To better understand the PS-AMO operator, I compute and
analyze its impulse response.
Figure compares the AMO impulse responses obtained with
the filters in equation (top) and equation (bottom).
Both are obtained with a value of and *v*_{p}=2.0 km/s, and are
kinematically equivalent.

Figure presents a similar comparison to
Figure for the case of converted waves. Here,
we use and *v*_{p}=2.0 km/s. Both impulse responses,
Figures and , also
illustrate the differences in the dynamic
behavior of the operator. The top panels for both figures show
the impulse responses using the operator from equation , which is
based on the known PS-DMO operator of Xu et al. (2001). In contrast,
the bottom panels show the PS-AMO operator
from equation , which is based on
the new PS-DMO operator, presented in Chapter 2, equivalent to the Zhou et al. (1996) PP-DMO operator.
The arrows in Figures and show that
the operator from equation has stronger amplitudes
for steeply dipping events than the operator from equation .
The area marked by the oval in the bottom panel for both
Figures and
shows that impulse response for the PS-AMO operator
is not center at zero inline and crossline midpoint location, as
it is the case of the PP-AMO operator.

Figure 2

Figure 3

Figure shows two important characteristics of PS-AMO. First, the PS-AMO operator is asymmetric because of the difference between the downgoing and upgoing raypaths. Second, the PS-AMO operator varies with respect to traveltime, even for a constant velocity medium; this behavior is caused by all the non-linear dependencies of the PS-AMO operator with respect to traveltime, P velocity, and . The vertical variation of the lateral shift reflects that the lateral displacement between the CMP and CRP also varies with the traveltime. Both characteristics are intrinsic of converted-wave data.

Figure 4

12/14/2006