Characterization of P$^{d}$P phases

To detect P$^{d}$P phases in the recordings of a short-period small-aperture array a reliable identification of these phases is necessary.
Figure 5.3 schematically shows an extract of the P-wave travel time panel in Figure 3.4 (after Shearer, 1991).

Figure 5.3: Detail of P-wave travel time panel computed using IASP91 (after Shearer, 1991). A distance range from 80$^{\circ}$ to 130$^{\circ}$ and the time window between P and PP is displayed. The travel times are aligned on the PP arrival and the different phases are labeled. For phases and nomenclature see Shearer (1991).

The travel times are aligned on PP with approximately 0 s travel times. The underside reflections from depths of 410 km and 660 km are marked by P$^{410}$P and P$^{660}$P. The discontinuity at 210 km is not included in IASP91 but its PP underside reflection has been added. As can be seen from the parallel branches of PP and the P$^{d}$P branches, the major phase PP and the P$^{d}$P phases are characterized by a similar slowness (u$_{PP}$ - u$_{P^dP}$ $\le$ 0.2 s/$^{\circ}$). The P (or P$_{diff}$) phase shows a slowness several s/$^{\circ}$ smaller than PP and P$^{d}$P ( 2.4 - 3.3 s/$^{\circ}$ smaller depending on distance). In the precursor time window up to 130 s before PP, not only the underside reflections P$^d$P but also phases resulting from upperside reflections at the discontinuities (Pp$_{410}$p and Pp$_{660}$p) arrive. Pp$_d$p are characterized by a slowness comparable to P. P$^d$P and Pp$_d$p show similar travel times in the epicentral distance range used here and, therefore, it is important to separate these phases by using array techniques to detect P$^d$P unambiguously.
Three criteria were chosen to classify P$^d$P arriving within the time window before PP:


1) Backazimuth: The phase must travel along the great circle path between source and receiver. This ensures that the phase was not reflected off the great circle-path and that it travelled directly from source to receiver. Reflections off the great circle path can be identified. Additionally, coherent phases from other sources can be identified. For example phases from a second event arriving within the time window or near receiver quarry blasts.
2) Slowness: A slowness comparable to PP ($\le$ 0.2 s/$^{\circ}$ smaller than PP) indicates P$^d$P. The P$^d$P slowness is 2.4 s/$^{\circ}$ to 3.3 s/$^{\circ}$ larger than the Pp$_d$p slowness and can be used to discriminate between the two phases. Also, other phases which might arrive within the precursor time window (e.g. PKiKP for distances larger than $\sim$104$^{\circ}$) can be identified.
3) Coherency: The coherency is used to distinguish between incoherent noise and coherent phases arriving at the array. By chance the noise might show the right slowness and backazimuth to be interpreted as P$^d$P, but as a statistical signal it is not coherent. The form of the fk-diagram can be used to interpret the coherency of the signal.
These criteria were tested using the fk-analysis. The first two criteria are 'hard' criteria, i.e. a possible P$^d$P phase must show a similar slowness and backazimuth as PP within the resolution of the fk-analysis. The third criterion is more qualitative and the correspondence between the fk-diagram and the ARF is examined by eye.