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

Abstract

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 M w > 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.

Obtaining free USArray data by multi-dimensional seismic reconstruction

“…Some effective methods for seismic data reconstruction have been proposed in the exploration seismology community. One type of the most widely used methods is based on a sparse transform that maps the seismic signals to certain domains (e.g., Fourier 18 , curvelet 19 , slant stacklet 20 , and seislet domains 21 ), where the useful information can be sparsely represented and separated from the missing data and random noise. Another type of mainstream methods is based on the Cadzow filtering or the singular spectrum analysis (SSA) 22 , which is a rank-reduction-based method that transforms the data to frequency-wavenumber or frequency-space domains to extract the spatial coherency of the entire dataset for reconstructing the missing information.…”

On the Detection of Upper Mantle Discontinuities with Radon-Transformed Ps Receiver Functions (CRISP-RF)

“…Recent extensions of the slowness slant stack methodology for global body-wave imaging improve resolution by incorporating the notion of the time-and-space locality as well as phase-coherence before stacking (Ventosa et al, 2012;Ventosa & Romanowicz, 2015a, 2015bZheng et al, 2015). Similar ideas have been applied to Ps-RFs in many variations (Guan & Niu, 2017;Gurrola et al, 1994;Shi et al, 2020), all borrowing slightly from exploration seismology, where velocity spectral analysis is used to disentangle phases, given a known earth model (O.…”

High resolution upper mantle discontinuity images across the Pacific Ocean from SS precursors using local slant stack filters

“…In the slowness domain, each coherent signal will form an energy peak centred at its slowness, and random noise will become low-amplitude background. One can then design specific filters, namely the LSSFs, to extract only one target slowness (or a range of slownesses) of interest and mask out the other undesired slownesses, and then transform back to the time-space domain to obtain a cleaned-up record section, in which only the signal of target slowness is preserved, whereas interfering signals with a different slowness (in other words, coherent noise) and random noise are removed (Ventosa et al 2012;Ventosa & Romanowicz 2015). This is very suitable for the case of SS precursors, because both the expected slownesses of the SS precursors and those of the interfering phases are known and can be calculated for reference models such as PREM.…”

“…A balance can be achieved by selecting an optimal stacking aperture in consideration of the sampling density of the array and the noise level. The details of the selection strategy is described in Ventosa et al (2012) for the exploration seismology case and in Ventosa & Romanowicz (2015) for the teleseismic case. In short, the minimum aperture (bin diameter) is approximately A = T/ p, where p is the slowness resolution to be achieved, and T is the dominant period of the signal.…”