DEFINING AN IMAGING CRITERION

The imaging conditions discussed in the previous section obtain an estimation of the imaging attribute at a particular point in the four-dimensional (for a 2D treatment) 2D-space$\times$time$\times$shot-position domain. The imaging criterion defines the statistical approach involved to reduce these information to the expectation value of the attribute in the three-dimensional domain spanned by 2D-space$\times$incidence-angle. There are two major paths to perform this reduction  

$$data(x_r,t;x_s) \;\; \begin{array} {l} \stackrel{A}{\longri... ...d{array} \;\; \stackrel{C}{\longrightarrow} \;\; R(x,z,\beta),$$ (7)

or

$$data(x_r,t;x_s) \;\; \stackrel{A}{\longrightarrow} \;\; R(x,... ...eta;x_s) \;\; \stackrel{C}{\longrightarrow} \;\; R(x,z,\beta).$$ (8)

In the first path A represents the depth extrapolation and imaging for time t, B represents the time integration process and C represents the final search over different shot-gathers to build the function $R(x,z,\beta)$.In the second path A also represents the depth extrapolation and imaging for time t, B represents the time integration process and C represents the integration over the shot-point axis. The first one starts with an independent estimation of the attribute and the angle for each shotpoint, while the second obtains from the beginning an estimation of the angular distribution of the attribute for each shotpoint.