Geophysical Journal International

SummaryPhase and group velocities along specific ray directions are needed for qP, qSV and SH wave traveltime computation in tilted transversely isotropic (TTI) media. The phase and group velocities are not unique functions of the ray direction, but of the slowness direction, so efficient computation of the slowness direction from a given ray direction becomes necessary. The eigenvalue method and the generalized method have been proposed to facilitate the computation by formulating governing equations for the phase angle, which requires efficient root-finding algorithms. In this work, we address this problem in two-dimensional (2D) TTI media by applying Newton’s method. For the eigenvalue method, a set of two nonlinear equations for the qP and qSV waves and one nonlinear equation for the SH wave must be solved. For the generalized method, only one nonlinear equation of the phase angle needs to be solved for the qP, qSV and SH waves. Numerical experiments, including phase and group velocity computation and their application in first-arrival traveltime calculation, are performed to verify the effectiveness of the proposed methods.

SummaryThis study evaluates the performance of the velocity model adopted for the CyberShake 24.8 (CS24.8) study when used to constrain wave propagation in three-dimensional regional-scale physics-based simulations for seismic hazard estimates. The CS24.8 study was developed to estimate seismic hazard in a subdomain surrounding the San Francisco Bay Area (SFBA) in California, adopting a physics-based finite-difference scheme for frequencies up to 1 Hz; above that, a stochastic scheme with site-specific adjustments is used. The velocity model adopted in the CS.24.8 study was a modified version of the USGS regional velocity model developed for the SFBA. The evaluation of the velocity model is based on comparisons between simulated and recorded ground motions for 18 small-to-moderate local earthquakes. Our analysis focuses on two frequency ranges: 0-1 Hz for estimating wave-propagation uncertainties for users of the CS24.8 study, and 1-5 Hz to provide insight into the performance of the velocity model for future Cybershake studies in this region. Metrics based on Fourier amplitude spectra (FAS) and waveforms’ duration are used for quantitative evaluation of the velocity model. Two aspects of the simulated ground motions are analyzed: (i) the median and variability of the ground motion in the region and (ii) wave propagation effects for specific source-site pairs. For (i), the velocity model leads to an underprediction of the FAS ranging from 0.1 LN-units at 0.3 Hz to 0.5 LN-units at 1 Hz for the horizontal component, and an underprediction of the duration by a factor of 2. The underprediction can be explained by the 400 m/s minimum shear-wave velocity adopted in the CS24.8 velocity model, which is larger than the actual values in the soft marine quaternary sediments of the SFBA, where most stations are located. The spatial variability of the FAS from the simulations over the region is lower than that from the observations over the frequency range 0.3 to 1 Hz, suggesting that the 3-D velocity structure is too smooth. When extending the analysis up to 5 Hz, the underprediction pattern increases up to 0.7 LN-units, and the spatial variability of the ground motions increases, reconciling the gap observed at lower frequencies. For (ii), the evaluation shows that the 3-D simulations improve the accuracy of wave propagation effects for the FAS compared to the ergodic ground-motion models (GMMs) for frequencies less than 0.7 Hz and have similar accuracy up to 1 Hz, being the maximum frequency solved in the physics-based scheme of the CS24.8 study. When extending the analysis above 1 Hz, misrepresentations in the 3-D velocity model introduce noise into the simulated ground motions, leading to a less accurate estimate of the FAS at these frequencies compared to GMMs. Our results inform users of the CS24.8 study that the physics-based simulation (up to 1 Hz) offers performance comparable to or better than standard GMMs, while accounting for wave-propagation uncertainties. These findings can guide future refinements of the velocity model.

SummaryGeophysical electrical methods are increasingly being used in civil engineering to characterize and monitor cementitious materials. However, there is currently a lack of understanding of the role of their electrical surface conductivity and there is no quantitative model explaining their complex conductivity (induced polarization) spectra. Therefore, our goal is to propose and to validate a mechanistic model. We prepared 20 cement paste samples of well-established cement compositions (named CEMI and CEMV in the cement nomenclature) and 16 corresponding mortar samples (labeled MORI and MORV), all cured for 60 days, with water-to-cement (w/c) ratios ranging from 0.35 to 0.60. Complex conductivity spectra were measured at 21°C in the frequency range 10 mHz-45 kHz. For the cement pastes, both the in-phase conductivity and the magnitude of the quadrature conductivity increase systematically with the increase of the w/c ratio. The electrical properties of the mortars scale proportionally with those of the corresponding cement pastes, and the proportionality coefficient can be predicted from the volume fraction of cement and the model. We observe that the normalized chargeability is proportional to the quadrature conductivity, consistent with theoretical expectations. The relationship between the normalized chargeability and the surface conductivity and between the normalized chargeability and the Cation Exchange Capacity (CEC) are explained using a dynamic Stern layer model associated with the polarization of the inner component of the double layer coating the surface of the minerals. In other words, the dynamic Stern layer initially developed for colloidal solutions and geomaterials can be applied to cementitious materials opening new doors in their non-intrusive monitoring. To our knowledge, this is the first study to provide a physically-based interpretation of the complex conductivity spectra of cement pastes and mortars. These results demonstrate that induced polarization displays strong potentials for imaging water content and the Cation Exchange Capacity (CEC) (alternatively the specific surface area) of cementitious materials at various scales. This opens new perspectives regarding the quantitative non-invasive geophysical monitoring of cement and concrete for both civil and nuclear engineering applications.

SummaryUniform density-contrast assumptions in gravity-derived bathymetry produce substantial systematic errors. This problem stands out in regions with strong lateral density variation, such as the central–northern South China Sea. Conventional constant or simple vertically varying density models fail to capture these complexities. To overcome this limitation, a spatially varying density-contrast field is constructed by integrating multi-source geophysical data (crustal, gravity, and bathymetric data) using a back-propagation (BP) neural network. This field is incorporated into an adaptive Parker–based inversion, yielding a high-resolution bathymetric grid with Root Mean Square (RMS) improvements of 2.6 m over the constant-density approach, together with the smallest systematic bias. The most significant gains occur in shallow reef-dominated waters (0 to −1500 m), where relative RMS reductions reach approximately 9%. By coupling neural network-derived density modelling with physically rigorous inversion, the approach overcomes limitations of uniform-density assumptions while retaining interpretability, providing an efficient and reliable approach to high-precision seafloor mapping in geologically complex regions.

SummaryInstrument correction is a fundamental step in broadband seismology, yet it is commonly treated as a purely numerical operation stabilized by heuristic procedures. In practice, inverse filtering of instrumental responses is constrained by causality, stability, discretization, and uncertainty in instrument parameters, which jointly limit the recoverable frequency content and the physical interpretability of corrected ground motion. Here I present a unified framework for causal and uncertainty-aware instrument correction that explicitly formulates deconvolution as a constrained inverse problem in the digital domain. The proposed approach enforces causal realizability and bounded inverse behaviour while introducing regularization as a physically interpretable control of the bias–noise trade-off. Discretization effects arising from the mapping between continuous- and discrete-time responses are quantified and shown to induce systematic, frequency-dependent amplitude bias that interacts nonlinearly with regularization. I further extend the formulation to incorporate parametric uncertainty in the instrument response, propagating it through the inverse filter to derive confidence bounds on effective amplitude response and noise amplification. A set of diagnostic metrics is introduced to jointly characterize amplitude bias, noise amplification, effective bandwidth, and robustness under uncertainty. These diagnostics are combined into a data-driven decision framework that supports objective selection of the inverse filter and explicitly defines the frequency range over which instrument correction is reliable. Time-domain kernel diagnostics complement the frequency-domain analysis by ensuring causal behaviour and controlled temporal support. The framework is summarized in an end-to-end algorithmic workflow designed for reproducible application to broadband seismic data without reliance on ad hoc stabilization choices. By making physical constraints, trade-offs, and uncertainties explicit, the proposed methodology enhances the robustness and interpretability of instrument-corrected seismic waveforms and provides a principled foundation for downstream analyses in source studies, spectral characterization, and waveform-based investigations.

SummaryAirborne transient electromagnetic (ATEM) inversion relies on efficient forward modeling, yet conventional numerical methods struggle to balance computational efficiency and accuracy when handling undulating terrain and large survey datasets. We present a fast forward modeling approach using multi-scale dilated residual networks that takes two-dimensional conductivity profiles with embedded terrain information as image inputs and directly predicts electromagnetic response tensors across multiple flight altitudes. The network architecture employs progressively increasing dilation rates to capture multi-scale geological features while preserving spatial resolution. A dual-domain loss function combining log-normalized and linear domains balances the fitting weights across electromagnetic responses spanning seven orders of magnitude. We trained and tested the model on 100,000 synthetic samples of random terrain and geoelectric structures generated with the SimPEG three-dimensional finite volume method. The network achieves mean absolute percentage errors (MAPE) of 2.24%-3.57% across four terrain types (flat, slope, peak, and valley). Spline interpolation enables accurate prediction at arbitrary flight altitudes not included in training, with errors of 1.69%-3.53%. On a 10 km survey profile, the method achieves approximately 2000-fold speedup compared to SimPEG. This approach provides a practical forward modeling solution for rapid ATEM inversion over complex terrain, and the proposed multi-scale feature extraction strategy and dual-domain loss function design offer transferable insights for other geophysical machine learning applications.

SummaryTo address the challenge in seismic exploration where strong-energy ground roll severely interferes with effective signals and conventional suppression methods tend to damage these signals, this paper proposes a self-supervised Swin-Unet network method for ground roll suppression based on Fourier Positional Encoding and a bespoke masking strategy. This method operates without the need for clean label data. By employing a specially designed fan-shaped masking strategy, it disrupts the spatio-temporal coherence of the ground roll, thereby guiding the network to learn the intrinsic characteristics of the effective signals and reconstruct the data. The core innovation lies in the introduction of Fourier Positional Encoding, which overcomes the inherent low-frequency bias of the Transformer architecture. This significantly enhances the network’s capability to model and recover high-frequency effective signals. Experimental results on synthetic data and field 2D/3D seismic datasets demonstrate that the proposed method not only effectively suppresses strong ground roll but also surpasses the traditional f – k filtering method in terms of signal fidelity, particularly in preserving deep, weak reflections and high-frequency components. This showcases its robustness and potential for application in complex seismic data processing.

SummaryAn innovative method is presented for full 3D pressure and temperature dominated stress evaluations in the subsurface using tetrahedra-based analytical elements combined with the inflation point source solution. A mesh-free approach suitable to industry standard 3D flow simulation models (based on hexahedral cells) is obtained by representing the grid cells in tetrahedral elements, effectively preserving the 3D geometrical complexities of the reservoir. Contributions from neighboring grid cells are added via a Tartan grid representation of point sources that enables the spatial resolution to increase and the stress evaluations to be carried out in parallel, both of which significantly improve computational efficiency. The novel approach is demonstrated for synthetic low enthalpy geothermal models with clastic reservoir characteristics and varying degrees of geometrical and structural complexity. The method is shown able to accurately capture the effects of stress arching on complex faults causing reservoir throw and flow compartmentalization, and along the rim of the cold-water volume. Results of a synthetic geothermal development model of the heavily faulted Gullfaks field show the novel method to provide an accurate and computationally highly efficient approach for evaluating pressure and temperature dominated stress changes in structurally complex sedimentary reservoirs.

SummaryPore-water pressure and clay content have influence on porosity and bonding/cementing the grain boundaries, thus affecting elastic properties, strength, and other physical properties of rocks. Similar processes take place in cementitious materials, where in particular hydration plays crucial role. This process leads to changes in pore water composition, specific surface area (or alternatively Cation Exchange Capacity, CEC), and water content. Analytical expressions can be obtained between both the CEC and porosity and a hydration state variable. The hydration state variable can be in turn related to the hydration time. These phenomena can be assessed by geoelectrical methods, which have been used for a long time to observe the evolution of the textural properties and rheology of rocks, as well as of cementitious materials. However, such use has been so far rather qualitative. The aim of this study is to better describe the evolution of complex conductivity spectra (induced polarization) in relation to the hydration, using the recently developed dynamic Stern layer model to the hydration time through Powers model. Comparisons between the model predictions and literature data are used to test the suitability of the proposed solution. The model is verified using monitoring experiments of the complex conductivity spectra of several cements to study the evolution of both the in-phase and quadrature conductivity versus the hydration time. Although the current method is still semi-empirical, it makes it possible to analyze and understand the evolution of complex conductivity spectra of geomaterials and technogenic cementitious materials with a wide variety of geophysical applications in civil engineering, especially for dams and underground civil constructions.

SummaryWe have developed a physics-guided deep learning framework for geophysical inversion that incorporates Markov chain Monte Carlo (MCMC) sampling to assess the uncertainty associated with model parameters of interest. To enhance computational efficiency, a statistical sampling method is utilized to reduce the number of samples required while ensuring the training data remain both diverse and informative. As the inversion progresses iteratively, the training dataset is dynamically expanded using outputs from the stochastic sampler along with their corresponding forward responses. A supervised deep learning model is utilized, in which the Jensen-Shannon divergence is adopted as the loss function, and a Gaussian assumption is applied for analytical computation. We test the workflow on a seismic velocity model inversion, and successfully capture the geological features and velocity distributions, with results that closely match the reference model. Compared to the MCMC sampler applied to the whole data cube, the proposed workflow is more computationally efficient, as a small fraction of data is chosen using the active learning paradigm. This workflow is strongly generalizable and effective, making it suitable for a wide range of other inversion applications as well.

SummaryThe origin of seismic discontinuities in the Earth’s mid-mantle (∼700–1400 km) remains debated, with competing hypotheses attributing them to either partial melting due to water transport across the transition zone or compositional heterogeneities (subducted crust). Distinguishing between these scenarios has been hindered by the inability of standard imaging techniques to extract robustly the polarity of weak seismic reflections amidst noise and reverberations that contaminate mid-mantle reflections. Here, we introduce a novel signal processing framework that combines curvelet-based wavefield separation with extended multitaper deconvolution to resolve this polarity ambiguity. We validate this approach by applying it to a high-quality dataset of SS and PP precursors beneath the Central Pacific. This application yields the robust detection of a discontinuity at approximately 800 km depth, characterized by a sharp positive shear velocity contrast (δVS ≈ +4 − 5%) and a negligible density contrast. The observed positive polarity precludes partial melt or thermal plumes as primary causal mechanisms. Instead, the high-velocity, neutral-density signature is consistent with a layer of stagnant, subducted oceanic crust in thermal equilibration with the ambient mantle. These results demonstrate the efficacy of the deconvolution framework and provide direct seismic evidence for compositional stratification in the mid-mantle, supporting geodynamic models where viscosity increases facilitate the long-term preservation of recycled lithosphere.

SummaryGeodetic observations, such as GNSS and InSAR, are increasingly used to investigate co-seismic surface deformation. Efficiently and simultaneously resolving fault geometry and slip distribution from surface displacements is essential for understanding earthquake processes, accurately estimating seismic magnitude and comprehensively assessing seismic hazard. Current mainstream approaches typically rely on Bayesian inference, such as Monte Carlo sampling. However, these methods typically suffer from long burn-in periods, low computational efficiency, strong sensitivity to initial parameter values and step sizes. Given these limitations, conventional approaches may yield suboptimal fits for the observations. To overcome these limitations, we propose and develop a novel Tree-structured Bayesian Optimization method (TBO), integrated with Helmert Variance Component Estimation (HVCE), to jointly determine fault geometry and slip distribution. To rigorously assess the feasibility and reliability of the proposed approach, we test it using both synthetic and real earthquake data. In the synthetic tests, we evaluate its robustness under a variety of conditions, including different fault types, varying types and densities of geodetic observations, diverse sub-fault sizes and asperities, and complex multi-fault scenarios. Four sets of synthetic experiments are designed, and the results conclusively demonstrate that the proposed method achieves stable and reliable performance in inverting fault geometry and slip distribution. Furthermore, comparative analysis with existing methodologies shows that our approach yields substantially improved computational efficiency, significantly reduced sensitivity to initial conditions, and smaller misfits to observations. Finally, we apply the method to the 2021 Mw 6.4 Yangbi earthquake in Yunnan, China. The retrieved fault geometry and slip distribution successfully explain the fault kinematics and the observed surface deformation field, thereby confirming the applicability and robustness of the method for real earthquake event analysis.

SummaryGravity inversion is an essential technique for recovering subsurface density variations. Constructing stratigraphic models from gravitational observations, however, remains challenging because gravity data provide limited vertical resolution and the inverse problem is strongly non-unique. To address these limitations, we develop a Bayesian geometry-based gravity inversion framework aimed specifically for stratigraphic reconstruction. Stratigraphic interfaces are parameterized using a Fourier series, which provides a compact set of variables, enables a controllable representation of layer geometry, and improves the vertical resolution of the recovered density model. Uncertainty in the inferred stratigraphy is quantified with Stein variational inference, yielding an ensemble approximation to the posterior distribution. The resulting posterior models reveal the confidence level and spatial variability of stratigraphic layers. The proposed method has been validated using two toy examples to illustrate the main concepts. Two synthetic lunar basin models, representing alternative interpretive hypotheses for upper-crustal layering, are further designed to evaluate algorithm performance. Finally, application to satellite gravity observations from the Orientale Basin demonstrates that the proposed framework can recover the basin’s large-scale tectonic structure.

SummaryThicknesses and bulk Vp/Vs ratios of crustal layers (or Poisson’s ratio) are fundamental parameters for understanding continental structure, composition, and tectonic evolution. Traditional receiver function (RF) methods analyze P-to-S converted phases to estimate these parameters but face significant challenges in regions with low-velocity sedimentary layers, where sediment-related multiples contaminate deeper crustal signals and bias parameter estimates. We present a sequential RF-AC H-κ phase-weighted stacking method that jointly analyzes RFs and coda autocorrelations (ACs) to simultaneously constrain sedimentary and underlying crystalline crustal properties. Integration of AC data provides independent constraints on P- and S-wave reflection times, improving estimation robustness. Synthetic tests demonstrate that our method effectively suppresses sediment multiple interference and yields more reliable layer thickness and Vp/Vs ratio estimates than conventional RF-only approaches. We apply this method to four broadband stations in contrasting tectonic settings: the extensional Bohai Bay Basin and stable Tarim Basin, China. Results reveal 2.0 – 10.0 km thick sedimentary layers with Vp/Vs ratios decreasing from ~ 2.90 to 2.00 with depth, consistent with progressive compaction. Crustal thickness estimates show significant tectonic variability: 28.0 – 32.0 km in the extensional Bohai Bay Basin versus ~ 40 km in the stable Tarim Basin. Crystalline crustal Vp/Vs ratios of 1.66 – 1.73 at three stations indicate predominantly felsic composition, while a higher ratio (~ 1.80) in southwestern Tarim suggests more mafic materials. These findings agree with independent geophysical observations and geological constraints, demonstrating that this method provides a robust framework for constraining layered continental crust with thick sedimentary basins.

SummarySurface waves are sensitive to the shear wave velocity and low-velocity zone (LVZ). Here, we analyze the subsurface anomalies in the upper mantle beneath the Central Indian Ocean Basin (CIOB) utilising the ocean bottom seismometer (OBS) data. The Rayleigh wave dispersion curve analysis between earthquake clusters and OBS stations shows a period range between 12 and 300 s for the fundamental modes. A significant decrease in group velocity is observed at an intermediate period (60-180 s). The estimated depth of the lithospheric base is ∼81 km, ∼68 km, ∼67 km, and ∼82 km for P1, P2, P3, and P4 profiles respectively. A significant reduction in Vsv velocity is observed beneath the lithospheric base (i.e. ∼22-24 km thick Lithosphere-Asthenosphere boundary). Our results show an anomalous LVZ between ∼80 km and ∼170 km depth interval beneath the CIOB. A ∼18–20 per cent reduction in Vsv velocity within the LVZ suggests the presence of ∼1.9–2.0 per cent melt fraction in the shallow asthenosphere along P2 (∼3.7 km/s) and P3 (∼3.73 km/s) profiles. An excess temperature of ∼230°C is inferred across the P1-P4 profiles in the vicinity of LVZ beneath the CIOB. Henceforth, we propose a mechanism in which the presence of an unextracted melt fraction, in conjunction with the northward movement of the Indian plate and supplemented by plume-lithosphere interaction, can account for the formation and persistence of anomalous LVZ in the upper mantle. An additional ∼1 per cent melt within the LVZ along the P2 and P3 profiles, relative to the P1 and P4 profiles, favours the possibility of the west-to-east channelized asthenospheric flow beneath the CIOB region.

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.