Waveform Complexity Processing
The travel times ΔT are the most stable showing the relatively slow Western United States (WUS). Sun and Helmberger (2011) show that at long-period, ΔLR maps generally correlates with the amplitude map, i.e., large ΔLR indicates strong multi-pathing and has low amplitude. Fig. 16 shows that some features following this pattern, but they do not match very well. It appears that the strong attenuation beneath WUS is an additional feature. These same complexities appear in the PKiKP maps but are not well correlated with what is observed in the PcP maps. Here, the overall amplitudes and ΔLR pattern agree better for PKiKP. Note that the amplitudes scatter about as much as in earlier mb bias measures, Lay and Helmberger (1983a, b), used in studying attenuation. They found that while the western US has lower amplitude than eastern US with a bias δmb of 0.26 (corresponding an average amplitude difference of 2), any one station sampled in either region can differ by this amount. Here is a much larger sample but generally in agreement. The average jump in S-wave travel times is about 6s, Grand and Helmberger (1984), Lay and Helmberger (1983a, b) and about half of this for P-waves. These features occur roughly along the Rocky Mountain Front. While PcP results displayed in Fig. 16 are in general agreement with these earlier studies, the PKiKP amplitude near the new Mexico-Texas boundary for event 20091126 are anomalously low. We think this is caused by the ICB as discussed later.
One of the remarkable fine-scale features of this mapping is the behavior of amplitudes between PcP and PKiKP along the northwestern coast, especially for event 20091126. Note the reversed strength between PcP and PKiKP, i.e., when PcP is weak, PKiKP is strong. We also found extreme differences in PKiKP amplitudes at neighboring stations, less than 50 km apart, where one is in the noise while the other is very strong, see Fig. 21. These observations appear to be related to the subduction zone as in the Tkalcic et al. (2010) study. However, most of stations in our datasets do not display such anti-correlations. The variation appears to be caused by upper mantle scattering as is known to some degree, i.e., Nielsen et al. (2003).
Significant progress in 3D modeling of global seismograms at the longer periods (17–100 s) becomes possible with the development of advanced computing systems, Komatitsch and Tromp (2002). Extending this to shorter periods is challenging because of computing demands. So hybrid techniques prove useful. Several axisymmetric methods can reach shorter periods such as Nissen-Meyer et al. (2007). The 2D pseudo-spectral approach as described in Cormier (2000) is particularly good at treating random media and used extensively in the recent study by Tkalcic et al. (2009). Some hybrid methods use a combination of analytic and finite-difference (FD) methods which are interfaced with the Kirchhoff integral. Essentially, one propagates a signal through simple regions using generalized rays and only uses numerical methods in the heterogeneous regions, Wen and Helmberger (1998). This method was used by Dai et al. (2012) in inserting a box-like structure at the ICB. We have reproduced their results using our new 2D FD code, Li et al. (2014), as discussed in the main text.
To obtain seismograms from a point source in 2D media, we need to consider in-plane propagation and out-of-plane spreading. Three difficulties needs to be addressed in implementing this procedure: (1) the mapping procedure involved in 3D source excitation for earthquakes; (2) 3D spreading corrections; and (3) reducing the spherical earth to a flattened model. We solved the first issue by using a modern moment tensor excitation approach. The out-of-plane geometric spreading is accounted for by applying a post-simulation filter. In addition, an earth-flattening transformation is used to obtain simulations in a spherical geometry using calculations based on Cartesian coordinates. Simulations are generated using the 2D staggered grid finite difference method on graphics processing units (GPUs), which proves to be highly efficient and flexible for modeling global seismograms, including core phases. The effectiveness of this method is demonstrated by comparing our synthetics with the frequency-wavenumber normal-mode and SEM synthetics, Li et al. (2014).
The 2D pseudo-spectral method has been used extensively for studying scattering effects near the CMB, i.e., Cormier (2000). Recently it was used to investigate receiver effects for plane-wave incidence of PcP and PKiKP, Tkalcic et al. (2010). We repeated this experiment but assumed a point source for the PREM model, Fig. 17. We place the “scattering boxes” either beneath the source or the receivers. We assume an explosion source and Gaussian random media. To test our code, we conducted a detailed reciprocity numerical experiment given in Fig. 18. In Fig. 17, we can see ray paths for PKiKP leaving the source region are nearly the same for receivers from 20° to 30° degree. The PcP rays are also compact but have an offset relative to PKiKP. In contrast, the ray paths are well separated at the receiver side with each path encountering a distinct structure. The synthetics for these two situations are given in Fig. 19 and the amplitudes variation is included in Fig. 17. Note the rapid amplitude decay of PKiKP and the gentle increase in PcP controlled by the PREM model which is similar to the AK135 results as shown in Tkalcic et al. (2009). The PKiKP/PcP ratio is also displayed where the effect from source side scattering (Fig. 17) is smaller than that from receiver side scattering.
See Figs. 20, 21, 22, 23, 24.