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 vp=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 vp=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 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.