Geophysical Journal International

SummaryThe amplitude of the ${{P}_s}$ phase relative to the direct P wave (i.e., the ${{P}_s}/P$ ratio) provides valuable information about the contrasts across the crust-mantle boundary. Understanding how these amplitudes respond to variations in subsurface parameters improve interpretation of lithospheric structures. We examined the sensitivity of eight key parameters, including compressional and shear wave velocities, lower crustal and upper mantle densities, ray parameter, and Moho depth, to receiver function (RF) amplitudes and ${{P}_s}/P$ ratios. Using the synthetic RF (synRF) code of Ammon et al. (1990), we applied a Monte Carlo approach to generate randomized parameter sets, incorporated random noise, and tested both sharp and gradational Moho structures. The results show that lower crustal shear velocity has the strongest influence on all RF amplitudes and ${{P}_s}/P$ ratios, while lower crustal ${{V}_p}$, density, and upper mantle ${{V}_s}$ have moderate effects, and upper mantel ${{V}_p}$ and density show weaker sensitivity. In both sharp and gradational models, lower crustal and upper mantle shear velocities largely control the ${{P}_s}/P$ ratio. Theoretical ${{P}_s}/P$ ratios exhibit higher correlation with observed RFs than synthetic ones. Compared with the Shen & Ritzwoller (2016) model, our analysis yields ∼10% lower uncertainties in lower crustal ${{V}_s}$ and smaller uncertainties in lower crustal density derived from ${{P}_s}/P$ ratios, with consistent results in complex regions such as the northern Rocky Mountains. This study establishes the first quantitative framework linking ${{P}_s}/P$ ratio variability to lower crustal velocity and density while explicitly quantifying parameter sensitivity and uncertainties, clarifying how Moho sharpness and noise affect amplitude stability.

SummaryMacnae (2025) presented a physical interpretation of the Cole Cole Complex Conductivity model in the case of porous materials with sulphides. According to his paper, the Cole Cole parameters determined from such model can be easily interpreted in terms of underlying physics. His model is partly based on the electrochemical polarization model of Wong (1979) to explain the relationship between the chargeability and the volumetric content of sulfide. None of the statements made by Macnae (2025) are however novel. That said, we agree with Macnae (2025) that the Cole Cole complex resistivity relaxation time is quite useless in deciphering the underlying physics of the induced polarization problem.

SummaryEfficient Markov chain Monte Carlo (MCMC) sampling from posterior distributions remains a central challenge in Bayesian geophysical inversion. Recent developments in computational statistics and optimal transport suggest that MCMC efficiency can be improved by reparameterising the sampling problem – specifically, by learning an invertible mapping that recasts the target distribution onto a simpler reference distribution. Here, we introduce a Metropolis–Hastings framework that leverages transport maps parameterised by invertible neural networks. These maps are trained on preliminary MCMC samples from the target distribution and used to propose new samples in a fixed reference space, where proposal design is independent of the target’s structure. The proposed samples are transformed back to the target space via the inverse map, and accepted or rejected according to a modified Metropolis–Hastings criterion. As sampling proceeds, the transport maps are updated, yielding proposals increasingly well adapted to the shape of the target distribution. Across a suite of numerical tests – including a 2-D Rosenbrock distribution, a 3-D earthquake location problem, and Gaussian mixtures up to 16 dimensions – transport-map-driven samplers consistently outperform standard MCMC, reducing integrated autocorrelation times by factors of 2.5 to over 6 (or equivalently, yielding sample sets 2.5–6 times larger for the same number of forward evaluations). This improvement comes at the non-negligible cost of training one or more transport maps, which we quantify systematically. We also provide a quantitative criterion for weighing training cost against sampling speed-up. This shows that transport-map MCMC is advantageous whenever the forward problem is nontrivial, making it a promising approach for Bayesian sampling in geophysics and beyond.

SummaryEarthquake locations and catalogs from routine earthquake monitoring are typically based on manually reviewed arrival-time picks from classical, rule-based automatic pickers. High-performance, deep-learning (DL) pickers can replace this standard approach, rapidly delivering much larger and complete catalogs. A transition to routine monitoring based on DL picks requires that resulting catalogs include all or almost all events identified by current procedures with locations of the same or higher quality. Here we verify these requirements by comparing the performance of DL and manual picking for earthquake relocation and tomographic inversion. We form a reference catalog with a subset of INGV bulletin events and picks from the 2016 Central Italy sequence. This catalog is re-picked using the DL picker PhaseNet trained on the Northern California Earthquake Data Center dataset and on the INSTANCE Italian dataset. We use these three pick sets for high-precision, non-linear earthquake relocation and for 3D tomographic inversion and relocation. Relative to the high-precision relocations using routine picks, those using DL picks show improved organization and clustering, and, in a ground-truth test, smaller hypocenter separation for event pairs with more similar waveforms. The tomographic inversions show statistically better convergence and more organized relocations using the DL picks than with the routine picks. We conclude that DL based monitoring can rapidly produce more consistent picks and higher quality catalogs than standard procedures, while freeing analyst time for improved quality control, assessment, interpretation, and dissemination of information on seismic activity, especially during significant seismic sequences.

SummaryFluid injection into the subsurface can trigger moderate-magnitude earthquakes days to months after shut-in, complicating hazard assessment. To investigate the governing mechanics, we implemented a fully coupled hydro–mechanical model that couples Darcy flow, poro-viscoelastic deformation and rate-and-state fault friction on a planar fault, allowing two-way feedbacks between pore pressure, volumetric strain and fault slip and the simulation of both aseismic and seismic transients. Compared with decoupled or one-way approaches, the fully coupled formulation generally yields longer post-injection delays, owing to poroelastic stress contributions and a more realistic evolution of volumetric strain. After shut-in, a slow poroelastic redistribution of volumetric compression broadens and migrates along the fault, constructively overlapping regions of elevated shear and reduced effective normal stress. This causes the nucleation of a delayed rupture away from the well, indicating that the point of peak instantaneous pressure does not necessarily coincide with the location of maximum coseismic slip. By scanning permeability and injection rate we construct an empirical injection-rate (IR)–permeability (k) phase diagram that delineates regimes of immediate, delayed and no induced seismicity; this diagram is offered as a conceptual, physics-informed screening tool that requires site-specific calibration. Our results indicate that two-way hydro-mechanical coupling and fault slip evolution should be considered when assessing post-injection seismic hazard and in the design of spatially distributed monitoring.

SummaryTraditional seafloor mapping relies on shipborne soundings which have limited spatial coverage. The Surface Water and Ocean Topography (SWOT) wide-swath altimetry satellite holds the potential for predicting more detailed seafloor topography. In this study, we integrate SWOT gravity data with single-beam shipborne depths to construct seafloor topography models in the Northwestern Pacific using the deep neural network (DNN) method. Compared to shipborne depth checkpoints, the root mean square (RMS) error of the differences between topography model predicted by DNN method and shipborne depths is approximately 97.5 m, improving by 19.5% and 9.9% compared to the gravity-geologic (GGM) method and the Smith and Sandwell (SAS) method respectively. Compared to traditional data, the integration of SWOT gravity data universally enhances prediction accuracy. Furthermore, the DNN method effectively demonstrates superior capability in balancing the characterization of overall structures with the retention of authentic topography features, which we demonstrated in the Mariana region of the NW Pacific Ocean. However, limited by spatial heterogeneity and physical mechanisms, accurate prediction of such complex, fine-scale topography using gravity data remains a significant challenge.

SummarySpatial autocorrelation (SPAC), the azimuthal average of the normalized cross-correlation between equidistant station pairs deployed in a 2-D array, is widely used to image the subsurface structure. However, the rigorous estimate of subsurface structure and its uncertainties as a function of depth using SPAC data is challenging due to the nonlinear relation between the SPAC data and Earth structure as well as the trade-off between depth and velocity. Additionally, data noise is strongly correlated due to data processing (e.g., filtering, stacking from multiple time segments and azimuthal averaging). Most studies do not account for the correlated noise and fix the ratio of compressional-wave velocity (${V}_P$) to shear-wave velocity (${V}_s$) (i.e., ${V}_P$/${V}_s$ ratio) and the number of layers, both of which are typically unknown. To address these challenges, we develop a hierarchical trans-dimensional Bayesian inversion of fundamental mode of SPAC data that properly accounts for the correlated data noise, samples the ${V}_P$/${V}_s$ ratio, and relaxes the number of layers (i.e., model parameterization) to be unknown in the inversion. We further examine the limitation of using only fundamental modes in the inversion. Our synthetic experiments show that the inversion recovers an incorrect model unless we sample the correlated noise and ${V}_P$/${V}_s$ ratio in the inversion. The inversion is then applied to SPAC data acquired at 19 sites across the Tacoma basin in Washington State to characterize the ${V}_s$ and the time-averaged ${V}_s$ over 30-m depth ($V{s}_{30}$). Our results show that the $V{s}_{30}\ $varies from ∼200 m/s to 800 m/s. The $V{s}_{30}$ within the basin is higher in the middle and lower on the east and west sides. We find that these $V{s}_{30}$ values vary with geologic unit. The uncertainties for $V{s}_{30}$ are within 20 m/s in average except for the most eastern site TB28. Additionally, the uncertainties are greater for deeper depths beneath most of the sites as the sensitivity decreases as a function of depth. The ${V}_s$ structure as a function of depth is also complex beneath some sites, possibly because the SPAC curves are affected by higher order Rayleigh modes that are not considered in the inversion. To better constrain the deeper ${V}_s\ $structure, $V{s}_{30}$, and/or other average measures of ${V}_s$ over depth, additional constraints from complementary data, such as ellipticity or geologic data are needed. Moreover, our synthetic experiments show that higher order modes can have significant effect in the inversion results, particularly when there is a low-velocity layer.

SummaryRegional geomagnetic field models are used to delineate intricate details of the Earth’s magnetic field and have significant application value in precision navigation and geomagnetic exploration. However, traditional modeling methods often encounter challenges when applied to sparse data, leading to issues like low model resolution and accuracy, as well as limited generalizability. The recently developed physics-informed neural networks (PINNs), a powerful modeling tool, presents a viable alternative for regional geomagnetic field modeling. This study employed the PINNs method to construct a geomagnetic field model for satellite altitudes over the Chinese region, based on the Swarm satellite dataset provided by the European Space Agency. An adaptive weight training method was used for the two-stage training process, involving an initial pre-training and subsequent fine-tuning of the model. Experimental verification shows that the proposed algorithm enhanced the model’s fidelity to physical laws, improved its resolution and prediction accuracy (reducing the root mean square errors for geomagnetic components to as low as 4 nT), and enhanced its generalizability, with the total field intensity F and the prediction accuracy of both the X- and Y-components demonstrating superiority over that of other traditional methods. Collectively, these advancements enable efficient regional geomagnetic field modeling while providing a foundation for more reliable and precise predictions.

SummaryDetermining the gravity potential is a fundamental task in geodesy and plays a critical role in various fields, including seismology, geodynamics and aerospace engineering. Grounded in the principles of general relativity, the high-precision determination of gravity potential using time and frequency signals has become a prominent research frontier in modern geodesy. This study employs multi-GNSS (Global Navigation Satellite System) carrier phase time and frequency comparison to determine the gravity potential. It develops a model for multi-GNSS Precise Point Positioning (PPP) time and frequency comparison, incorporating gravity potential estimation, and further investigates simulation methods for high-precision clock offsets and GNSS observations. Ten time and frequency links formed by eleven stations from the IGS (International GNSS Service) were analyzed using a simulation framework. The experiment incorporated simulated GNSS observations and eight types of clocks with varying performance levels to assess the capability of the multi-GNSS PPP time and frequency comparison model in determining gravity potential. The results demonstrate that the accuracy of gravity potential determination with multi-GNSS time frequency signal after coverage is approximately 0.1 m²/s². These findings affirm the feasibility and reliability of using GNSS time and frequency signals to determine gravity potential. Moreover, the convergence speed and accuracy of PPP solutions with ambiguity resolution show notable improvements over ambiguity float solutions, with accuracy enhanced by roughly 10 per cent. As atomic clock performance and GNSS satellite products continue to advance, GNSS-based time and frequency comparison holds great promise for achieving even higher precision in gravity potential measurements and contributing to the unification of the global vertical height datum.

SummaryCoulomb failure stress change (ΔCFS) quantifies the earthquake-induced difference of shear stress and frictional resistance on a receiver fault, with the latter being proportional to the effective normal stress change. ΔCFS has become a widely used measure for studying earthquake triggering, dynamic rupture processes and earthquake-induced secondary disasters. In simple layered or half-space elastic media, methods for computing static ΔCFS have been well established, with programs such as Coulomb3, PSGRN-PSCMP, and AutoCoulomb being widely used. In contrast, dynamic ΔCFS evaluation generally relies on numerical discretization schemes, such as finite-difference, finite-element, boundary-element and discontinuous Galerkin methods, which, while suitable for complex structures, are computationally expensive. To overcome these limitations, we develop DynCFS, a user-friendly, Green’s function based and therefore computationally efficient program for calculating both static and dynamic ΔCFS in layered elastic media. The tool enables rapid assessment of dynamic triggering effects, both between successive earthquakes and among multiple sub-events or faults during an earthquake.

SummaryIn February-March 2025 a seismic sequence occurred in the western sector of the Aeolian Archipelago (Southern Tyrrhenian Sea, Italy), a seismotectonic complex region located along the Africa-Eurasia plate boundary and mainly controlled by their NW-trending convergence. The seismicity, located ∼20 km south of Alicudi Island and ∼40 km north of the coast of Sicily, started on February 7 with an earthquake of magnitude Mw 4.7 that was followed in the next month by 42 events with local magnitudes between 1.2 and 3.4. Notwithstanding its moderate energy, this recent seismicity offers a unique opportunity to investigate seismogenic processes in a region for which a seismic potential of ∼M7 or even more has been suggested and a relevant data paucity mainly related to its offshore location was widely recognized. We tackle the limitations of not-optimal network configuration, by designing an ad-hoc approach, which integrates different advanced techniques. Specifically, we combine Bayesian methodology for accurate absolute hypocenter locations, machine learning techniques for detection of weaker events, Distance Geometry Solvers for relative locations, and a probabilistic inversion tool for source mechanism estimation. Our analysis led us to strongly enrich the dataset of detected earthquakes, and to define the causative source of the 2025 sequence as a NE-SW trending N-dipping thrust faulting structure. The proposed source agrees with the regional seismogenic stress field and with the structural architecture of the southern Tyrrhenian portion of the Africa-Eurasia plate margin by also adding new constraints in a sector where no known fault segments were previously reported. This study provides new insights on seismogenic processes in the investigated area, while proving the effectiveness of the employed combined approach for characterizing seismogenic sources in poor network configurations.

SummaryDecomposing spectral responses in induced polarization on the basis of elementary Debye relaxation kernels with a distribution of time constants (Relaxation Time Distribution) is a powerful tool for analysing observations in this low-frequency electromagnetic method. Notably, it enables the estimation of the sizes of polarisation sites, particularly in the presence of metallic particles, as well as facilitating environmental studies. These decompositions generalise a plethora of historical models, some of which can be considered equivalent to each other in the sense of mathematical equivalence classes. Here, we explicit several types of these equivalence relations, which we recall in their definition in relation to a common property, the elements of a given class belong to a given set. For example, we present a class of models that fall under the same differential equation, meaning this is the class of models that belong to the set of distributions that verify the differential equation. We also exhibit another class of models where we can pass from one to the other by an elementary calculation. Among all the possibilities, a particular class often interests us in IP: RTD classes such as spectra are practically indistinguishable as they are so close according to a defined criterion. In this particular case, we study here the equivalence (or non-equivalence) of certain classical models. We confirm that two models play major roles: the lognormal distribution (because it is the most natural) and the Cole-Cole distribution, which is empirical but also often used for its simplicity (and the associated RTD is analytical, unlike that of the lognormal which requires numerical evaluations). It turns out that these two distributions are equivalent in terms of their quasi-equal spectra, a fact known since Cole and Cole (1941), but whose scope is extended here by an in-depth study of the objective function which separates them in the least squares sense.

SummaryRegarding the potential impact of groundwater storage changes on principal fault stresses and seismic activity in the North China Plain before and after the implementation of the South-to-North Water Diversion Project, this paper constructs a three-dimensional finite element model to calculate stress field variations induced by groundwater level changes from 1959 to 2023. Combined with Coulomb stress change calculations, the study evaluates the influence of groundwater extraction and replenishment processes on the crustal stress field before and after the diversion project. Research findings indicate that between 1959 and 2015, excessive groundwater extraction increased Coulomb stress on major faults across the North China Plain by up to 10 kPa. Following the official operation of the central route of the South-to-North Water Diversion Project in 2015, groundwater level changes induced fault Coulomb stress changes ranging between -2 kPa and 2 kPa. Consequently, groundwater deficit prior to 2015 promoted regional seismic activity, while groundwater recovery after 2015 exhibited certain mixed effects on seismic activity, resulting from spatial distribution differences in groundwater deficit and replenishment across the North China Plain. This research provides scientific evidence for assessing the potential impact of the South-to-North Water Diversion Project on seismic activity and offers valuable reference for future earthquake risk assessment and groundwater resource management.

SummaryDetermining earthquake focal mechanisms is a fundamental task in seismology, essential for understanding the fault structures and stress states in faulting regions. We present a new method for determining focal mechanisms of small earthquakes using 360° S-wave polarization alongside traditional P-wave polarity and S/P amplitude ratio. Ideally, measuring accurate 360° S-wave polarizations at near-source stations allows for a full recovery of the double-couple radiation patterns of direct body waves. By employing a process involving P–SV–SH transformation and correction for S-wave splitting, we show that S-wave polarizations for events with magnitudes less than 3 can be measured with average errors smaller than 7°. Our statistical analyses indicate that reliable focal mechanism solutions can be obtained with as few as two to three near-source stations. The method is particularly effective for strike-slip earthquakes, as their highly variable S-wave polarization patterns provide stronger constraints. We applied this method to the ML 2.8 and 2.9 sequences located in the centre of a dense seismic array in southeastern Korea, successfully determining focal mechanisms for events with magnitudes ranging from 2.9 down to −0.4. While the ML 2.8 sequence events display almost identical focal mechanisms along the main fault, those in the ML 2.9 sequence show variable mechanisms associated with off-fault microseismicity. We further validated the approach using the 2023 Mw 4.3 Parkfield and 2011 Mw 5.8 Mineral earthquake sequences, representing different tectonic settings. Despite using only 2–4 S-wave polarization measurements in Parkfield and 1–2 in Mineral, incorporating S-wave polarization significantly improved the accuracy of focal mechanisms in both cases. This research demonstrates that 360° S-wave polarization allows for robust determination of focal mechanisms in small earthquakes and offers a valuable tool for analyzing microseismic activity.

SummaryPore structure is an important parameter controlling the storage capacity and transport properties of porous rocks and determining their pressure dependent elastic properties. However, pore structure is predominantly inverted from velocities with increasing confining pressure and it remains unclear whether the pore structure from velocities with increasing pore pressure differs. We develop an improved pore-structure inversion method that incorporates the linear reduction of stiff porosity with pressure to extract the complete aspect ratio distribution of compliant cracks from pressure dependent velocities. We also measure the compressional and shear wave velocities and porosity of two dry Berea sandstone samples as a function of both increasing confining pressure and increasing pore pressure. The pore-structure inversion method is applied to the two samples to obtain and compare their pore structures from the velocities measured with different pressure paths. The results show systematically higher velocities and lower porosities for the increasing pore pressure path at equivalent differential pressures. The inverted pore structures show a substantially greater cumulative crack porosity and density from velocities with increasing confining pressure, and reveal a markedly smaller population of compliant cracks, albeit distributed over a slightly broader range of lower aspect ratios from velocities with increasing confining pressure. The difference in the pore structures from velocities with different pressure paths is explained in terms of the crack hysteresis mechanism. The results have helped to explain the greater velocities and smaller porosity of the samples measured with increasing pore pressure, and would help for the estimation of capacity and permeability of CO2 and hydrogen stored reservoirs and for the more accurate prediction of pore pressure in hydrocarbon generated overpressure zones.

SummaryThe aim of this study is to assess the potential of rotational and strain measurements to provide complementary information on seismic wave scattering, in addition to the conventional seismological observables. We begin by evaluating the accuracy of numerical solutions to the elastic wave equation, solved via the Spectral Element Method, for modeling wave propagation in 3D complex heterogeneous media. These simulations are benchmarked against predictions from the Radiative Transfer Equation (RTE), which models energy transport in scattering media. The comparison focuses on key scattering parameters: mean free path, diffusion onset, and temporal evolution of P/S energy partitioning. Three levels of velocity heterogeneity (10%, 17%, and 25%) are tested in both full-space and half-space configurations. The analysis highlights how scattering strength, numerical accuracy, and theoretical assumptions, such as those underlying the Born approximation, affect the agreement between the two modeling approaches. This comparison helps define the conditions under which RTE and wave equation-based simulations produce consistent results. Following this assessment, we analyze the energy envelopes of the displacement wavefield and its spatial gradients. The results demonstrate that rotational measurements preserve source-induced polarization longer than other observables. This persistence can provide valuable information for better constraining the source mechanism. Furthermore, analysis of the rotational components can provide complementary constraints on the medium’s elastic and scattering properties.

SummaryThis study develops a Bayesian optimisation method of coseismic slip distributions and the correlation lengths of the von Kármán autocorrelation function, which can realize more reliable regularisation grounded in geophysical analysis (VKR). To validate VKR and its dependence on the observation, synthetic tests using data from inhomogeneously distributed Global Navigation Satellite System (GNSS) stations and Synthetic Aperture Radar (SAR) were conducted. When observation stations surround the source fault, the assumed slip distribution and the correlation length were well recovered with some artificially extended slip due to the inhomogeneity of the observation network. Moreover, when observation stations exist only on one side of the fault, the method recovered the slip and other parameters with accuracy comparable to that of the surrounding-case scenario, albeit with slightly increased uncertainty of the parameters. This highlights the importance of uncertainty evaluation for slip and correlation length parameters, especially under biased observation networks. Applying existing Laplacian smoothing methods to the same experiments produced models globally consistent with VKR, demonstrating that the proposed method, despite additional non-linear parameters, achieves comparable estimation accuracy. Existing method showed isotropic correlations of slip variables, whereas VKR exhibited correlations elongated along the strike direction, reflecting its ability to independently regularise along strike and dip via correlation length parameters. These correlation patterns were most pronounced in deeper fault regions, where regularisation dominated over observational constraints. Cluster analysis of the Markov samples revealed that VKR captured a more diverse set of slip distribution models, with cluster differences most evident in deeper fault regions. These analyses underscore the importance of regularisation choice and its impact when evaluating and interpreting slip distributions. We also applied VKR to the actual data of the 2024 Noto Peninsula earthquake in Japan, observed by dense GNSS networks and SAR. The estimated slip distribution featured multiple slip areas in the eastern and western peninsula, consistent with previous studies and Laplacian smoothing-based results. The correspondence between estimated slip distribution and correlation length was confirmed, although it did not match previous empirical findings. To further examine the effect of observation network configuration, we performed additional inversions using a reduced set of actual data. The resulting slip distribution was smoother, and the estimated correlation lengths were larger and more uncertain. Our results reconfirm that simultaneous estimation of slip distribution and correlation length produces mutually consistent values, both of which depend on the spatial distribution of observation points. The results also demonstrate the strong dependence of estimated slip distribution and correlation lengths on the observation network. Therefore, future studies of coseismic slip self-similarity, using observed data, should incorporate parameter analyses that account for network resolution effects.

SummaryThe precise extraction of tidal signals from non-stationary gravity observations is a central challenge in geophysics, where accuracy is often limited by mode mixing in data preprocessing algorithms. This study evaluates the performance of the Time-Varying Filter-based Empirical Mode Decomposition (TVF-EMD) method to address this issue. We employed a progressive validation pipeline: the method was first verified on simulated signals, then rigorously tested against a high-fidelity benchmark from a superconducting gravimeter (SG), and finally applied to one month of continuous data from an Atom Gravimeter (AG) at the Yilan station. Results demonstrate that TVF-EMD dramatically suppresses mode mixing, with the energy of transient spikes in its residual being an order of magnitude lower than that from the conventional Ensemble Empirical Mode Decomposition (EEMD) method. The tidal signal reconstructed by TVF-EMD achieved the highest cross-correlation coefficient and the smallest root mean square error when compared to the theoretical gravity tide. Subsequent harmonic analysis confirmed that TVF-EMD yielded the lowest errors across all major tidal constituents. These findings validate TVF-EMD as a superior preprocessing framework for tidal analysis, particularly for enhancing the reliability of geophysical parameter inversion from short-duration records obtained with next-generation quantum sensors.

SummaryStructural boundaries are often the features of most interest geologically, but imaging them can be difficult due to wavefield scattering and interference caused by the sharp velocity contrasts. One example of this is the apparent Rayleigh-wave anisotropy (1-psi anisotropy) that has been observed near major structural boundaries using seismic arrays. The cause of the apparent anisotropy is the interference between the incident surface wave and waves scattered from velocity discontinuities. In this study, we first investigate the sensitivity of apparent anisotropy measurements to lateral boundary sharpness through 2D full waveform simulations. We demonstrate that 1-psi anisotropy can vary based on boundary sharpness, station spacing, and period of surface waves. We show that a misfit defined using triple-difference travel times, i.e. the difference in double-difference travel times between station pairs with opposite propagation directions, well characterizes the apparent anisotropy. The sensitivity kernel for this triple-difference misfit can be constructed using the adjoint method. We show that triple-difference travel times are mainly sensitive to velocity contrasts rather than absolute velocities, in contrast to double-difference travel times. With sensitivity kernels constructed, we demonstrate how triple-difference travel times can be combined with double-difference travel times into a tomography inversion. We show that by including triple-difference travel times, seismic inversions converge faster and resolve boundary and average structure better in early iterations, compared to using double-difference travel times alone. Recent advancements in dense array experiments could facilitate the application of this method to better delineate tectonic and basin structural boundaries.

SummaryWe present a probabilistic framework for evaluating earthquake forecasting models that use an alarm-based approach. In this approach, alarms are triggered by specific precursor signals. In a previous paper we compared such models and two ensemble models combining them in additive and multiplicative mode, with the ETAS (Epidemic Type Aftershock Sequence) forecasting model, which is defined in a probability-based approach, by making the latter to issue an alarm when the expected rate exceeds a predefined threshold. In this work we compare the alarm-based models with the ETAS and with another probability-based model, EEPAS (Every Earthquake a Precursor According to Scale) previously applied to Italy, using the testing procedures developed for probability-based models within the Collaboratory Study for Earthquake Predictability (CSEP) initiative. To do that, for the four alarm-based models, we compute empirical probabilities (frequencies) of Mw ≥ 5.0 earthquakes in Italy, inside and outside alarm time intervals issued by such models from 1990 to 2011. We then compare pseudo-prospectively the forecasting ability of all six models, by applying the CSEP tests on the time interval from 2012 to 2023. We found that the evaluation method used has a strong impact on the ranking of model performance. Probabilistic models like ETAS and EEPAS tend to score better under the CSEP testing framework whereas alarm-based models generally outperform probability-based ones when assessed using alarm-based metrics.