Spectra of whole Earth oscillations or normal modes provide important constraints on Earth’s large scale structure. The most convenient way to include normal mode constraints in global tomographic models is by using splitting functions or structure coefficients, which describe how the frequency of a specific mode varies regionally. Splitting functions constrain 3D variations in velocity, density structure and boundary topography. They may also constrain anisotropy, especially when combining information from spheroidal modes, which are mainly sensitive to P-SV structure, with toroidal modes, mainly sensitive to SH structure. Spheroidal modes have been measured extensively, but toroidal modes have proven to be much more difficult and as a result only a limited number of toroidal modes have been measured so far. Here we expand the splitting function studies by Resovsky and Ritzwoller (1998) and Deuss et al. (2013), by focusing specifically on toroidal mode overtone observations. We present splitting function measurements for 19 self-coupled toroidal modes of which 13 modes have not been measured before. They are derived from radial and transverse horizontal component normal mode spectra up to 5 mHz for 91 events with MW ≥ 7.4 from the years 1983-2018. Our data include the Tohoku event of 2011 (9.1MW), the Okhotsk event of 2013 (8.3MW) and the Fiji Island event from 2018 (8.2MW). Our measurements provide new constraints on upper and lower mantle shear wave velocity structure and in combination with existing spheroidal mode measurements can be used in future inversions for anisotropic mantle structure. Our new splitting function coefficient data set will be available online.

Abstract. Ray-Tracing software tools have been widely used in the optical design of solar concentrating collectors. In spite of the ability of these tools to assess the geometrical and material aspects impacting the optical performance of concentrators, their use in combination with experimental measurements in the framework of collector testing procedures as not been implemented, to the date, in none of the current solar collector testing standards. In the latest revision of ISO9806 an effort was made to include linear focusing concentrating collectors but some practical and theoretical difficulties emerged. A Ray-Tracing analysis could provide important contributions to overcome these issues, complementing the experimental results obtained through thermal testing and allowing the achievement of more thorough testing outputs with lower experimental requirements. In order to evaluate different available software tools a comparison study was conducted. Taking as representative technologies for line-focus concentrators the Parabolic Trough Collector and the Linear Fresnel Reflector Collector, two exemplary cases with predefined conditions -geometry, sun model and material properties -were simulated with different software tools. This work was carried out within IEA/SHC Task 49 "Solar Heat Integration in Industrial Processes".

The Global Seismographic Network (GSN)—a global network of ≈150 very broadband stations—is used by researchers to study the free oscillations of the Earth (≈0.3–10 mHz) following large earthquakes. Normal-mode observations can provide information about the radial density and anisotropic velocity structure of the Earth (including near the core–mantle boundary), but only when signal-to-noise ratios at very low frequencies are sufficiently high. Most normal-mode observations in the past three decades have been made using Streckeisen STS-1 vault seismometers. However, these sensors are no longer being manufactured or serviced. Candidate replacement sensors, the Streckeisen STS-6 and the Nanometrics T-360GSN, have been recently installed in boreholes, postholes, and vaults at several GSN stations and GSN testbeds. In this study, we examine normal-mode spectra following three Mw 8 earthquakes in 2021 and from one Mw 8.2 earthquake in 2014 to evaluate the change in GSN low-frequency performance on the vertical component. From this analysis, we conclude that the number of GSN stations capable of resolving normal modes following Mw 8 earthquakes has nearly doubled since 2014. The improved observational capabilities will help better understand the radial velocity and density estimates of the Earth.

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.

We present free oscillations Python (FrosPy), a modular Python toolbox for normal mode seismology, incorporating several Python core classes that can easily be used and be included in larger Python programs. FrosPy is freely available and open source online. It provides tools to facilitate pre- and postprocessing of seismic normal mode spectra, including editing large time series and plotting spectra in the frequency domain. It also contains a comprehensive database of center frequencies and quality factor (Q) values based on 1D reference model preliminary reference Earth model for all normal modes up to 10 mHz and a collection of published measurements of center frequencies, Q values, and splitting function (or structure) coefficients. FrosPy provides the tools to visualize and convert different formats of splitting function coefficients and plot these as maps. By giving the means of using and comparing normal mode spectra and splitting function measurements, FrosPy also aims to encourage seismologists and geophysicists to learn about normal mode seismology and the study of the Earth’s free oscillation spectra and to incorporate them into their own research or use them for educational purposes.