PP and SS precursors

For PP and SS phases precursors exist, which are generated in a similar way as for P'P'. The ray path of the mother phase (PP or SS) and the underside reflection at the discontinuity (P$^d$P or S$^d$S) is displayed in figure 3.3 b). Arrivals preceeding PP and SS have been studied intensively (Bolt et al. 1968; Bolt, 1970; King et al., 1975), but early array studies showed that these precursors have slownesses significantly different than predicted for P$^d$P (Wright and Muirhead, 1969; Wright, 1972). Therefore, these phases are interpreted as asymmetric reflections of PP (Wright 1972), as the result of scattering (King et al., 1975) or can be seen as upper side reflections from the discontinuities at the receiver side. The ray path of an upper side reflection (Pp$_d$p) is shown in Figure 3.3 b). The wave is reflected at the free surface near the receiver and, between this surface reflection point and the receiver, once more at the upper side of the discontinuity. Pp$_d$p phases show slownesses and waveforms similar to P and pP, respectively
However, phases from deeper discontinuities have been found with correct travel times and slownesses to be interpreted as P$^d$P.

Figure 3.4: Results for stacks of a huge number of seismograms stacked with respect to the source receiver distance, IASP91 theoretical travel times for the PP and SS time windows and number of seismograms used to compute the stacks (after Flanagan and Shearer, 1998 and 1999). The top panels show travel time curves calculated for IASP91. The major phases and the reflections at the upper mantle discontinuities are labelled. The middle panel on the left hand side shows the stacks for SS and precursors, the right hand side for PP. The same time window as for the theoretical travel times was chosen. The bottom panels show the number of stacked seismograms for each distance. The strong horizontal lines at $\sim$0 min travel time mark the SS and PP phase. The precursor of the 410 and the 660 form approximately parallels to PP and SS and are marked. The phase P$^{660}$P is not visible, as discussed in chapter 2.2.3. Due to the long period nature of the stacked seismograms, shallow discontinuities (H, G and L) and the fine structure of the discontinuities can not be resolved.

These precursors have been used to resolve the structure of the upper mantle beneath the reflection point (Shearer, 1990; Wajeman, 1988; Neele and Snieder, 1992; Vasco et al., 1995; Flanagan and Shearer, 1998 and 1999).
The stacking of a huge number of globally recorded long period seismograms impressively shows the existence of P$^d$P and S$^d$S phases. Stacks for PP and SS depending on epicentral distance are shown in the mid panel of Figure 3.4 (Flanagan and Shearer, 1998 and 1999). The stacked seismograms are aligned on the PP (SS) arrival at a travel time of 0 s. The P$^d$P (S$^d$S) phases are approximately parallel to PP (SS) indicating similar slownesses. Due to the longer differential travel times S$^d$S - SS, the S$^d$S phases are easier to detect. As described in section 2.2.3, the stacks for PP lack the reflection from the 660, although the theoretical travel time for the reflection from the 660, computed for IASP91, is marked. The top panels show the theoretical travel times for IASP91. The bottom panels show the number of seismograms used to compute the stacks. The globally recorded seismograms and the stacking methods used to generate the stacks of Figure 3.4 can be used to generate maps of the 410 and 660 to infer regional differences. For this purpose events with reflection points in a similar region are stacked. These ''topography'' maps of the discontinuities may reflect the movements of cold and hot material in the mantle (Shearer, 1990).
In the stacks, the shallower discontinuities (H, G and L) discussed in chapter 2 are not detected, partly due to the long period data used.
The inversion of P$^d$P - PP (S$^d$S - SS) differential travel times to discontinuity depth may contain gross errors, because of the use of geometrical optics for the inversion (Neele et al., 1997).
The global studies of the underside reflections give a good overview on the structure of the discontinuities. However, as a result of the use of long period waves and the correlated huge Fresnel zones (PP: $\sim$ 10$^{\circ}$ x 15$^{\circ}$, SS $\sim$ 18$^{\circ}$ x 23$^{\circ}$ ), the resolution is poor. But these studies are well suited to constrain velocity and density jumps across the discontinuities (Shearer and Flanagan, 1999).