Improvement of coda phase detectability and reconstruction of global seismic data using frequency–wavenumber methods

Abstract

Due to uneven earthquake source and receiver distributions, our abilities to isolate weak signals from interfering phases and reconstruct missing data are fundamental to improving the resolution of seismic imaging techniques. In this study, we introduce a modified frequencywavenumber (fk) domain based approach using a 'Projection Onto Convex Sets' (POCS) algorithm. POCS takes advantage of the sparsity of the dominating energies of phase arrivals in the fk domain, which enables an effective detection and reconstruction of the weak seismic signals. Moreover, our algorithm utilizes the 2-D Fourier transform to perform noise removal, interpolation and weak-phase extraction. To improve the directional resolution of the reconstructed data, we introduce a band-stop 2-D Fourier filter to remove the energy of unwanted, interfering phases in the fk domain, which significantly increases the robustness of the signal of interest. The effectiveness and benefits of this method are clearly demonstrated using both simulated and actual broadband recordings of PP precursors from an array located in Tanzania. When used properly, this method could significantly enhance the resolution of weak crust and mantle seismic phases.

Obtaining free USArray data by multi-dimensional seismic reconstruction

“…Despite the best effort in acquisition design, earthquake data are rarely recorded on a perfectly even-spaced seismic array. Similar to earlier interpolation methods 17,28,34 , the first step of our reconstruction algorithm is to bin the data onto a regular grid. To this end, we use a weighted interpolation method for the binning process.…”

“…The high-quality data with a regular spatial sampling can greatly benefit data analysis, processing and visualization, and also improve the numerical stability and accuracy for grid-based seismic imaging techniques (e.g., Eikonal 4 and Helmholtz tomography 14 ). As a result, regularization approaches that suppress the noise and interpolate the missing traces of array data are highly demanded 15–17 .…”

“…Also implemented are methods based on high-resolution Radon transform 32 , singular spectrum analysis 33,34 and, more recently, non-linear waveform stretching-and-squeezing 35 . Aside from interpolating the receiver functions, Schneider et al 17 reconstructed the weak-amplitude under-side reflections from the mantle transition zone (i.e., PP precursors) while utilizing a compressive-sensing-based approach that seeks the sparsity of dominating energy in the frequency-wavenumber domain. A recent study also applied the idea of compressive sensing to reconstruct the synthetic surface wavefields via a sparse representation using a plane-wave basis 36 .…”

Sensitivity Kernels of PP Precursor Traveltimes and Their Limitations for Imaging Topography of Discontinuities

“…It has to be mentioned that more powerful array methods (Rost & Thomas, , ; Rost & Weber, ) can help dealing with wave interference as interfering phases may be identified and isolated from the PP precursors. Stacking techniques, such as velocity spectral analysis (Davies et al, ) or frequency‐wavenumber methods (Schneider et al, ) employed in array studies, are capable of detecting signals that correspond to the PP precursors by significantly reducing interference of other phases. Although such techniques may prove useful, they can only be applied to the limited regions with a dense station coverage.…”

Toroidal mode observations and their interpretation in terms of anisotropy and density

“…Depending on the source-receiver geometry this can lead to several phases arriving at the same time at the receiver. Therefore stacking techniques using for instance receiver arrays are needed to decipher phases mapping distinct regions of Earth's deep interior (Montagner and Kennett, 1996;Rost and Thomas, 2002;Schneider et al, 2018). However, recently reflected phases have been used succesfully to constrain anisotropy too (Huang et al, 2019).…”