Algorithms based on Empirical Mode Decomposition (EMD) and Iterative Filtering (IF) are largely implemented for representing a signal as superposition of simpler well-behaved components called Intrinsic Mode Functions (IMFs). Although they are more suitable than traditional methods for the analysis of nonlinear and nonstationary signals, they could be easily misused if their known limitations, together with the assumptions they rely on, are not carefully considered. In this work, we examine the main pitfalls and provide caveats for the proper use of the EMD- and IF-based algorithms. Specifically, we address the problems related to boundary errors, to the presence of spikes or jumps in the signal and to the decomposition of highly-stochastic signals. The consequences of an improper usage of these techniques are discussed and clarified also by analysing real data and performing numerical simulations. Finally, we provide the reader with the best practices to maximize the quality and meaningfulness of the decomposition produced by these techniques. In particular, a technique for the extension of signal to reduce the boundary effects is proposed; a careful handling of spikes and jumps in the signal is suggested; the concept of multi-scale statistical analysis is presented to treat highly stochastic signals.

The Lunar Gravitational-wave Antenna (LGWA) is a proposed array of next-generation inertial sensors to monitor the response of the Moon to gravitational waves (GWs). Given the size of the Moon and the expected noise produced by the lunar seismic background, the LGWA would be able to observe GWs from about 1 mHz to 1 Hz. This would make the LGWA the missing link between space-borne detectors like LISA with peak sensitivities around a few millihertz and proposed future terrestrial detectors like Einstein Telescope or Cosmic Explorer. In this article, we provide a first comprehensive analysis of the LGWA science case including its multi-messenger aspects and lunar science with LGWA data. We also describe the scientific analyses of the Moon required to plan the LGWA mission.

We present the BVAL method, designed to forecast potentially damaging earthquakes (Mw ≥ 5.0) in Italy based on temporal variations of the b-value of the Gutenberg–Richter frequency–magnitude distribution. The b-value is used as an indicator of stress within the Earth's crust, with lower b-values associated with higher stress levels and an increased likelihood of significant seismic events. This method issues alarms when the b-value falls below a critical threshold. It is optimized using the HOmogenized instRUmental Seismic catalogue data from 1990 to 2004 and validated pseudo-prospectively using data from 2005 to 2022. Our analysis uses the recently developed b-positive (b+) method to compute the b-value from magnitude differences, providing resilience against data incompleteness. We compare the performance of the BVAL method with two established models: the Epidemic Type Aftershock Sequence (ETAS) model, which forecasts earthquake rates based on the epidemic principle that each shock triggers subsequent shocks, and the FORE model, which relies on the occurrence of strong foreshocks. Additionally, we evaluate two ensemble models that combine BVAL and FORE through additive (EADD) and multiplicative (EMUL) strategies to balance false alarms and missed events. The EADD model declares an alarm when either BVAL or FORE signals it, while the EMUL model triggers alarms only when both methods agree. We assess the predictive efficiency of these models using the area skill score, derived from Molchan diagrams, which plot the miss rate against the fraction of space-time occupied by alarms. Our results demonstrate that BVAL is less effective than FORE and ETAS at high space-time fractions, but it outperforms ETAS at low fractions (⁠ τ < 2–4 per cent), indicating its potential utility in scenarios where minimizing false alarms is critical. This comprehensive comparison highlights the strengths and limitations of each method, suggesting that integrating multiple forecasting strategies can enhance the reliability of earthquake preparedness and response efforts in Italy.

We present the first application of Full-Waveform Inversion (FWI) for a radially anisotropic 3D velocity model of the lithosphere beneath central Italy. The retrieved model CI23 constrains P-wave (VPV, VPH) and S-wave velocities (VSV,VSH) in the period range 8–50 s. CI23 model correlates well with regional lithological formations and highlights a negative radial anisotropy anomaly (VSH < VSV) localized beneath the epicentral region of the 2016–2017 Amatrice-Visso-Norcia (AVN) seismic sequence. An opposite trend (positive radial anisotropy anomaly, i.e. VSH > VSV) is observed in the area affected by the 2009 L’Aquila (AQ) seismic sequence. We interpret the velocity anomalies in terms of local tectonic structures, particularly the Olevano-Antrodoco-Sibillini (OAS) thrust—Gran Sasso Thrust (GST) systems, while also considering possible evidence of overpressured fluids and fluid migration. Additionally, the observed anomalies may reflect transient velocity variations induced by the ANV and AQ seismic sequences.

The Global Navigation Satellite System (GNSS) can provide users with high-precision positioning information continuously and benefits all walks of life, e.g., unmanned driving, urban navigation, deformation monitoring, etc. The important scientific research and application value of GNSSs have prompted many countries and regions to develop GNSS technologies. GNSS core positioning technologies, such as Precise Point Positioning (PPP) and Real-Time Kinematic positioning (RTK), can provide decimeter-level or even centimeter- level positioning accuracy in open environments. However, active GNSS positioning technologies are susceptible to complex conditions, including canyon environments, low- cost receivers, and multi-GNSS situations, and, on occasion, cannot provide accurate, continuous, and reliable positioning information. The diversification of GNSS systems and constellations, receiver types, and observation environments puts forward higher requirements for technology and algorithms to maintain high-precision positioning and navigation services. Advanced algorithms are key to solving GNSS practical application problems and expanding the scope of GNSS applications. This Special Issue aims at studies covering improved methods and the latest chal- lenges in precise GNSS positioning and navigation, especially under complex conditions for various research investigations as well as a range of practical applications. Both the- oretical and applied research contributions to the GNSS high-precision technology in all disciplines are considered. Topics may cover anything from precise muti-GNSS positioning algorithms and GNSS data processing to more comprehensive targets and scales. Therefore, new algorithms for high-precision positioning and navigation, GNSS receivers, software development for data collection and processing, and their applications in various fields are all included.

The research scope of the papers published in this Special Issue mainly focuses on high- precision and high-reliability positioning, navigation, and timing (PNT) with Global Navigation Satellite System (GNSS) or multi-source sensors, resilient PNT with GNSSs or multi-source sensors in challenging environments, integrated PNT with GNSSs and multi-sensor systems, applications of PNT with GNSSs or multi-source sensors, etc.

The 2020 MW 6.4 Petrinja (Croatia) earthquake induced extensive and diversified liquefaction and lateral spreading phenomena within ≈ 20 km radius from the epicenter. A detailed investigation from field and Unmanned Aerial Vehicle (UAV) surveys was carried out by a European researcher team (EUTeam) in the months following the mainshock. This work focuses on 61 surveyed sites: field observations were coupled with laboratory tests for soil classification and sediment composition. The adopted procedure provides an in-depth geological and geotechnical characterization of the liquefied sites in the Petrinja region. The liquefaction evidences are mainly associated to alluvial plain environments, in particular to meander paleochannels, and the ejected material is predominantly siliciclastic, made up of very rounded quartz-rich lithics. Few sites are dominated by angular carbonate rock fragments, related to liquefaction in cataclastic deposits along tectonic fractures. The ejected sediment includes a wide range of grain-size from silt to gravel. The peculiar presence of gravel in the liquefied deposits (up to 28% in some samples) confirms the need of expanding the grain-size boundaries for liquefiable coarse-grained gravelly soils. The information gathered from the post-earthquake surveys and from the sedimentological and geotechnical analysis for each studied site were compiled in organized data sheets, providing a striking instrument for in-depth earthquake studies, both for geological and geotechnical engineering purposes. The format defined for the data sheet can be functional and applicable also in liquefaction studies from different geological and depositional settings.

Although not specifically conceived for tackling short‐term aftershock incompleteness (STAI), earthquake detection methods such as template matching (TM) and machine learning (ML) can help mitigate the under‐reporting of aftershocks after large earthquakes by detecting low‐magnitude events hidden in seismic noise. So far, the ability of TM and ML to address STAI has not been evaluated against benchmark data sets reconstructed by independent methods. In this study, we use events reconstructed by RESTORE (REal catalogs STOchastic REplenishment), a Python toolbox specifically designed to tackle STAI, as a stochastic benchmark to assess the ability of TM and ML in recovering the bulk statistical properties of aftershocks missed during STAI period. Our results show overall good compatibility between the TM/ML detections and the RESTORE benchmark in the space–time–magnitude domain, though some discrepancies in detection rates and in the upper bounds of magnitudes are noted. This study also highlights the complementary use of stochastic and enhanced detection techniques. Stochastic algorithms like RESTORE can be implemented for immediate STAI mitigation in short‐term forecasting and operational earthquake forecasting, whereas enhanced detection techniques can be used over longer time scales to precisely recover unrecorded events.

Wind turbines generate considerable seismic noise and interfere with sensitive instruments, such as permanent and temporary seismic sensors installed nearby, hampering their detection capabilities. This study investigates the seismic noise emission from one of Italy's largest wind farms, consisting of 69 turbines (2 MW each), located in northeastern Sardinia. Characterizing the noise emission from this wind farm is of particular importance due to its proximity to the Italian candidate site for hosting the Einstein Telescope (ET), the third-generation observatory for gravitational waves. We run a passive seismic experiment, “Wind turbIne Noise assEsSment in the Italian site candidate for Einstein Telescope” (WINES), using a linear array of nine broadband stations, installed at increasing distances from the wind farm. Spectral analysis, based on the retrieval of spectrograms and power spectral densities at all stations, shows a significant increase in noise amplitude when the wind farm is in operation. The reconstruction of noise polarization points out that the noise wavefield originates from a direction consistent with the wind farm's location. We recognize four dominant fixed spectral peaks at 3.4, 5.0, 6.8, and 9.5 Hz, corresponding to the modes of vibration of the wind turbine towers. While decreasing in amplitude with distance, the 3.4 Hz peak remains detectable up to 13 km from the nearest turbine. Assuming an amplitude decay model of the form r−α, where r is the distance, we estimate a damping factor of α∼2, which remains rather constant for each of the four main peaks, an observation that we relate to the good geomechanical characteristics of the local terrain, consisting of granitoid rocks. To better evaluate the possible impact of the wind farm noise emission on the ET, we also analyze the seismic data from two permanent stations bordering the ET candidate site area, each equipped with both a surface sensor and a borehole sensor at approximately 250 m depth. Power spectral density analysis for the surface and borehole sensors exhibits similar results and very low noise levels. When the wind farm operates at full capacity, the borehole sensors show an effective noise suppression at depth in the frequency range of interest (1–10 Hz). However, small residual spectral peaks at 3.4 Hz and between 4–6 Hz remain detectable.

The movement of large masses on the Earth’s surface, including landslides or debris flows, transfers energy to the ground, inducing both permanent and transient deformation. This gener- ates measurable motion and seismic radiation that can be detected by proximal seismic networks. On November 26, 2022, during heavy rainfall, several debris flows inundated the northern slope of the active volcanic island of Ischia in southern Italy, causing fatalities and extensive damage. The island of Ischia is one of the most land- slide-prone localities in Italy. It has already suffered comparable, even larger, events over the past two centuries, and with a popula- tion of around 60,000 and more than 300,000 tourists per year, it is considered a high natural risk zone. In this study, we performed seismological analyses over an extended range of frequencies and scales, using broadband data recorded by the local permanent seis- mic network, to study the dynamics of the November 26, 2022, event and to quantitatively characterise its evolution over time. Unlike post-event static surveys, a major advantage of the seismological approach is its ability to track the progression of the debris flow motion from the instant of the initial detachment. Our analyses allowed us to estimate the spatial and temporal origin of the rock detachments, the mass of the flowing material, the size of the coarse boulders, the speed at which the landslide approached the nearest seismic station, and the impacting overpressure that caused the most severe damage. These results further demonstrate that spe- cifically designed instrumental (seismic and tiltmetric) networks represent an essential tool for real-time monitoring and for activat- ing early warning systems prior to potential damage to inhabited localities.

Swarm‐like seismicity manifests as earthquake clusters driven by aseismic transients. The investigation of the mechanisms behind their occurrence is generally based on automatic detection and characterization of swarm‐like clusters. In this study, we investigate four different (de‐)clustering algorithms to identify earthquake clusters, and then classify these clusters as either swarm‐like or mainshock–aftershocks sequences. The classification uses the clusters’ distribution of seismic moment over time, quantified by standardized central moments. Synthetic catalogs from an epidemic‐type aftershock sequence model are used to establish confidence bounds for swarm classification. The workflow is applied to the swarm‐dominated regions Húsavík–Flatey fault, Iceland, and Pollino range, Italy. Our workflow effectively detects/classifies earthquake clusters, but their inherent variability in duration and seismic moment release can bias automated swarm/mainshock–aftershocks labeling. The results provide benchmarks for future swarm‐like seismicity analyses, highlighting the importance of a posteriori careful inspection of clusters to understand the underlying physical mechanisms.