Geophysical Journal International

SummaryThe magnitudes of earthquakes are generally described by an empirical relation called the Gutenberg-Richter law. This relation corresponds to a well-known statistical distribution, i.e. the exponential distribution. In this work, we verify the validity of the Gutenberg-Richter law using a 44-year-long worldwide seismic catalog of strong (Mw ≥ 6.5) events, by testing the exponentiality and the independence of the magnitudes. Moreover, we suggest a new way to visualize the distribution of the magnitudes, which complements the classical magnitude frequency distribution plot.

SummaryThe Cole-Cole (CC) equation was introduced as an empirical formula that in many cases matched laboratory measurements of dispersive frequency-dependent dielectric, conductive or resistive physical properties. The CC formula has four parameters, a high and low frequency limit, one of which is often normalised into a polarizability η or a chargeability m, a time constant τ and a frequency dependence c. The chargeability can be directly related to the volume fraction of polarizable material in a uniform conductive background. In an electrically resistive host, the chargeability is given by the fraction of pores blocked by sulphides or other electronically conductive polarizers in the Pelton conceptual model. Fundamentally, an electrochemical model predicts that uniformly sized, non-reactive polarizers would produce exponential or Debye decays during the return to equilibrium after excitation, while uniformly-sized, chemically-reactive materials such as sulphides should exhibit Warburg decays. Numerically, the frequency dependence c can be matched and predicted from the standard deviation of a log-normal size distribution of polarizable material. Using a simple circuit analogy, excitation by a Voltage or a Current source can produce very different decay time-constants. This analogy and mathematical analysis predict that the time constants from fitting a CC conductivity model (${{\tau }_\sigma }$) can be very different from a CC resistivity model (τρ). A published laboratory sulphide measurement example with ${{\tau }_\rho }$ = 10 days, m = 0.96 and c = 0.2 corresponds to ${{\tau }_\sigma }$ = 88 ms, or 7 orders of magnitude shorter in time. Further, the physical circuit analogy confirms the electrochemical model that while the different time constants are mathematically independent of m and c, ${{\tau }_\sigma }$ is an intrinsic time-constant fundamentally related to the grain size of polarizable material and as such a far better parameter than τρ to use for mineral discrimination studies. Published tabulations of fitted parameters need to specify c as well as the chargeability and CC time-constant to allow for transformation between conductivity and resistivity time-constants. The maximum phase time constant ${{\tau }_\phi } = \sqrt {{{\tau }_\sigma }{{\tau }_\rho }} $ is a fitting rather than experimentally measurable parameter, that is still dependent on m and c, but less dependent than ${{\tau }_\rho }$ as previously discussed in the literature.

SummaryThe northeastern Nam Co region, historically impacted by significant earthquakes such as the 1951 Ms 8.0 Beng Co and 1952 Ms 7.5 Gulu events, exhibits intricate crustal deformation patterns shaped by strike-slip and extensional fault systems. This study integrates multi-source geodetic data to analyze three-dimensional deformation patterns and fault interaction. In this region, we established 16 new GNSS campaign-model observation stations. By aligning these with existing GNSS data within a unified reference frame, we obtained a high-resolution horizontal velocity field. Additionally, ascending and descending InSAR deformation velocity fields were derived utilizing Sentinel-1A data and SBAS-InSAR technology. By fusing the GNSS and InSAR velocity fields, we extracted and analyzed the three-dimensional deformation velocity field. Utilizing an enhanced back-slip dislocation model that accounts for fault dip angles, we inverted the slip behaviors of three major faults and investigated their tectonic transition patterns. The deformation field reveals distinct kinematic behaviors among these faults. Specifically, the Beng Co fault demonstrates dextral strike-slip motion, increasing from 4.8 ± 0.1 mm/yr in west to 5.4 ± 0.1 mm/yr east, accompanied by thrusting at a rate of 3.5 ± 0.1 mm/yr. Notably, the locking depths deepen eastward from 12.6 ± 0.6 km to 17.4 ± 0.8 km. In contrast, the Dong Co and northern Yadong-Gulu faults exhibit sinistral strike-slip rates of 1.0 ± 0.1 mm/yr and 4.2 ± 0.1 mm/yr, respectively, paired with maximum extensional rates of 2.0 ± 0.3 mm/yr and 5.2 ± 0.5 mm/yr. Collectively, these faults form a stable strike-slip to extension coupled system, modulating regional crustal deformation through kinematic interactions. This study quantifies a tectonic transition model, elucidating how strike-slip faulting evolves into extensional structures in central Tibetan Plateau. Our findings contribute to a deeper understanding of strain partitioning and intracontinental deformation mechanisms within the central Tibetan Plateau.

SummarySeismic activity induced by underground engineering projects often involves complex causal mechanisms, and represents significant hazards, including ground subsidence, disruption of surface and underground water systems, ecological damage, structural damage to buildings, and even casualties. Consequently, induced seismicity has become an important topic in the risk assessment and protective measures for underground engineering projects. During the construction of the Hongtu Tunnel on the Dafenghua Expressway in Guangdong, China, a series of earthquakes occurred nearby, with the biggest of magnitude ML = 3.7, alongside significant water inflows at multiple locations. This study analyzed seismic network data from 2017 to 2022 around the tunnel area to investigate the potential relationship between the seismic swarm and tunnel construction and uncover the underlying mechanisms. After velocity model corrections and double-difference relocation, the earthquakes were primarily distributed at depths of 1∼4 km. Three concealed, steeply dipping NE-trending faults, each 3∼7 km in length, were identified based on the earthquake distribution. The swarm began about one month after the onset of water inflows in the tunnel and grew significantly after the peak daily inflow, culminating in the ML 3.7 mainshock. A strong spatiotemporal correlation was observed between the seismic swarm and the water inflows. During the first year of the swarm, the seismicity displayed migration characteristics consistent with pore pressure diffusion, with an initial diffusion depth of approximately 2 km and a diffusion rate of 0.0039∼0.0446 m²/s, and best fit by the classical parabolic diffusion model (α = 0.5). After 2021, the earthquakes occurred more consistently, mainly exhibiting stress-triggering characteristics. Over time, the seismicity gradually extended to greater depths, with focal mechanisms changing from normal faulting to strike-slip faulting. The local stress field shifted from extensional to shear, which reflected the sustained influence of pore pressure diffusion on fault activation. Fluid diffusion not only initially activated the faults but also promoted repeated fault slip during the seismic swarm, indicating that prolonged water inflow significantly altered fault activity patterns and the regional stress field. This study is the first to reveal the phenomenon of long-distance induced seismicity caused by tunnel water inflow and the role of pore pressure diffusion in triggering such events, which offers new insights into the safety of underground construction and the study of fluid-related geological processes.

SummaryThe phenomenon of transient strain from seismic waves triggering earthquakes is a robust observation. However, our understanding as to why seismic waves can trigger earthquakes remains incomplete. In this study, we use particle simulations to investigate the response of sheared granular matter to dynamic strain perturbations in order to better understand the dynamic triggering of earthquakes. In our simulation, an unstable slip is triggered when the dynamic strain above a threshold (critical strain) is applied to the system. We show that the critical strain is of the same order (10–6 to 10–9) as those in some experimental and observational studies. This enhanced response is observed at resonance wavelengths. Resonant vibration decreases the shear modulus of the granular system, and accordingly the shear strength is reduced, leading to unstable slip. This modulus softening is due to the increase in slipping contacts between particles. The relevance of simulation results to natural earthquake faults is discussed as to whether seismic waves can satisfy the resonance condition.

SummaryAs seismic migration is increasingly applied to more and more complex media, more sophisticated imaging techniques are required to generate accurate images of the subsurface. Currently, the best results for imaging are achieved by Least-Squares Migration (LSM) methods, such as Least-Squares Reverse Time Migration (LS-RTM) and Full-Wavefield Migration (FWM). These methods iteratively update the image to minimize the misfit between the forward modelled wavefield and the recorded data at the surface. However, a key challenge for these techniques is the speed of convergence. To accelerate the speed of convergence, pre-conditioning is commonly applied. The most common preconditioner is the reciprocal of the Hessian operator. However, this operator is computationally expensive to calculate, making it difficult to apply directly. In this paper, we present a novel, alternative, preconditioner for FWM. This preconditioner is based on applying Galerkin projections to a linear system, which projects the system onto a set of known basis vectors. To find an appropriate set of basis vectors for this approach we apply Proper Orthogonal Decomposition (POD) to a set of partial solutions of the linear system. The resulting method gives an approximation to the pseudo-inverse based on these basis vectors. To test this technique, which we name Model-Order Reduced FWM (MOR-FWM), we apply it to the synthetic Marmousi model as well as to field data from the Vøring basin in Norway. For these examples, we show that MOR-FWM yields an improved data-misfit compared to the standard FWM approach. In addition, we show that the result for the field data case can be improved by normalizing the partial solutions before applying POD.

SummarySeismic interferometry, applied to continuous seismic records, yields correlation wavefields that can be exploited for information about Earth’s subsurface. The coda of the correlation wavefield has been described as multiply scattered waves that are highly sensitive to crustal heterogeneity and its changes. Therefore, the coda of consecutive correlation wavefields allows to monitor velocity variations over time to detect weak changes in the medium at depth. Ocean microseisms, generated by ocean-land interactions, are the dominant continuous source of seismic energy at frequencies below 0.5 Hz. It is well-understood that these oceanic sources are not homogeneously distributed over Earth and change over the seasons, which commonly results in asymmetric correlation wavefields from seismic data. The impact of these seasonal changes on the coda of the correlation wavefield is typically considered negligible. In contrast, we demonstrate that oceanic noise sources and their changes directly impact the composition of the coda. We compute correlation wavefields between several master stations throughout Europe and the Gräfenberg array in Germany. We beamform these correlation wavefields, in the microseism frequency band, to detect coherent waves arriving at the Gräfenberg array. We perform this analysis for a two-year period, which enables us to compare variations in source direction over the seasons. We find seismic waves arriving from dominant sources to the North-Northwest of Gräfenberg in boreal winter (with slownesses corresponding to surface waves) and towards the South in summer (with slownesses corresponding to body waves) throughout the entire correlation wavefield, including its late coda. Beamforming the original recordings before cross-correlation confirms that the seasonally dominant source regions are directly detected also in the correlation wavefield coda. We derive that seismic waves propagating from isolated microseism source regions will be present in correlation wavefields even if the master station, or ”virtual source”, used for correlation recorded no physical signal at all. The findings we present raise concerns about velocity monitoring approaches relying on the coda being comprised exclusively of scattered waves. Our results also suggest that higher-order correlations do not achieve an effectively more homogeneous source distribution, and instead may even enhance such bias.

SummaryMagnetic data often require interpolation onto a regular grid at constant height before further analysis. A widely used approach for this is the equivalent sources technique, which has been adapted over time to improve its computational efficiency and accuracy of the predictions. However, many of these adaptations still face challenges, including border effects in the predictions or reliance on a stabilising parameter. To address these limitations, we introduce dual-layer gradient-boosted equivalent sources to: (1) use a dual-layer approach to improve the predictions of both short- and long-wavelength signals, as well as, reduce border effect; (2) use block-averaging and the gradient-boosted equivalent sources method to reduce the computational load; (3) apply block K-fold cross-validation to guide optimal parameter selection for the model. The proposed method was tested on both synthetic datasets and the ICEGRAV aeromagnetic dataset to evaluate the methods ability to interpolate and upward continue onto a regular grid, as well as predict the amplitude of the anomalous field from total-field anomaly data. The dual-layer approach proved better compared to the single-layer approach when predicting both short- and long-wavelength signals, particularly in the presence of truncated long-wavelength anomalies. The use of block-averaging and the gradient-boosting method enhances the computational efficiency, being able to grid over 400,000 data points in under 2 minutes on a moderate workstation computer.

SummaryThe stratification stability in the Earth's fluid outer core, which is challenging to constrain with seismology, could potentially be revealed by core undertones (typical inertial-gravity waves). Radial motions from internal inertial-gravity waves are believed to induce minuscule gravity variations at the Earth's surface, yet no conclusive observational evidence has been reported. In this study, we present a systematic search for core undertones within two intertidal bands by stacking a global dataset of superconducting gravimeter observations, comprising 59 gravity residual sequences from 42 stations between July 1, 1997 and February 29, 2024. Under the hypotheses of seismic excitation and sustained excitation, the optimal sequence estimation is used to retrieve spatially coherent signals associated with low-degree (l ≤ 4) spherical harmonic patterns; the z-domain autoregressive power spectrum is used to highlight the weakly damped harmonic signal against the background noise. Rigorous statistical significance analyses indicate that seismic events are insufficient to excite core undertones to the currently observable level. Assuming that core undertones are sustainably excited, we identify three candidate undertones with periods of 9.93, 9.73, and 9.51 hours, associated with spherical harmonic patterns Y2,+1, Y2,–2, and Y3,+2, respectively, which suggest that the liquid outer core near the core surface may contain a strongly stabilized layer characterized by a relatively higher buoyancy frequency. The findings may contribute new insights into the structure and dynamics of the Earth's deep interior as inferred from surface gravimetry.

SummaryExpanding the lower-frequency band of seismic energy sources, particularly below 2.0 Hz, is crucial for improving the stability and effectiveness of full waveform inversion (FWI). Conventional active sources including airguns are ineffective at generating low-frequency wavefields, while ambient seismic wavefields, driven by natural energy sources such as ocean waves, offer a promising alternative. Effectively using ambient wavefield energy for seismic imaging or inversion analyses, though, requires understanding key physical control factors contributing to observations - including ambient source mechanisms and distribution, ocean-bottom bathymetry, and Earth model heterogeneity - which influence wave-mode excitation and partitioning, particularly in the context of ocean-bottom ambient seismology interferometry. This study presents a modeling framework for simulating cross-correlation wavefields generated by ambient seismic sources for dense ocean-bottom sensor arrays within a coupled acoustic-elastic system, without relying on Green’s function retrieval assumptions. We model velocity and pressure cross-correlation wavefields to explore the effects of ocean-bottom velocity structure, ambient source distributions, and bathymetric variations on seismic wave excitation and propagation in the low (0.01-2.00 Hz) frequency band. Our results show that the distribution of ambient energy source locations, whether at the seabed or sea surface, significantly affects excited wave-mode characteristics. Love waves are particularly evident in the presence of substantial lateral and vertical bathymetric variations and heterogeneous Earth structure. The distribution of azimuthal ambient energy sources also influences Love-wave excitation, with the most prominent waves observed in the direction of the highest source concentration. Additionally, different particle velocity component and pressure virtual shot gathers exhibit varying sensitivity to surface waves. This work improves the understanding of low-frequency ambient seismic wavefields in ocean environments, with potential applications in long-wavelength structural imaging and elastic velocity model estimation from FWI analysis.

SummaryPredicting seafloor topography (ST) from altimetry-derived gravity data is an effective method for obtaining ST in sea areas with sparse bathymetry. Classical ST inversion methods primarily utilize gravity anomaly, whereas vertical deflection (VD)—a fundamental product of altimetry that exhibits greater sensitivity to high-frequency ST is infrequently employed. We propose an iterative method for optimization to predict ST using VD in the spatial domain, which addresses the major problem—high nonlinearity between VD and ST. It considers the Airy-isostatic compensation and removes the non-topographic components while preserving short-wavelength signals. Our method predicts the optimal ST by iteratively minimizing the squared 2-norm of the weighted residual vector between the forward-modelled and observed VD. A synthetic test conducted in a part of the South China Sea preliminarily validates the method’s effectiveness. A real-data experiment in the Arctic Ocean shows that the root-mean-square (RMS) of differences between the ST_VD model constructed using our method and checkpoints is 110.43 m, representing improvements of 6.45, 18.85, and 13.95 per cent over the topo_27.1, ETOPO1, and IBCAO V3, respectively. Accuracy verification in different depth ranges and profile analysis indicate that ST_VD exhibits significant advantages in shallow depth (≤2,000 m), while it is relatively inferior in deep depth (>2,000 m). Radial power spectra reveal that ST_VD possesses higher energy at short wavelengths (less than ∼10 km), and its energy at intermediate-long wavelengths is consistent with the comparison models. The results demonstrate our method can effectively recover detailed ST in shallow areas and enhance the short-wavelength ST.

SummaryMagnetite-apatite (MtAp) deposits have attracted considerable attention due to their complex genesis and economic importance. These deposits are rich in magnetite ore and can bear significant rare-earth elements, but their exact formation mechanisms remain controversial. This study aims to understand the formation processes of MtAp deposits by investigating the role of iron-rich magmatic liquids. Focusing on the El Laco deposit, northern Chile, we follow the hypothesis that iron-rich liquids separate from silicate magma through liquid immiscibility. Building on previous research, this study employs a three-phase one-dimensional (1D) mechanical model to simulate the separation and accumulation of immiscible iron-rich melts within increasingly crystalline magma. The model reproduces the previously suggested transition from isolated droplet settling to an interconnected drainage network and quantifies the relative efficiency of both modes of phase separation. Using scaling analysis, we define porous, mush, and suspension flow regimes and construct a regime diagram for three-phase flow. The results indicate that the separation efficiency of immiscible iron-rich melts is maximised in the mush flow regime at intermediate crystallinity. The model-derived accumulation rate of iron-rich melts can be used to estimate the time required to form magnetite deposits of a given scale. Our findings support the physical viability of the liquid immiscibility hypothesis for the genesis of MtAp deposits, offering new insights into the mechanical efficiency of melt separation and contributing to a broader understanding of the formation mechanisms of other valuable deposits that have been linked to immiscible melts.

SummaryThis study focuses on the hydrophone component of a dense ocean bottom cable dataset from the North Sea. This data had already been used in the past to illustrate the high resolution power of full waveform inversion based strategies. We have developed a highly scalable implementation of a visco-acoustic full waveform inversion engine making it possible to double the frequency content of the inverted data compared to previous studies, using simultaneously up to almost 50,000 CPU. This results in a multi-parameter reconstruction of the subsurface, where the P-wave velocity, the density and the quality factor are reliably reconstructed down to 2 km depth, with a resolution of about 10 meters.

SummaryHarmaliére is an active landslide located in a mountainous region of southern France where the presence of a thick layer of clays provides favorable conditions for the development of slowly moving landslides. However, at Harmaliére, the alternation of sudden reactivation and quiet episodes suggests that specific structural and geomechanical properties control its kinematics. In order to shed light on its subsurface properties, we deployed for one month a dense network of seismic nodes within the landslide and recorded active-source and ambient noise seismic data. These datasets have been first independently processed with dedicated interferometry-based processing and inversion workflows to reconstruct P-wave (active sources) and S-wave (seismic noise) velocity models. Full wave-equation tomography is then performed to improve the reliability and resolution of the obtained elastic model by iteratively fitting the virtual gathers obtained by cross-correlation of the ambient-noise recordings. As opposed to conventional ambient-noise tomography, the approach fully accounts for topography and 3D elastic heterogeneities. The obtained high-resolution 3D models are then qualitatively interpreted in terms of landslide properties and geological lithologies, that can influence landslide kinematics.

SummaryDebris flows pose a significant threat to the sustainable development of mountainous regions. As an effective real-time sensing technique, microseismic monitoring plays a critical role in the detection and analysis of debris flow activity. However, current microseismic monitoring technologies face challenges in distinguishing mixed signals originating from different sources, limiting our understanding of the full dynamic evolution of debris flow events. To address this issue, we propose an unsupervised deep clustering-based signal classification framework, which focuses on analyzing the signal characteristics at various stages of debris flow events. A two-dimensional spectrogram dataset was constructed, encompassing signals from debris flows, rockfalls, earthquakes, and environmental noise. A deep autoencoder was employed to compress spectral features into a 16-dimensional latent space, followed by clustering using deep embedded clustering and Gaussian Mixture Models. Experimental results demonstrate that, after optimizing the feature space and data partitioning strategy, the proposed method achieves an average classification accuracy of 96.81 per cent across the four signal types. Power spectral density distribution analysis further confirms that this method not only accurately identifies debris flow signals but also effectively captures their energy distribution and dynamic evolution at different stages. Interpretability analysis reveals strong correlations between the extracted latent features and conventional seismological parameters, particularly the peak count of the time-domain autocorrelation function and the first quartile of the central frequency. Based on this method, a complete segmentation of debris flow events was successfully achieved, revealing the typical signal characteristics and temporal evolution of each stage. Cross-station validation indicates that the proposed framework demonstrates strong robustness and generalization across different monitoring locations. In addition, preliminary exploration of its integration with supervised learning suggests its potential applicability in real-time monitoring scenarios, offering a novel approach for debris flow early warning. This study presents an efficient and intelligent method for debris flow signal recognition and dynamic monitoring.

SummaryBayesian formulations of inverse problems are attractive due to their ability to incorporate prior knowledge, account for various sources of uncertainties, and update probabilistic models as new information becomes available. Markov chain Monte Carlo (MCMC) methods sample posterior probability density functions (pdfs) provided accurate representations of prior information and many evaluations of likelihood functions. Dimensionality-reduction techniques such as principal component analysis (PCA) can assist in defining the prior pdf and the input bases can be used to train surrogate models. Surrogate models offer efficient approximations of likelihood functions that can replace traditional and costly forward solvers in MCMC inversions. Many problem classes in geophysics involve intricate input/output relationships that conventional surrogate models, constructed using samples drawn from the prior pdf fail to capture, leading to biased inversion results and poor uncertainty quantification. Incorporating samples from regions of high posterior probability in the training may increase accuracy, but identifying these regions is challenging. In the context of full waveform inversion, we identify and explore high-probability posterior regions using a series of successively-trained surrogate models covering progressively expanding wave bandwidths. The initial surrogate model is used to invert low-frequency data only as the input/output relationship of high-frequency data are too complex to be described across the full prior pdf with a single surrogate model. After a first MCMC inversion, we retrain the surrogate model on samples from the resulting posterior pdf and repeat the process. By focusing on progressively narrower input domain regions, it is possible to progressively increase the frequency bandwidth of the data to be modeled while also decreasing model errors. Through this iterative scheme, we eventually obtain a surrogate model that is of high accuracy for model realizations exhibiting significant posterior probabilities across the full bandwidth of interest. This surrogate model is then used to perform an MCMC inversion yielding the final estimation of the posterior pdf. Numerical results from 2D synthetic crosshole Ground Penetrating Radar (GPR) examples demonstrate that our method outperforms ray-based approaches, as well as results obtained when only training the surrogate model using samples from the prior pdf. Our methodology reduces the overall computational cost by approximately two orders of magnitude compared to using a classical finite-difference time-domain forward scheme.

SummaryWe revisit the challenge of estimating velocities from global navigation satellite system (GNSS) coordinate time series by incorporating stochastic processes to address the quasi-periodic oscillations (QPOs) in weighted least-squares estimation. We examine two advanced stochastic seasonal models (i.e., Fractional Sinusoidal Waveform (FSW) and Varying Periodic Band-Pass (VPBP)) and evaluate their efficacy on mitigating velocity biases by using both synthetic data and 14 Antarctic GNSS stations. The result shows that pure FSW cannot fully capture the spectral shape of the QPOs since the FSW's spectral shape is controlled by the fractional parameter d, which is unfortunately dependent on the global spectra slope of the GNSS data. In contrast, VPBP can fit the QPOs more freely by using the parameter phi. Nevertheless, both FSW and VPBP models, when used without augmentation, tend to underestimate velocity uncertainties due to spectral flattening at low frequencies. This poses a risk for applications requiring high-confidence geodetic velocity estimates. To solve this issue, adopting a hybrid noise model that is compensated with an additional appropriate noise background (e.g., power law) is recommended. This knowledge can guide future research on secular velocity estimation of GNSS stations.

SummarySpectral induced polarization (SIP) aims to characterize geological materials by measuring the dispersion of their complex conductivity in the frequency domain. Despite the complex-valued nature of SIP data, most machine learning models used for its analysis rely on real-valued representations that discard phase information and may limit performance. This study investigates the benefits of complex-valued neural networks (CVNN) for SIP applications by comparing their performance against real-valued neural networks (RVNN) across three tasks: mineral classification, Cole-Cole parameter estimation, and mechanistic modelling of ionic and electric potential perturbations around polarizable minerals. To ensure fair comparisons and emphasize the effect of complex-valued representations, we design CVNN and RVNN models with matched capacity, aspect ratio, and training duration. Our numerical experiments show that CVNNs consistently outperform RVNNs in the classification task, achieving lower validation loss and up to 5 percent higher classification metrics (p-value = 2.9 × 10−7). We test the Cole-Cole inversion networks on laboratory SIP measurements and validate the parameter estimation accuracy using synthetic data. Test results indicate that CVNNs produce curve fits that are ≈4 % more accurate for the imaginary part of resistivity (p-value = 3.1 × 10−4), and validation results show accuracy improvements of up to 2 percent for chargeability, relaxation time, and the Cole-Cole exponent (p-value = 1.7 × 10−7). CVNNs also yield more accurate approximations of mechanistic model variables, with error reductions of up to 1 percent for ionic concentrations (p-value = 1.6 × 10−4). Our experiments suggest that CVNNs provide modest but statistically significant benefits in SIP applications involving laboratory or synthetic data. While RVNNs may eventually reach comparable predictive accuracy if trained longer, we observe that CVNNs converge more rapidly under matched training conditions. This study provides a reproducible framework for benchmarking neural network architectures in SIP and supports the integration of CVNNs into geophysical workflows where phase responses encode physically meaningful information.

SummaryDistributed Acoustic Sensing (DAS) is a recent technology that turns optical fibers into multi-sensor arrays. In the marine environment, it offers new possibilities for measuring seismic and environmental signals. While DAS can be applied to existing fiber optic cables used for communications, a major limitation of such efforts is that the position of the cable is not always known with sufficient accuracy. In particular, for submarine telecommunication cables, the positioning accuracy decreases with increasing depth. This problem affects the accuracy of earthquake locations and source parameters based on DAS signals. This limitation calls for methods to retrieve the cable’s position and orientation. Here, we propose a method for relocating a linear section of cable “or multiple connected segments” using incidental acoustic sources, particularly boats moving in the vicinity of the cable. The method is based on Target Motion Analysis (TMA) for sources in uniform rectilinear motion. We consider Bearing-Only TMA (BO-TMA) and the Bearing and Frequency TMA (BF-TMA), which respectively use changes in back azimuth (called bearing in navigation) and changes in both back azimuth and Doppler frequency shift as the source moves. We adapt these methods to the 3D case to account for the difference in depth between the fiber and the sources. Both cases lead to a non-linear inverse problem, which we solve by the Levenberg-Marquardt method. On synthetic data, we test both TMA techniques on single and multiple source trajectories and evaluate their accuracy as a function of source trajectory and velocity. We then test the BO-TMA on real DAS recordings of acoustic signals produced by passing ships near a 42 km-long fiber optic cable off the coast of Toulon, southeastern France. In this study case, the position and characteristics of the acoustic source are known. While the Doppler frequency shift at low frequency (30 Hz) is difficult to measure with sufficient accuracy (<0.1○), we demonstrate that effective cable location can be achieved by BO-TMA using multiple ship passages with a variety of trajectories. Once the linear sections of the cable have been relocated, the stage is set to reconstruct the entire cable configuration. More generally, the three-dimensional TMA on linear antennas developed here can be used to locate either the sources or the antenna situated at different depths.

SummaryWe present a full-wave inversion algorithm (FWI) to accurately delineate the subsalt body using seismic borehole data. This ill-posed inverse problem is constrained by introducing geological a priori information through the parameterization of the salt boundary using a level set function. The implicit level set function is spanned by a set of B-spline basis functions for their ability to represent a wide range of shapes. Furthermore, the proposed FWI algorithm combines a meshed discretization with the implicit representation of shapes throughout the inversion process. A weak deformation of the mesh is applied at each iteration of the inversion to maintain the explicit discretization of the shapes when the level set boundary is updated. This method is very accurate when it comes to modelling the scattered wavefields and computing the Fréchet derivatives at interfaces. Three numerical examples using synthetic borehole seismic data illustrate the ability of the method to accurately retrieve the size, location and shape of the salt body when the density and seismic velocities are known.