Geophysical Journal International

SummaryMagnetic inversion is a key tool for imaging subsurface geological structures, but conventional 3-D magnetic inversion in the spatial domain is often limited by the computational and memory cost of large dense kernel matrices. Existing transformed-domain approaches improve efficiency, yet pseudo-3D implementations still rely on layer-by-layer accumulation and repeated Fourier transforms. In this study, we develop a unified wavenumber-domain framework for the forward modelling and inversion of total-field magnetic anomalies and magnetic gradient-tensor data. For regularly discretized rectangular prisms beneath a planar observation surface, the wavenumber-domain Green operator is reformulated into a factorized representation consisting of two explicitly stored diagonal/block-diagonal spectral factors and one implicitly applied separable horizontal operator. This implementation avoids repeated vertical layer superposition and reduces the forward evaluation to a single FFT/IFFT pair together with structured spectral multiplications. The factorized forward operator is then embedded in a Tikhonov-regularized inversion and solved through a Sherman-Morrison-Woodbury (SMW) reduced system. The transformed-domain data term is defined as an unweighted complex-valued least-squares residual, and its relation to the spatial-domain least-squares formulation is stated under the corresponding padding and truncation assumptions. Synthetic examples show that the method reproduces conventional spatial-domain responses and recovers the principal features of prescribed magnetization models under 5% Gaussian noise. For a 200×200×100 model, the forward modeling and core inversion times are 0.172 s and 31.73 s, respectively, on a standard laptop. Application to field data is used as a practical feasibility test and shows a data-consistent recovered magnetization distribution, but it should not be regarded as an independent geological validation of the recovered model. The current implementation assumes a planar observation surface, a regular FFT-compatible grid, and a spatially uniform magnetization direction. It does not yet address strong remanence, spatially variable magnetization, irregular topography, irregular acquisition geometries, depth weighting, focusing stabilizers, or geological constraints. Under these assumptions, the proposed framework provides an efficient, memory-economical, and scalable alternative for large-scale magnetic anomaly interpretation.

SummaryWe present a high-resolution three-dimensional P-wave attenuation tomography model of the northern Chilean subduction zone (21°–22°S), derived using the coda-normalization approach implemented in the MuRAT algorithm and a dense local earthquake dataset. This region represents an important segment of the South American margin, where the Nazca Plate subducts beneath the South American Plate, generating frequent intermediate-depth seismicity and sustained volcanic activity along the Western Cordillera. Understanding the distribution of attenuation and its relation to seismicity and fluid pathways is essential for constraining the physical state of the subduction system and its role in arc magmatism and crustal deformation. The inversion incorporates 147,639 high-quality waveforms from 42,460 local earthquakes recorded by 76 broadband stations between 2007 and 2021. The inversion was carried out using a three-dimensional velocity model with 10 km node spacing, and the resulting attenuation grid was parameterized at 14 × 25 km horizontally and 10 km vertically. The attenuation model reveals two main low-Q anomalies. The first extends along and immediately above the top of the subducting Nazca slab between 50 and 90 km depth, interpreted as the locus of fluid release from slab dehydration. The second low-Q zone ascends from the mantle wedge towards the lower crust beneath the volcanic arc, indicating fluid migration. These features coincide with high-Vp/Vs regions from velocity tomography models. Low-Q regions are generally found above seismicity concentrations in the downgoing Nazca slab, reaffirming the association of intraslab earthquakes with fluid release processes. Resolution tests confirm the robustness of the imaged structures. The obtained anomalies trace subduction-related fluids from their source in the downgoing slab through the mantle wedge towards the magmatic arc.

SummaryThe explicit inertial modes in spheres and oblate spheroids, owing to their clear and concise mathematical formulations, have been applied in many geophysical and astrophysical studies. In contrast, the implicit inertial modes are rarely used because of their mathematical complexity. Due to the presence of factorials and double factorials inherited from the associated Legendre polynomials, the computation of explicit inertial modes becomes intractable at high orders. Based on the implicit inertial modes, this research, for the first time, develops a new algorithm that enables fast computation of the inertial modes in spheres and spheroids of arbitrary eccentricity even at high orders. In addition, it offers an efficient approach to computing the geostrophic polynomials, which are a set of special inertial modes with zero frequency in spheres and spheroids. In this new algorithm the inertial modes and the half-frequencies are expressed as functions of the associated Legendre polynomials and their first derivatives with respect to the modified oblate spheroidal coordinates. Several numerical experiments demonstrate the efficiency of this new algorithm. It is also verified that both the non-penetrable boundary condition and the incompressible condition are satisfied by the numerical results produced by this algorithm.

SummaryTectonic gravity anomalies are commonly assumed as static, except during major geodynamic events like earthquakes or plate reorganizations. This study challenges such an assumption at the regional scale by examining the ongoing rifting in the Gulf of Aden. Using 3D finite element and gravitational modelling, it can be shown that horizontal motion between oceanic and continental crusts – characterized by a density contrast of 400 kg/m3 and a divergence rate of 1.25 cm/yr – generates a potentially measurable gravity rate of change, forming a dipolar pattern with peak amplitudes of ±40 nGal/yr. Numerical simulations were conducted to evaluate whether this signal could be actually measured by the forthcoming MAGIC satellite mission. To this aim, the time-variable gravity field derived from the 3D finite element was propagated into orbit simulations, considering only instrumental noise. A series of 1-year least squares solutions were computed from the simulated data in terms of spherical harmonics. Then gravity disturbance grids at 5 km height covering the Gulf of Aden were derived and the gravity rate was estimated at each point of the grid, considering different maximum harmonic degree. Results indicate that the noise level of the MAGIC instrumentation is low enough to make it sensible to this signal, despite spatial resolution limitations. The two opposing gravity stripes cannot be distinguished, but a central bump of gravity rate with an amplitude of about 6 nGal/yr can be well identified by considering a maximum harmonic degree of 70. Of course, the detectability of such a signal from MAGIC observations becomes unfeasible when considering the temporal aliasing induced by other geophysical phenomena involving stronger and faster mass transport. Nevertheless, these findings suggest that tectonic processes associated with rifting can induce measurable gravity variations (given the accuracy level of MAGIC instrumentation), even in the absence of episodic seismic activity, offering new prospects for satellite gravimetry in monitoring active plate boundaries.

SummarySeismic full waveform inversion (FWI) is a powerful technique that uses seismic waveform data to generate high resolution images of the Earth’s interior. However, significant uncertainty exists in all FWI solutions due to imperfect acquisition geometries, inherent noise in the data, nonlinearity of the forward problem, and the under-determined nature of real-world tomographic problems in which the target is heterogeneous over all length scales. Probabilistic Bayesian FWI addresses this non-uniqueness by estimating the entire family of possible model solutions and thus the solution uncertainty, described by the so-called posterior probability density function (pdf) over model parameter values. The posterior pdf can be estimated using nonlinear inversion methods to quantify full uncertainties, including those created by nonlinearity in the physics. Alternatively, by linearising (approximating) the physics relating parameters and observations around a chosen reference model solution, the posterior pdf is usually approximated by a compact distribution centred around the maximum a posteriori solution, typically a Gaussian pdf. This is referred to as the linearised method. In this work, we apply both nonlinear and linearised methods to 2D acoustic Bayesian FWI problems. We use one variational inference algorithm for the nonlinear case, in which a transformed Gaussian distribution is optimised to approximate the unknown, full posterior pdf, and a second, independent nonlinear variational algorithm – Stein variational gradient descent – for comparison. The results of both are then compared with those from a linearised, locally-Gaussian based method. The results show that while both the linearised and nonlinear methods recover the posterior mean models accurately, they exhibit different posterior uncertainty structures, especially around layer interfaces, due to the linearisation of wave physics. The differences become most obvious in partially constrained regions of the model, where posterior solutions are constrained jointly by data, prior information, and the nonlinearity of wave physics rather than being dominated by any single factor. We also demonstrate that linearised uncertainty estimates are significantly less accurate: they provide far less accurate fits to observed waveform data, and yield biased estimates of inferred or interpreted meta-properties such as volumes of geological bodies. This work therefore motivates the application of fully nonlinear inversion methods in Bayesian FWI if either accurate uncertainty estimates over parameters, or inferred or interpreted meta-properties are important.

SummaryReliable automatic phase picking is important for many seismic applications. With the development of machine learning approaches, many algorithms are proposed, evaluated and applied to different areas. Many of these algorithms are single station based, while recent proposed methods start to combine surrounding stations into consideration in the problem of phase picking. Among these algorithms, the Phase Neural Operator (PhaseNO) shows promising results on regional datasets comparing to existing algorithms. But there are many use cases for the local seismic networks in our community, therefore in this paper we evaluate the performance of PhaseNO on 4 different local datasets and compare the results to PhaseNet and EQTransformer. We used both individual phase picking metrics as well as association metrics to illustrate the performance of PhaseNO. By manually reviewing the newly detected events, we find the PhaseNO model outperforms the single station-based approaches in the local-scale use cases due to its consideration of coherent signals from multiple stations. We also explored PhaseNO’s behaviors when only using one station, as well as gradually increasing the number of stations in the seismic network to better understand its behavior. Overall, using the off-the-shelf machine learning based phase pickers, PhaseNO demonstrated its good performance on local-scale seismic networks.

SummaryEarthquake fault slip arises from nonlinear coupling among frictional evolution, elastic loading, and pore-pressure changes. When pore pressure evolves dynamically, the resulting hydro-mechanical rate-and-state models can be stiff and strongly coupled, making parameter inversion computationally demanding. Here we develop a physics-informed neural network (PINN) solver for a coupled spring–slider system that combines rate-and-state friction with pore-pressure/porosity evolution. The network approximates the time-dependent state variables and is trained by enforcing the governing differential equations together with initial conditions and, for inverse problems, observational constraints. To improve training stability, we employ adaptive inverse-residual weighting and a two-stage optimization schedule (Adam followed by L-BFGS). In forward simulations, PINN predictions closely match a Runge–Kutta reference solution across steady sliding and slow-slip transients, with normalized mean squared error below 0.08 and Pearson correlation coefficient above 0.975 for block velocity and frictional shear stress in the cases tested. In inverse experiments, the framework recovers the applied normal stress from noisy shear-stress observations; uncertainty increases with noise amplitude, but the ensemble mean remains stable, and at the highest noise level considered (q = 1) the inferred normal stress deviates by less than ~1% from the reference value. These results suggest that PINNs provide a differentiable alternative for forward modeling and parameter inversion in coupled hydro-mechanical rate-and-state fault models.

SummaryWe estimated seismic moment tensors (MTs) for the 2017 magnitude M6 Hojedk, Central Iran, earthquake triplet and their aftershocks, employing 1D and 3D regional and global velocity models to evaluate source parameter stability and resolution fitting in-country waveform data. We used the Moment Tensor Uncertainty Quantification (MTUQ) software, which performs a grid search for MT estimation and uncertainty analysis. For the regional 3D velocity model, we used MEAD-M20, a full-waveform inversion model of the Middle East derived from fitting 15-s body waves with 30-s body and surface waves. We compared the regional 1D- and 3D-based results with an existing database of deviatoric MT solutions, and for both regional velocity models, we found good agreement. However, for periods T ≥ 25–30 s and events with moment magnitudes Mw≥ 4.5, the 3D regional synthetic seismograms outperformed the 1D regional model, reducing waveform misfits, time shifts, and non-double-couple contributions. We consider non-double-couple contributions spurious and their reduction an improvement, as previous studies of the sequence found predominantly shear faulting on reverse faults. Furthermore, uncertainty analysis shows that the moment tensor, non-double-couple component, magnitude, and depth are more tightly constrained for the 3D model. The current 3D model shows no clear improvements relative to the 1D model in terms of misfit, time-shifts, and non-double-couple contributions at short periods T ≈ 15-25 s relevant for modeling smaller events. Using the regional models results in lower misfits and tighter constraints on the MT solutions than with the global 1D PREM and the 3D S2.9EA models. Improved MT estimation and parameter resolution for moderate-to-large events using in-country data validate the recently developed 3D Middle East velocity model. Further model refinements are needed to model shorter-period data required to analyze and improve the resolution of smaller (M ≤ 4) seismic events. Such improvements are within reach by using available in-country data and well-constrained MT solutions from a regional moment tensor database.

SummaryMonitoring the activity of non-natural seismic events is crucial for constructing an accurate seismic catalog, overseeing the safety of industrial operations, and mitigating the potential threats to local residents. However, recent studies have shown that neural network models trained on local data sets may not generalize well to a different region. Here, we leverage the Siamese neural network (SNN) to enhance the generalization of neural network models in discriminating between blasts, collapses, and natural earthquakes under regional shifts. Two distinct data sets are analyzed. The model is trained on a data set from northeastern China and tested on an out-of-region data set from the Inner Mongolia Autonomous Region and Gansu Province. We evaluate the prediction performance of the SNN model against the Convolutional neural network (CNN) model using the K-fold cross-validation technique. Results show that both the CNN and the SNN models achieve highly comparable performance on the in-domain validation data set. However, when applied to the out-of-region test data set, the SNN model with target-region anchors can improve the predicted AUPRC values by 7% and 4% compared with that of the out-of-region CNN model and the CNN model with transfer learning using target-region anchors, respectively. Furthermore, Grad-CAM importance weight analysis shows that the SNN model mainly relies on early-arrival P- and S-wave trains. The study suggests that SNN model with target-region anchors can deliver better generalization and flexibility than the conventional CNN model under regional shifts, which is particularly valuable for regions lacking labeled data sets.

SummaryAfter the 2015 Ms 6.5 Pishan earthquake, three moderate-magnitude earthquakes, the Ms 5.4 Pishan earthquake on September 4, 2021, the Ms 5.4 Yecheng earthquake on September 5, 2021 and the Ms 5.4 Pishan earthquake on October 23, 2022, occurred in the seismically active western Kunlun Range foreland thrust system. The seismogenic structures responsible for the three most recent earthquakes and their relationships with the 2015 Ms 6.5 Pishan event are still not understood. Integrated analysis of relocation results of the three main events and their aftershock sequences, focal mechanism solutions, and regional geology has identified the seismogenic fault and structural geometry near the earthquake source. Our results recognize a gentlely S-dipping Kuoshi fault ramp, which is the frontal structure at the west part of the WKFTS and is responsible for the three most recent moderate-magnitude earthquakes. The 2015 Ms 6.5 Pishan earthquake and the recent moderate-magnitude events were all generated by the frontal fault ramp, indicating a deformation pattern characterized by simple outward thrusting. In the western Kunlun Range foreland, the most active deformation and topographic growth have migrated northward relative to those of the higher terrace folds as the rear ramp slip ceases. Our results provide new insights into deformation pattern and seismic hazard in the region.

SummaryWe present a new, regionally adjusted local magnitude (ML) model for Switzerland and surrounding regions. The model is derived based on Wood-Anderson displacement amplitudes (AWA) calculated from 150,000 high-quality waveforms from 15,000 earthquakes between 2000 and 2025, recorded by more than 700 seismic instruments. This dataset is substantially richer than those used in previous ML studies in Switzerland, with a large number of near-source recordings and data from low-magnitude events, which were notably sparse in earlier works. AWA attenuation over hypocentral distance is parametrised through linear and logarithmic distance terms along with hinge distance points, which allow proper modelling of the attenuation characteristics at long distances and changes in attenuation associated with post-critical reflected phases. Regional differences in attenuation between the Alpine region in southern Switzerland and the northern Foreland are smoothly modelled through a ray-path-specific regional adjustment parameter, allowing the model coefficients and the hinge distances to vary spatially. The coefficients of the parametric attenuation curves are estimated using mixed-effects regressions, and the model is anchored to yield a magnitude 3 for an AWA of 10 mm measured at a hypocentral distance of 17 km. The station terms are calculated with respect to Swiss reference rock conditions. The new ML model reduces uncertainty by 33 per cent compared to the current ML scale used by the Swiss Seismological Service and does not exhibit any residual trends with respect to hypocentral distance, earthquake depth, local site conditions, or event magnitude. Empirical radiation pattern corrections are derived, further reducing the uncertainty by 8 per cent for strike-slip events. Alternative models, based on non-parametric and cell-based 2D approaches, are derived independently to validate the parametrisation of the parametric model. The new model – MLS26 – yields lower magnitudes for smaller events (with catalogue magnitudes lower than about 2.5) and for events located in the northern Foreland, whereas the magnitudes of the larger Alpine events remain similar. The reduced magnitudes of smaller events decrease the b-value of the input earthquake catalogue from 1.00 to 0.93, corresponding to a reduction of about 7 per cent. MLS26 scales one-to-one with moment magnitude (MW) for MLS26 > 4, while for smaller events, it scales with the logarithm of the seismic moment.

SummaryThis study aims to understand the recurrent seismicity that occurs in a limited volume along a major fault in the French western Alps, the Vuache Fault, which crosses the geological Jura in a flat-and-ramp zone. In 1996, an M5.3 earthquake occurred near Annecy (France), located at a depth of approximately 2 km. In this article, we analyze the seismicity that has occurred since then and calculate the seismic velocity variations at local permanent seismic stations. The magnitude and focal mechanism of the 1996 M5.3 earthquake indicate that the process was tectonic in origin. However, the duration of the Omori decay of its aftershocks, their migration, the variations in spring flow, the existence of repeated swarms, the seasonal variations in seismic velocity and their relationship to rainfall and seismicity show that the continuation of this seismicity is linked to the pressurization of fluids in a deep, fractured aquifer connected to the surface. This aquifer appears to be limited to the sedimentary formations. Earthquakes, especially during the M5.3 aftershock migration, reach the depth of the Triassic gypsum. The aftershock sequence occurred in two different phases: an initial phase lasting around ten days, during which the earthquakes did not show any migration but rather a random spatial distribution, and a second phase showing a clear migration, suggesting a fluid diffusion process. During this last phase, the hydraulic diffusivity of the aquifer was calculated and estimated at around 2 m²/s. The same order of magnitude was obtained by using the correlation between seismic velocity variations and rainfall. This is a high value, close to those found during man-made fluid injections. This aquifer forms a confined, pressurized reservoir between two thrusts in the regional flat-and-ramp structure. The scenario described in this article could be found, at various scales, in flat-and-ramp regions where tectonic stresses are sufficient to generate seismicity.

SummaryModeling seismic wave attenuation and dispersion in fluid-saturated porous media is essential for reservoir characterization; however, significant challenges remain in accurately capturing the effects of anisotropy. Unified theoretical frameworks that combine Biot and squirt flow mechanisms have often been limited by two key factors: they are typically based on the isotropic assumptions and rely on oversimplified physical models for squirt flow. Consequently, a time-domain numerical implementation for advanced, physically-based anisotropic squirt models has been lacking. This study presents a unified theoretical and numerical framework that, for the first time, integrates Biot’s theory of anisotropic poroelasticity with a state-of-the-art model for anisotropic squirt flow based on one-dimensional fluid pressure diffusion in cracks partially connected to spherical pores. The core innovation is a time-domain implementation achieved through a semi-analytical conversion of the complex, frequency-dependent frame moduli into a Generalized Zener Model representation. With parameters optimized via a genetic algorithm, the system is expressed as a set of differential equations with memory variables, enabling efficient finite-difference time-domain (FDTD) simulations in complex heterogeneous media. Our numerical results demonstrate that the model accurately captures frequency- and angle-dependent velocity dispersion and attenuation in VTI media due to squirt flow in the seismic-to-sonic frequency band. The FDTD algorithm is rigorously validated against analytical solutions, and simulations in heterogeneous media highlight its capability to capture spatially-varying anisotropic attenuation effects. This framework bridges a critical gap between advanced rock physics theory and practical wavefield simulation, providing an accurate forward modeling tool for interpreting seismic data to characterize complex reservoir rocks.

SummaryDuring the Early Medieval Ages, unusually strong and rapid geomagnetic field variations have been reported in several European regions; however, archeomagnetic data from Central Europe remain scarce. To help filling this gap, we present new archeointensity results from eight archeological sites in Germany, Austria, and Poland, dated between 500 and 1200 AD. The investigated materials mainly consist of potsherds, together with two in situ baked clay structures that also provided archeodirectional information. Archeointensities were determined using the MT4 protocol, a Thellier-type technique including cooling-rate and anisotropy corrections. For two sites, the multi-specimen domain-state-corrected paleointensity protocol was additionally applied. Rock magnetic experiments indicate that the main remanence carriers are low-coercivity magnetite and high-coercivity ε-maghemite and hematite. The presence of these phases suggests incomplete transformation to hematite during firing. To further assess the archeointensity determinations, the Bias Corrected Estimation of Paleointensity (BiCEP) method was applied, particularly for specimens showing curved Arai plots. This analysis confirmed the reliability of the Thellier results for most investigated structures, whereas no reliable BiCEP outcome could be obtained for one structure from Chobienia (Poland). For four structures, the classical Arai plot evaluation agrees with the BiCEP results and, for one site, also with the independently obtained multi-specimen results. In another case, the comparison between Thellier and BiCEP estimates allowed a more realistic assessment of intensity uncertainty. One site mean value (~ 50 µT) around 600 AD yields a lower geomagnetic field intensity than other contemporaneous European records. Overall, the data suggest an increase in field intensity between 600 and 800 AD, with values becoming more consistent with previously published regional results after this period. However, given the relatively large uncertainties and the still limited number of available studies, additional archeointensity data from 500-800 AD are needed to determine whether the observed regional differences reflect genuine geomagnetic field heterogeneity during this period. Furthermore, new chronological constraints were obtained through archeomagnetic dating approaches applied to the two available full-vector records.

SummaryHuang et al. (2025) reported the detection of 67 teleseismic marsquakes identified by P and S wave arrivals. The authors used a deep learning phase picker trained on local earthquake data and applied it to narrow-bandpass filtered seismic data recorded by NASA’s InSight seismometer, making use of similarities between local earthquake and teleiseismic marsquake recordings when adjusting for sampling rate and S-P time scaling relations. We review all detections as similarly done for the Marsquake Service catalogue and other studies on this data set, using the complementary wind and pressure data recorded by InSight. As these auxiliary data were not recorded in the second half of the mission, we also infer wind contamination from bandwidths in the seismic data that contain wind-sensitive lander modes. Additionally, we analyse the signal polarisation to compare it with the expected characteristics of P and S waves and the background noise. Our review indicates that all 67 detections reported by the authors correspond to atmospheric noise. In most cases, the detections relate to the seismic signature of small wind bursts followed by larger wind bursts, onsets of which are interpreted as P and S waves by the authors. Further, we show that if these events were interpreted as genuine marsquakes, their inferred epicentral distance distribution would not match typical marsquake distances, while their magnitudes would make them the largest events of the catalogue. For future studies that deal with seismic event detection and interpretation from InSight, we recommend a careful consideration of the established event and noise signal markers described in this comment and in the literature to avoid misinterpretation of noise as event signals.

SummaryHigh-speed train (HST) signals offer an abundant and eco-friendly seismic source along the railway, but their application to full waveform inversion (FWI) presents unique challenges due to complex source characteristics and field constraints. We develop an HST-based elastic FWI framework that models the train as a distributed pier-force: a chain of time-delayed excitations applied continuously along deeply embedded bridge piers. This source mechanism generates predominantly S- and Rayleigh-wave energy, providing enhanced shallow subsurface illumination. The synthetic anomaly experiment demonstrates that the distributed pier-force enables superior multi-parameter reconstruction, particularly achieving higher density accuracy than the explosive and single-force sources. Additional sparse acquisition tests validate the robustness of the method under limited receiver coverage. The field data application successfully reconstructs subsurface layering through simultaneous source and parameter inversion, supporting the physical plausibility of the distributed source model. Overall, this study establishes the distributed pier-force as an effective and computationally efficient HST source for shallow subsurface characterisation, while also highlighting limitations under realistic field conditions.

SummaryThe Laji Shan-Jishi Shan Tectonic Belt (L-JTB), situated at a crucial tectonic transfer position on the northeastern margin of the Tibetan Plateau, is important for understanding regional deformation partitioning and seismic hazard. Although it has traditionally been regarded as a zone of relatively modest deformation, the 2023 Jishishan Mw 6.0 earthquake highlights the need to reassess its present-day kinematics and mechanical role. In this study, we integrate GNSS and Sentinel-1 InSAR data to derive a high-resolution three-dimensional interseismic crustal deformation field. We then apply an enhanced dip-aware velocity-profile model within a Bayesian framework to estimate the slip rates and locking characteristics of the major faults, and we further calculate the regional strain-rate field using a multiscale spherical wavelet approach. The results indicate that: (1) The L-JTB exhibits a modest average regional strain level relative to the first-order boundary faults to its north and south, but also displays pronounced along-strike heterogeneity and localized deformation focusing within the belt; (2) The Laji Shan Fault is characterized by a comparatively weak interseismic signal and is dominated by shortening and uplift, with only a minor fault-parallel component, whereas the Jishi Shan Fault is more strongly active, accommodating dextral strike-slip at 1.7 ± 0.3 mm/yr together with shortening-related dip-slip at 3.5 ± 1.2 mm/yr; and (3) the L-JTB is better interpreted as an internal strain transfer belt between the dextral Riyue Shan Fault and the sinistral West Qinling Fault, in which part of the transferred deformation is converted into crustal shortening, uplift, and localized internal strain. Our study reveals that even within a tectonic transfer belt characterized by only modest average regional strain, moderate earthquakes may still nucleate where deformation becomes localized through favorable stepover geometry, structural segmentation, and local strain focusing.

SummaryWe investigate the 410 km discontinuity (thereafter the ‘410’) beneath Europe using teleseismic S-to-P converted waves. This discontinuity—associated with the olivine–wadsleyite phase transition at the top of the mantle transition zone (MTZ)—is widely used as an indicator of thermal variations linked to mantle upwellings and subducting slabs. Our results reveal complex structures of the ‘410’, including closely spaced discontinuities above and below 410 km depth, within laterally confined regions (∼100-200 km wide). These features are predominantly aligned along a corridor extending from the western Alpine front (Western Alps, Rhone Graben) through the Eifel volcanic fields and the Eger Graben to the eastern Alpine front (Western Carpathians, northern Pannonian Basin, Eastern Carpathians), along the European Cenozoic Rift System (ECRIS). In several locations, the disturbed ‘410’ is associated with an elevated lithosphere–asthenosphere boundary (LAB), suggesting a link between lithospheric processes and MTZ structure. We interpret these observations as evidence for small-scale lithospheric dripping, potentially initiated during or following the Alpine orogenesis. Additional occurrences of apparent ‘410‘ doubling are identified beneath the southern Scandes and the northern Adriatic region; beneath the Scandes, this feature spatially correlates with extensional tectonics. Overall, our results indicate that the ‘410’ beneath Europe is strongly influenced by smaller-scale mantle dynamics, closely related to the ECRIS, rather than reflecting solely large-scale thermal anomalies.

SummaryRayleigh wave dispersion curves inversion is an important method for shallow shear wave velocity structure imaging, which can be achieved through different frameworks such as deterministic inversion and Bayesian inversion. The deterministic methods with fixed parametrization usually require pre-set model complexity, and are difficult to directly provide posterior uncertainty estimation. In contrast, trans-dimensional Bayesian method can probabilistically estimate the dimensions of the model during the sampling process and quantify the uncertainty of the inversion results. However, in the inversion of multimode Rayleigh wave dispersion curves, the posterior space usually has high-dimensional, multi-modal, and strongly nonlinear characteristics. How to achieve efficient posterior exploration and stable trans-dimensional mixing is still a key issue in practical applications. In response to this issue, we constructed and evaluated a trans-dimensional Parallel Tempering reversible jump Markov Chain Monte Carlo (PT-rjMCMC) inversion workflow for multi-modal Rayleigh wave dispersion curves in shear wave velocity imaging, denoted as All-Pair-Sweep PT-rjMCMC (APS-PT-rjMCMC). The method integrated Voronoi trans-dimensional parameterization, multi-modal dispersion likelihood function, reversible jump model update, and parallel tempering sampling into a unified framework. In the replica exchange stage, it adopted an all-pair-sweep replica-exchange schedule with randomized ordering to enhance the inter chain information propagation and trans-dimensional mixing ability under a limited number of temperature chains. The inversion results of synthesized model and measured data indicated that compared with the benchmark implementation, the workflow exhibited better performance in convergence behavior, posterior structure recovery, and layer identification. Our technology provides a solution that combines adaptability and reliability for fine survey of shallow geological structures. It is effectively improving the inversion accuracy of shear wave velocity structures under complex geological conditions. It has broad application space and significant application value in fields such as engineering survey, geological hazard assessment, and water resources investigations.

AbstractThe Poisson equation governing a planet’s gravitational field is posed on the unbounded domain, $\mathbb {R}^3$, whereas finite-element computations require bounded meshes. We implement and compare three strategies for handling the infinite exterior in the finite-element method: (i) naive domain truncation; (ii) Dirichlet-to-Neumann (DtN) map on a truncated boundary; (iii) multipole expansion on a truncated boundary. While all these methods are known within the geophysical literature, we discuss their parallel implementations within modern open-source finite-element codes, focusing specifically on the widely-used MFEM package. We consider both calculating the gravitational potential for a static density structure and computing the linearised perturbation to the potential caused by a displacement field—a necessary step for coupling self-gravitation into planetary dynamics. In contrast to some earlier studies, we find that the domain truncation method can provide accurate solutions at an acceptable cost, with suitable coarsening of the mesh within the exterior domain. Nevertheless, the DtN and multipole methods provide superior accuracy at a lower cost within large-scale parallel geophysical simulations despite their need for non-local communication associated with spherical harmonic expansions. The DtN method, in particular, admits an efficient parallel implementation based on an MPI-communicator limited to processors that contain part of the mesh’s outer boundary. A series of further illustrative calculations are provided to show the potential of the DtN and multipole methods within realistic geophysical modelling.