Full waveform inversion (FWI) has become a widely adopted technique for high-resolution subsurface imaging. However, its inherent strong nonlinearity often results in convergence toward local minima. Recently, deep image prior-based reparameterized FWI (DIP-FWI) has been proposed to alleviate the dependence on massive training data. By exploiting the spectral bias and implicit regularization in the neural network architecture, DIP-FWI can effectively avoid local minima and reconstruct more geologically plausible velocity models. Nevertheless, existing DIP-FWI typically use a fixed random input throughout the inversion process, which fails to utilize the mapping and correlation between the input and output of the network. Moreover, under complex geological conditions, the lack of informative prior in the input can exacerbate the ill-posedness of the inverse problem, leading to artifacts and unstable reconstructions. To address these limitations, we propose a self-reinforced DIP-FWI (SRDIP-FWI) framework, in which a steering algorithm alternately updates both the network parameters and the input at each iteration using feedback from the current network output. This design allows adaptive structural enhancement and improved regularization, thereby effectively mitigating the ill-posedness in FWI. Additionally, we analyze the spectral bias of the network in SRDIP-FWI and quantify its role in multiscale velocity model building. Synthetic tests and field land data application demonstrate that SRDIP-FWI achieves superior resolution, improved accuracy and greater depth penetration compared to multiscale FWI. More importantly, SRDIP-FWI eliminates the need for manual frequency-band selection and time-window picking, substantially simplifying the inversion workflow. Overall, the proposed method provides a novel, adaptive and robust framework for accurate subsurface velocity model reconstruction.

Environmental variables are increasingly affecting agricultural decision-making, yet accessible and scalable tools for soil assessment remain limited. This study presents a robust and scalable modeling system for estimating soil properties in croplands, including soil organic carbon (SOC), total nitrogen (N), available phosphorus (P), exchangeable potassium (K), and pH, using remote sensing data and environmental covariates. The system employs a hybrid modeling approach, combining the indirect methods of modeling soil through proxies and drivers with direct spectral modeling. We extend current approaches by using interpretable physics-informed covariates derived from radiative transfer models (RTMs) and complex, nonlinear embeddings from a foundation model. We validate the system on a harmonized dataset that covers Europes cropland soils across diverse pedoclimatic zones. Evaluation is conducted under a robust validation framework that enforces strict spatial blocking, stratified splits, and statistically distinct train-test sets, which deliberately make the evaluation harder and produce more realistic error estimates for unseen regions. The models achieved their highest accuracy for SOC and N. This performance held across unseen locations, under both spatial cross-validation and an independent test set. SOC obtained a MAE of 5.12 g/kg and a CCC of 0.77, and N obtained a MAE of 0.44 g/kg and a CCC of 0.77. We also assess uncertainty through conformal calibration, achieving 90 percent coverage at the target confidence level. This study contributes to the digital advancement of agriculture through the application of scalable, data-driven soil analysis frameworks that can be extended to related domains requiring quantitative soil evaluation, such as carbon markets.

Accurate long-range forecasting of the El \Nino-Southern Oscillation (ENSO) is vital for global climate prediction and disaster risk management. Yet, limited understanding of ENSO's physical mechanisms constrains both numerical and deep learning approaches, which often struggle to balance predictive accuracy with physical interpretability. Here, we introduce a data driven model for ENSO prediction based on conditional diffusion model. By constructing a probabilistic mapping from historical to future states using higher-order Markov chain, our model explicitly quantifies intrinsic uncertainty. The approach achieves extending lead times of state-of-the-art methods, resolving early development signals of the spring predictability barrier, and faithfully reproducing the spatiotemporal evolution of historical extreme events. The most striking implication is that our analysis reveals that the reverse diffusion process inherently encodes the classical recharge-discharge mechanism, with its operational dynamics exhibiting remarkable consistency with the governing principles of the van der Pol oscillator equation. These findings establish diffusion models as a new paradigm for ENSO forecasting, offering not only superior probabilistic skill but also a physically grounded theoretical framework that bridges data-driven prediction with deterministic dynamical systems, thereby advancing the study of complex geophysical processes.

In multi-temporal InSAR, phase linking refers to the estimation of a single-reference interferometric phase history from the information contained in the coherence matrix of a distributed scatterer. Since the phase information in the coherence matrix is typically inconsistent, the extent to which the estimated phase history captures it must be assessed to exclude unreliable pixels from further processing. We introduce three quality criteria in the form of coefficients, for threshold-based pixel selection: a coefficient based on closure phase that quantifies the internal consistency of the phase information in the coherence matrix; a goodness-of-fit coefficient that quantifies how well a resulting phase history estimate approximates the phase information according to the characteristic optimization model of a given phase linking method; and an ambiguity coefficient that compares the goodness of fit of the original estimate with that of an orthogonal alternative. We formulate the phase linking methods and these criteria within a unified mathematical framework and discuss computational and algorithmic aspects. Unlike existing goodness-of-fit indicators, the proposed coefficients are normalized to the unit interval with explicit noise-floor correction, improving interpretability across stacks of different size. Experiments on TerraSAR-X data over Visp, Switzerland, indicate that the closure phase coefficient effectively pre-screens stable areas, the goodness-of-fit coefficient aligns with and systematically generalizes established quality indicators, and the ambiguity coefficient flags solutions that fit well but are unstable. Together, the coefficients enable systematic pixel selection and quality control in the interferometric processing of distributed scatterers.

Inversion of gravity data is an important method for investigating subsurface density variations relevant to diverse applications including mineral exploration, geothermal assessment, carbon storage, natural hydrogen, groundwater resources, and tectonic evolution. Here we present a scientific machine-learning approach for three-dimensional gravity inversion that represents subsurface density as a continuous field using an implicit neural representation (INR). The method trains a deep neural network directly through a physics-based forward-model loss, mapping spatial coordinates to a continuous density field without predefined meshes or discretisation. Positional encoding enhances the network's capacity to capture sharp contrasts and short-wavelength features that conventional coordinate-based networks tend to oversmooth due to spectral bias. We demonstrate the approach on synthetic examples including Gaussian random fields, representing realistic geological complexity, and a dipping block model to assess recovery of blocky structures. The INR framework reconstructs detailed structure and geologically plausible boundaries without explicit regularisation or depth weighting, while significantly reducing the number of inversion parameters. These results highlight the potential of implicit representations to enable scalable, flexible, and interpretable large-scale geophysical inversion. This framework could generalise to other geophysical methods and for joint/multiphysics inversion.

High-resolution processing of seismic signals is crucial for subsurface geological characterization and thin-layer reservoir identification. Traditional high-resolution algorithms can partially recover high-frequency information but often lack robustness, computational efficiency, and consideration of inter-trace structural relationships. Many deep learning methods use end-to-end architectures that do not incorporate prior knowledge or address data domain disparities, leading to limited this http URL overcome these challenges, this paper presents the Domain-Adaptive Knowledge Distillation Network (DAKD-Net), which integrates a knowledge distillation strategy with a domain adaptation mechanism for high-resolution seismic data processing. Trained on datasets from forward modeling, DAKD-Net establishes physical relationships between low and high-resolution data, extracting high-frequency prior knowledge during a guided phase before detail restoration without prior conditions. Domain adaptation enhances the model's generalization to real seismic data, improving both generalization capability and structural expression this http URL-Net employs a U-Net backbone to extract spatial structural information from multi-trace seismic profiles. The knowledge distillation mechanism enables prior knowledge transfer, allowing recovery of high-resolution data directly from low-resolution inputs. Domain-adaptive fine-tuning further enhances the network's performance in actual survey areas. Experimental results show that DAKD-Net outperforms traditional methods and classical deep networks in longitudinal resolution and complex structural detail restoration, demonstrating strong robustness and practicality.

Climate hazards can escalate into humanitarian disasters. Understanding their trajectories -- considering hazard intensity, human exposure, and societal vulnerability -- is essential for effective anticipatory action. The International Disaster Database (EM-DAT) is the only freely available global resource of humanitarian disaster records. However, it lacks exact geospatial information, limiting its use for climate hazard impact research. Here, we provide geocoding of 9,217 climate-related disasters reported by EM-DAT from 1990 to 2023, along with an open, reproducible framework for updating. Our method remains accurate even when only region names are available and includes quality flags to assess reliability. The augmented EM-DAT enables integration with other geocoded data, supporting more accurate assessment of climate disaster impacts and adaptation deficits.

Full waveform inversion (FWI) is a high-resolution subsurface imaging technique, but its effectiveness is limited by challenges such as noise contamination, sparse acquisition, and artifacts from multiparameter coupling. To address these limitations, this study develops a deep reparameterized FWI (DR-FWI) framework, in which subsurface parameters are represented by a deep neural network. Instead of directly optimizing the parameters, DR-FWI optimizes the network weights to reconstruct them, thereby embedding structural priors and facilitating optimization. To provide benchmark guidelines for the design of DR-FWI, we conduct a comparative analysis of three representative architectures (U-Net, CNN, MLP) combined with two initial model embedding strategies: one pretraining the network to generate predefined initial models (pretraining-based), while the other directly adds network outputs to the initial models. Extensive ablation experiments show that combining CNN with pretraining-based initialization significantly enhances inversion accuracy, offering valuable insights into network design. To further understand the mechanism of DR-FWI, spectral bias analysis reveals that the network first captures low-frequency features and gradually reconstructs high-frequency details, enabling an adaptive multi-scale inversion strategy. Notably, the robustness of DR-FWI is validated under various noise levels and sparse acquisition scenarios, where its strong performance with limited shots and receivers demonstrates reduced reliance on dense observational data. Additionally, a backbone-branch structure is proposed to extend DR-FWI to multiparameter inversion, and its efficacy in mitigating cross-parameter interference is validated on a synthetic anomaly model and the Marmousi2 model. These results suggest a promising direction for joint inversion involving multiple parameters or multiphysics.

Physics-Informed Neural Networks (PINNs) have gained increasing attention for solving partial differential equations, including the Helmholtz equation, due to their flexibility and mesh-free formulation. However, their low-frequency bias limits their accuracy and convergence speed for high-frequency wavefield simulations. To alleviate these problems, we propose a simplified PINN framework that incorporates Gabor functions, designed to capture the oscillatory and localized nature of wavefields more effectively. Unlike previous attempts that rely on auxiliary networks to learn Gabor parameters, we redefine the network's task to map input coordinates to a custom Gabor coordinate system, simplifying the training process without increasing the number of trainable parameters compared to a simple PINN. We validate the proposed method across multiple velocity models, including the complex Marmousi and Overthrust models, and demonstrate its superior accuracy, faster convergence, and better robustness features compared to both traditional PINNs and earlier Gabor-based PINNs. Additionally, we propose an efficient integration of a Perfectly Matched Layer (PML) to enhance wavefield behavior near the boundaries. These results suggest that our approach offers an efficient and accurate alternative for scattered wavefield modeling and lays the groundwork for future improvements in PINN-based seismic applications.

Solving inverse problems with the reverse process of a diffusion model represents an appealing avenue to produce highly realistic, yet diverse solutions from incomplete and possibly noisy measurements, ultimately enabling uncertainty quantification at scale. However, because of the intractable nature of the score function of the likelihood term (i.e., $\nabla_{\mathbf{x}_t} p(\mathbf{y} | \mathbf{x}_t)$), various samplers have been proposed in the literature that use different (more or less accurate) approximations of such a gradient to guide the diffusion process towards solutions that match the observations. In this work, I consider two sampling algorithms recently proposed under the name of Diffusion Posterior Sampling (DPS) and Pseudo-inverse Guided Diffusion Model (PGDM), respectively. In DSP, the guidance term used at each step of the reverse diffusion process is obtained by applying the adjoint of the modeling operator to the residual obtained from a one-step denoising estimate of the solution. On the other hand, PGDM utilizes a pseudo-inverse operator that originates from the fact that the one-step denoised solution is not assumed to be deterministic, rather modeled as a Gaussian distribution. Through an extensive set of numerical examples on two geophysical inverse problems (namely, seismic interpolation and seismic inversion), I show that two key aspects for the success of any measurement-guided diffusion process are: i) our ability to re-parametrize the inverse problem such that the sought after model is bounded between -1 and 1 (a pre-requisite for any diffusion model); ii) the choice of the training dataset used to learn the implicit prior that guides the reverse diffusion process. Numerical examples on synthetic and field datasets reveal that PGDM outperforms DPS in both scenarios at limited additional cost.

This paper examines mathematical models for processing classical horizontal geodetic (triangulation and trilateration) networks. Two rigorous parametric adjustment models are discussed. The first one is a well-known model of adjustment in the geodetic coordinate system. This model is completely rigorous (functional and stochastic parts) and uses unreduced distance and direction observations. The proposed alternative is a model of planar network adjustment with closed-form reductions of observations directly to the mapping plane. These ground-to-grid reductions are simple and universal, regardless of which map projection is used. Slightly different results of the planar network adjustment are obtained. The differences are attributed to a nonrigorous stochastic model. In theory, the stochastic properties of the reduced observations should also be adapted. However, these differences are very small and can always be neglected in geodetic and surveying practice.

We develop a 2-D numerical model of magmatism and mantle convection to understand the volcanism on the Procellarum KREEP terrane (PKT) of the Moon, which continued for billions of years with two peaks of activities at 3.5-4 Gyr ago and around 2 Gyr ago. In our model, the effects of the PKT on lunar evolution are considered by initially imposing a region of localized radioactive enrichment. The calculated volcanism has two peaks induced by different mechanisms. The first peak occurs at 3.5-4 Gyr ago when magma generated in the deep mantle by internal heating ascends to the surface as partially molten plumes. The basaltic blocks in the uppermost mantle formed by this magmatism, then, sink to the deep mantle, triggering further plumes that cause the resurgence of volcanism at $\sim$2 Gyr ago. Our model shows that localized radioactive enrichment is important for the long-lasting volcanism with a couple of peaks.

Successful deployment of geological carbon storage (GCS) requires an extensive use of reservoir simulators for screening, ranking and optimization of storage sites. However, the time scales of GCS are such that no sufficient long-term data is available yet to validate the simulators against. As a consequence, there is currently no solid basis for assessing the quality with which the dynamics of large-scale GCS operations can be forecasted. To meet this knowledge gap, we have conducted a major GCS validation benchmark study. To achieve reasonable time scales, a laboratory-size geological storage formation was constructed (the "FluidFlower"), forming the basis for both the experimental and computational work. A validation experiment consisting of repeated GCS operations was conducted in the FluidFlower, providing what we define as the true physical dynamics for this system. Nine different research groups from around the world provided forecasts, both individually and collaboratively, based on a detailed physical and petrophysical characterization of the FluidFlower sands. The major contribution of this paper is a report and discussion of the results of the validation benchmark study, complemented by a description of the benchmarking process and the participating computational models. The forecasts from the participating groups are compared to each other and to the experimental data by means of various indicative qualitative and quantitative measures. By this, we provide a detailed assessment of the capabilities of reservoir simulators and their users to capture both the injection and post-injection dynamics of the GCS operations.

Frequency-domain simulation of seismic waves plays an important role in seismic inversion, but it remains challenging in large models. The recently proposed physics-informed neural network (PINN), as an effective deep learning method, has achieved successful applications in solving a wide range of partial differential equations (PDEs), and there is still room for improvement on this front. For example, PINN can lead to inaccurate solutions when PDE coefficients are non-smooth and describe structurally-complex media. In this paper, we solve the acoustic and visco-acoustic scattered-field wave equation in the frequency domain with PINN instead of the wave equation to remove source singularity. We first illustrate that non-smooth velocity models lead to inaccurate wavefields when no boundary conditions are implemented in the loss function. Then, we add the perfectly matched layer (PML) conditions in the loss function of PINN and design a quadratic neural network to overcome the detrimental effects of non-smooth models in PINN. We show that PML and quadratic neurons improve the results as well as attenuation and discuss the reason for this improvement. We also illustrate that a network trained during a wavefield simulation can be used to pre-train the neural network of another wavefield simulation after PDE-coefficient alteration and improve the convergence speed accordingly. This pre-training strategy should find application in iterative full waveform inversion (FWI) and time-lag target-oriented imaging when the model perturbation between two consecutive iterations or two consecutive experiments can be small.

Seismic interpretation is now serving as a fundamental tool for depicting subsurface geology and assisting activities in various domains, such as environmental engineering and petroleum exploration. However, most of the existing interpretation techniques are designed for interpreting a certain seismic pattern (e.g., faults and salt domes) in a given seismic dataset at one time; correspondingly, the rest patterns would be ignored. Interpreting all the important seismic patterns becomes feasible with the aid of multiple classification techniques. When implementing them into the seismic domain, however, the major drawback is the low efficiency particularly for a large dataset, since the classification need to be repeated at every seismic sample. To resolve such limitation, this study first present a seismic pattern interpretation dataset (SpiDat), which tentatively categorizes 12 commonly-observed seismic patterns based on their signal intensity and lateral geometry, including these of important geologic implications such as faults, salt domes, gas chimneys, and depositional sequences. Then we propose a seismic pattern interpretation network (SpiNet) based on the state-of-the-art deconvolutional neural network, which is capable of automatically recognizing and annotating the 12 defined seismic patterns in real time. The impacts of the proposed SpiNet come in two folds. First, applying the SpiNet to a seismic cube allows interpreters to quickly identify the important seismic patterns as input to advanced interpretation and modeling. Second, the SpiNet paves the foundation for deriving more task-oriented seismic interpretation networks, such as fault detection. It is concluded that the proposed SpiNet holds great potentials for assisting the major seismic interpretation challenges and advancing it further towards cognitive seismic data analysis.

We developed two machine learning frameworks that could assist in automated litho-stratigraphic interpretation of seismic volumes without any manual hand labeling from an experienced seismic interpreter. The first framework is an unsupervised hierarchical clustering model to divide seismic images from a volume into certain number of clusters determined by the algorithm. The clustering framework uses a combination of density and hierarchical techniques to determine the size and homogeneity of the clusters. The second framework consists of a self-supervised deep learning framework to label regions of geological interest in seismic images. It projects the latent-space of an encoder-decoder architecture unto two orthogonal subspaces, from which it learns to delineate regions of interest in the seismic images. To demonstrate an application of both frameworks, a seismic volume was clustered into various contiguous clusters, from which four clusters were selected based on distinct seismic patterns: horizons, faults, salt domes and chaotic structures. Images from the selected clusters are used to train the encoder-decoder network. The output of the encoder-decoder network is a probability map of the possibility an amplitude reflection event belongs to an interesting geological structure. The structures are delineated using the probability map. The delineated images are further used to post-train a segmentation model to extend our results to full-vertical sections. The results on vertical sections show that we can factorize a seismic volume into its corresponding structural components. Lastly, we showed that our deep learning framework could be modeled as an attribute extractor and we compared our attribute result with various existing attributes in literature and demonstrate competitive performance with them.

We present a method to downscale idealized geophysical fluid simulations using generative models based on diffusion maps. By analyzing the Fourier spectra of images drawn from different data distributions, we show how one can chain together two independent conditional diffusion models for use in domain translation. The resulting transformation is a diffusion bridge between a low resolution and a high resolution dataset and allows for new sample generation of high-resolution images given specific low resolution features. The ability to generate new samples allows for the computation of any statistic of interest, without any additional calibration or training. Our unsupervised setup is also designed to downscale images without access to paired training data; this flexibility allows for the combination of multiple source and target domains without additional training. We demonstrate that the method enhances resolution and corrects context-dependent biases in geophysical fluid simulations, including in extreme events. We anticipate that the same method can be used to downscale the output of climate simulations, including temperature and precipitation fields, without needing to train a new model for each application and providing a significant computational cost savings.

Recent observations show that certain rupture phase can propagate backward relative to the earlier one during a single earthquake event. Such back-propagating rupture (BPR) was not well considered by the conventional earthquake source studies and remains a mystery to the seismological community. Here we present a comprehensive analysis of BPR, by combining theoretical considerations, numerical simulations, and observational evidences. First, we argue that BPR in terms of back-propagating stress wave is an intrinsic feature during dynamic ruptures; however, its signature can be easily masked by the destructive interference behind the primary rupture front. Then, we propose an idea that perturbation to an otherwise smooth rupture process may make some phases of BPR observable. We test and verify this idea by numerically simulating rupture propagation under a variety of perturbations, including a sudden change of stress, bulk or interfacial property and fault geometry along rupture propagation path. We further cross-validate the numerical results by available observations from laboratory and natural earthquakes, and confirm that rupture "reflection" at free surface, rupture coalescence and breakage of prominent asperity are very efficient for exciting observable BPR. Based on the simulated and observed results, we classify BPR into two general types: interface wave and high-order re-rupture, depending on the stress recovery and drop before and after the arrival of BPR, respectively. Our work clarifies the nature and excitation of BPR, and can help improve the understanding of earthquake physics, the inference of fault property distribution and evolution, and the assessment of earthquake hazard.

In a variety of geoscientific applications scientists often need to image properties of the Earth's interior in order to understand the heterogeneity and processes taking place within the Earth. Seismic tomography is one such method which has been used widely to study properties of the subsurface. In order to solve tomographic problems efficiently, neural network-based methods have been introduced to geophysics. However, these methods can only be applied to certain types of problems with fixed acquisition geometry at a specific site. In this study we extend neural network-based methods to problems with various scales and acquisition geometries by using graph mixture density networks (MDNs). We train a graph MDN for 2D tomographic problems using simulated velocity models and travel time data, and apply the trained network to both synthetic and real data problems that have various scales and station distributions at different sites. The results demonstrate that graph MDNs can provide comparable solutions to those obtained using traditional Bayesian methods in seconds, and therefore provide the possibility to use graph MDNs to produce rapid solutions for all kinds of seismic tomographic problems over the world.