Extraction of weak PcP phases using the slant-stacklet transform — I: method and examples

S U M M A R Y In order to study fine scale structure of the Earth’s deep interior, it is necessary to extract generally weak body wave phases from seismograms that interact with various discontinuities and heterogeneities. The recent deployment of large-scale dense arrays providing high-quality data, in combination with efficient seismic data processing techniques, may provide important and accurate observations over large portions of the globe poorly sampled until now. Major challenges are low signal-to-noise ratios (SNR) and interference with unwanted neighbouring phases. We address these problems by introducing scale-dependent slowness filters that preserve time-space resolution.We combine complex wavelet and slant-stack transforms to obtain the slant-stacklet transform. This is a redundant high-resolution directional wavelet transform with a direction (here slowness) resolution that can be adapted to the signal requirements. To illustrate this approach, we use this expansion to design coherence-driven filters that allow us to obtain clean PcP observations (a weak phase often hidden in the coda of the P wave), for events with magnitude Mw > 5.4 and distances up to 80◦. In this context, we then minimize a linear misfit between P and PcP waveforms to improve the quality of PcP–P traveltime measurements as compared to a standard cross-correlation method. This significantly increases both the quantity and the quality of PcP–P differential traveltime measurements available for the modelling of structure near the core–mantle boundary. The accuracy of our measurements is limited mainly by the highest frequencies of the signals used and the level of noise. We apply this methodology to two examples of high-quality data from dense arrays located in north America. While focusing here on body-wave separation, the tools we propose are more general and may contribute to enhancing seismic signal observations in global seismology in situations of low SNR and high signal interference.