Continually learning neural-operator surrogate for three-dimensional airborne electromagnetic Bayesian inversion

Three-dimensional probabilistic inversion of time-domain airborne electromagnetic (AEM) data is limited by the cost of the forward solve. Even though one simulation takes only tens of seconds, a Bayesian inversion of a survey of millions of soundings requires of order $10^{10}$ forward evaluations. To address this, we develop a continually learning neural-operator surrogate of the three-dimensional AEM forward operator that replaces the solver inside the Bayesian inversion. We start from the point of view that regardless of what geological prior is specified, Maxwell's laws remain invariant. Secondly, we avoid the limitation of learning on a single prior by continual learning on consecutive priors, which means our surrogate becomes richer as it is applied in future case studies, either by the authors, or by the scientific community. We use a validity check built on ensemble disagreement to divert cases with measurements outside the training range to the solver. Driven by the surrogate, the identical Markov chain Monte Carlo sampler reproduces the full-solver posterior, and its credible intervals cover the truth within 2.6 percentage points. Applied to the 2013 Capricorn TEMPEST survey in Western Australia, the surrogate inverts over two million soundings in seconds, a computation infeasible for the solver. Testing the geological prior against the entire survey costs minutes. The framework delivers uncertainty-quantified conductivity imaging at survey scale, which we believe is essential to perform near real-time mineral-systems targeting with geophysics.

ROMNet: a hybrid reduced order modeling and machine learning approach to waveform inversion

Waveform inversion seeks to estimate the wave speed of a heterogeneous, inaccessible medium, from time-resolved measurements of the waves at user controlled sensors. We consider this inverse problem for acoustic waves and an active array of source/receiver sensors that emit probing signals and measure the generated pressure waves. The forward map, from the wave speed to the measurements, is nonlinear and oscillatory. The oscillations cause cycle skipping, the main impediment to using the standard, nonlinear least-squares data fitting formulation, known as full waveform inversion (FWI). A recently introduced alternative waveform inversion approach computes from the measurements an algebraic surrogate of the wave operator, a reduced order model (ROM) matrix, which is then used to estimate the wave speed. The mapping from the measurements to the ROM is nonlinear, but well understood. It is computed efficiently, in a non-iterative manner. The nonlinear mapping from the ROM to the wave speed is less understood, and its approximation involves time-consuming optimization. Our goal in this paper is to use a neural network to map the ROM matrix to a nearby one, that has a simpler and explicit dependence on the wave speed. This simplifies and reduces the computational cost of the ROM-based waveform inversion. We introduce the methodology, called ROMNet, and test it with numerical simulations, using two training data sets: The first set consists of random media with variations of the wave speed modeled by a superposition of Gaussians with random amplitudes and standard deviations. The second is the publicly available GeoFWI dataset introduced for benchmarking FWI using deep learning. We compare the performance of ROMNet with the direct ROM-based inversion and with two representative deep learning approaches to FWI: ``Fourier-DeepONet" and ``InversionNet".

Voxel-based 3D Facies Segmentation from Seismic Data: A Comparative Study

Seismic facies segmentation has emerged as a significant challenge in geophysics, requiring robust methods and systems to effectively identify geologically analogous facies with limited labeled data. Although existing studies have shown promising results in 2D facies segmentation, they often preprocess the original 3D seismic volumes into sets of 2D slices, typically the inline and crossline directions, and treat this problem as a purely 2D segmentation task. This simplification introduces discontinuities across slices and fails to preserve the spatial and structural continuity in 3D seismic data, thus limiting the model's ability to learn coherent geological patterns. In this work, we present a comparative and reproducible benchmark for voxel-based 3D seismic facies segmentation, built upon publicly available seismic volumes including the Netherlands F3 and the Parihaka datasets, with standardized data splits and evaluation metrics. By evaluating the three representative families of modern 3D segmentation architectures, we establish strong baseline results that highlight the potential and remaining challenges for future research in this domain.

Consensus-gated Multi-Agent Neural Architecture Search for Seismic Fault Segmentation

Neural networks for seismic fault segmentation are often borrowed from computer vision and medical imaging domains where they train under relatively much larger labeled data resources. Optimizing their architecture under tight labeled data budgets as are common in geophysical applications is not a trivial problem. Manually designing data-optimal architectures is time-consuming while classical neural architecture search (NAS) is restricted to hand-crafted search spaces and large compute budgets. We present an agentic NAS system in which a panel of three large language models (Claude, GPT-5.1, and Gemini~2.5~Pro) debates each candidate architecture to unanimous consensus, authors the complete PyTorch implementation, cross-reviews it, and submits it to an automated validate-train-score loop with a hard 450K parameter budget, keep-or-revert lineage, and a memory of failed mechanisms. Operating on source code rather than a predefined operation menu, the search ran on a single consumer GPU and trained only eight candidates. It discovered \ours{}: a 425K-parameter encoder-decoder with a strip-pooling bottleneck, squeeze-and-excitation gating, an asymmetric one-conv decoder, and a feature-pyramid fusion neck. Trained under a protocol identical to all baselines on sections derived from the Thebe fault dataset, it attains the highest F1 (0.578) and IoU of all models tested while being the smallest, outperforming a published-capacity U-Net (31M parameters, F1 0.484), DeepLabV3-ResNet50 (39.6M, 0.516), an Attention U-Net(1.83M, 0.502). The search cost 101 LLM calls ($\sim$1.15M input / 0.39M output tokens) and roughly one GPU-day, making consensus-gated LLM panels a practical, low-cost route to domain-specific architecture discovery.

Depth-Aware Implicit Neural Representation Priors for 3D Gravity Inversion

Gravimetry images subsurface density contrasts associated with geological structures, geothermal systems, and intrusive bodies. Recovering a three-dimensional density model from gravity observations is highly ill-posed because of its non-uniqueness, limited data coverage, and the attenuation of the gravity field with depth. Classical inversion methods rely on explicit regularization and parameter tuning, whereas supervised deep-learning approaches require representative gravity--density pairs that are rarely available. This paper proposes an unsupervised depth-aware implicit neural representation for 3D gravity inversion. The density volume is represented by multiple coordinate-based neural networks assigned to overlapping depth slabs and optimized directly from the observed gravity measurements through the sensitivity matrix. Slab-specific Fourier features, physics-based depth gains, and scheduled regularization provide structural priors without requiring labeled density models. Experiments on four synthetic scenarios show that the proposed method provides better overall performance in terms of RMSE, PSNR, and SSIM than the evaluated conventional and neural baselines. It also recovers more compact and spatially coherent density bodies, improves the separation of nearby anomalies, preserves internal structures, and reconstructs their vertical extent better. These results indicate that the proposed depth-aware formulation helps to mitigate the depth ambiguity inherent in gravity inversion. In the field experiment, where no ground-truth density model was available, the method produced compact, separated, and vertically coherent anomalies consistent with the observed gravity pattern.

Juxtaposition of Shallow Reservoir-Triggered Seismicity and Deep Tectonic Locking in the Qiaojia-Dongchuan Seismic Gap

Identifying the critical state of mature seismic gaps is challenging, especially when anthropogenic stress perturbations, such as reservoir impoundment, superimpose on tectonic loading. Here, utilizing a high-resolution dense array catalog from the Qiaojia-Dongchuan seismic gap (hosting the second-largest hydropower station in the world), we reveal a distinct vertical decoupling mechanism. The shallow activities exhibit high b-values (1.0), indicative of fluid-driven reservoir-triggered seismicity. Conversely, deep seismicity (20 km) outlines a 'locked asperity' characterized by low b-values (less than 0.8) and high Coulomb stress accumulation rate. We further identify a complex dipping structure, suggesting compound fault kinematics. Additionally, the calculated stress accumulation suggests this seismic gap is in a critical state with elevated rupture potential. Our findings indicate that shallow induced seismicity can mask the silent accumulation of deep tectonic strain. This decoupling model provides a new framework for assessing seismic risks in reservoir-fault systems globally.

Probabilistic Inversion with Flow Matching

We demonstrate the application of Flow Matching, a technique originating from generative Artificial Intelligence, to probabilistic inversion in geophysical settings, such as seismic Full-Waveform inversion. We adapt the well-established mathematical theory of Flow Matching from generative Artificial Intelligence to the context of probabilistic inversion. We evaluate the approach with two case studies: a simple 2D velocity model to illustrate the general features of the method, and the OpenFWI dataset to show its capabilities for probabilistic inversion of more complex seismic velocity models.

Tensor Train Decomposition-based 3D Implicit Full Waveform Inversion with Multi-scale Structural Similarity

Three-dimensional full waveform inversion (3DFWI) is a powerful technique for reconstructing high-resolution subsurface velocity models. However, its application is often limited by high memory requirements, computational costs, and sensitivity to cycle skipping. To overcome these challenges, we propose a novel tensor train (TT) decomposition-based 3D implicit full waveform inversion framework (TT-3DIFWI) combined with a multi-scale structural similarity (M-SSIM) objective function. In this framework, the 3D velocity model is represented by TT decomposition as a product of a series of low-rank core tensors. Then, three axis-specific implicit neural network representations (INR) based on one-dimensional vector coordinates as input are constructed to predict these core tensors, rather than directly predicting the velocity model. This INR reparameterization method based on TT decomposition can significantly reduce the memory consumption of INR training while maintaining the accuracy and resolution of the 3D velocity model reconstruction. Meanwhile, the low-rank structure of TT decomposition also ensures the structural consistency of the reconstruction velocity, thereby improving the accuracy and continuity of the inversion result. Furthermore, the M-SSIM objective function can compare the multi-scale structural differences between predicted and observed data, and utilize the ultra-low frequency features to reduce cycle skipping. Numerical experiments on synthetic and challenging land datasets demonstrate that TT-3DIFWI with M-SSIM achieves accurate and continuous velocity reconstruction, even with poor initial models or missing low-frequency data.

Contrastive Learning for Seismic Horizon Tracking with Domain-Specific Priors

Unsupervised 3D seismic horizon tracking faces a key limitation: signal-based propagators provide accurate trace-level alignment but often fail near faults, whereas texture-driven deep models are more robust to discontinuities, typically at the cost of labeled data requirements and reduced trace-level precision. We propose a self-supervised fusion of both paradigms in which signal-derived local horizon correspondences act as domain-specific priors to train a texture-based deep learning model. Specifically, we estimate reliable trace-to-trace flows from reflector slopes and use them to form positive pairs in a contrastive objective, while restricting training to high-confidence neighborhoods, optionally augmented with a fault mask. The objective is not to infer ambiguous correspondences close to discontinuities, but to preserve horizon identity across them. As a result, the network learns voxel-wise embeddings that preserve local signal continuity while enabling horizon propagation beyond discontinuities through similarity search. Experiments on the public F3 dataset and a faulted synthetic dataset achieve lower mean absolute error (MAE) than unsupervised baselines and competitive performance against a semi-supervised method using a single labeled slice.

Domain-Guided Prompting of the Segment Anything Model for Seismic Interpretation: The Role of Attributes, Visualization, and Hybrid Prompts

The advent of large pretrained foundation models for computer vision has significantly improved the efficiency of visual data interpretation. The Segment Anything Model (SAM), in particular, offers powerful zero shot segmentation capabilities through prompt based interaction, thus making it a promising tool for seismic interpretation. However, most existing applications of SAM rely on fine tuning for specific geological targets, which requires extensive labeled data, incurs high computational cost, and often compromises the model's generalization capability. In this study, we introduce a principled framework for zero shot adaptation of foundation models to seismic data. The framework is built on two key components: (1) aligning seismic attributes and visualization choices (e.g., colormaps) with the geological target of interest, and (2) employing a hybrid prompting strategy that combines sparse user defined point prompts with dense mask prompts derived from SAM's internal feature activations. We systematically evaluate this framework across multiple geological targets, datasets, prompt configurations, and seismic attribute representations. Our results demonstrate that geologic target aware selection of seismic attributes and colormaps, combined with hybrid prompting, enhances the separability of geological features and improves boundary delineation and segmentation accuracy relative to point based prompting alone. Our findings show that, when these components are jointly applied, SAM can achieve competitive segmentation performance in a fully zero shot setting, thereby eliminating the need to retrain SAM for each geologic feature. This work establishes a practical and scalable pathway to leverage foundation models in seismic interpretation, reducing reliance on labeled data while preserving model generality.

GNSS-FM: A Self-Supervised Foundation Model for Daily GNSS Displacement Time Series

Displacement time series from Global Navigation Satellite Systems (GNSS) are essential for a wide range of applications, including monitoring tectonic crustal deformations and investigating the different stages of the earthquake cycle. Machine learning methods have proven promising for GNSS applications; however, most remain fully supervised. This creates a bottleneck as labeled data are scarce, even though large amounts of unlabeled GNSS data are freely available. We present GNSS-FM, a self-supervised foundation model for daily GNSS time series. The model uses a dual-stream input combining displacement and velocity-like increments, and is pretrained using a masked latent prediction objective with vector-quantized targets adapted from wav2vec 2.0, with several modifications for geodetic data. Pretrained on data from over 17,000 globally distributed GNSS stations, an analysis of the learned codebook suggests that the representations capture the main signal types in GNSS displacement data, including seismic offsets, tectonic drift, and seasonal patterns. The foundation model is later fine-tuned on two downstream tasks, namely 90-day displacement forecasting and seismic step localization, where it outperforms strong task-specific baselines in both cases. These results show that self-supervised pretraining is a promising approach for GNSS time series analysis.

DualTCN: A Physics-Constrained Temporal Convolutional Network for 2 Time-Domain Marine CSEM Inversion

DualTCN is the first deep-learning framework for inverting time-domain marine controlled-source electromagnetic (MCSEM) transient data. Moving away from traditional subsurface discretization, the framework regresses four earth-model parameters -- $σ_1$, $σ_2$, $d_1$, $d_2$ -- and reconstructs conductivity-depth profiles using a differentiable soft-step decoder. The optimized architecture (379K parameters) features a Temporal Convolutional Network (TCN) encoder paired with a late-time branch and an auxiliary seafloor-depth head. This design achieves a 25.3\% loss reduction over baseline models, with high predictive accuracy ($R^2 = 0.898$ for $σ_2$) and an inversion speed of 3.5~ms per sample on an A100 GPU. The framework demonstrates high robustness to noise through curriculum-based amplitude augmentation, maintaining a mean $\bar{R}^2$ of 0.858 at $\pm2\%$ random amplitude error, compared to $0.363$ without augmentation. DualTCN generalizes effectively to three-layer extensions (seawater/resistive layer/basement), accurately resolving basement conductivity ($R^2 \approx 0.88$), though thin-layer resolution remains a physical limitation ($R^2 \approx 0.23$). In comparative benchmarks, DualTCN significantly outperforms traditional local optimization methods like Levenberg-Marquardt and L-BFGS-B, yielding a mean $\bar{R}^2 = 0.877$ versus 0.129-0.439 for multi-start baselines, while operating at up to 21,000$\times$ lower computational cost. Finally, the framework incorporates uncertainty quantification via Monte Carlo (MC) Dropout. While well-calibrated for $σ_1$ (PICP90 = 0.944), inherent signal limitations at short offsets (200m) lead to under-coverage for $d_2$ (PICP90 = 0.572), which can be mitigated through post-hoc temperature scaling or split conformal prediction.