frequency, k_x is lateral wavenumber and k_z is vertical wavenumber to give us:

 

 11#11 (3)

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