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Transport-Map Proposals for Efficient Markov Chain Monte Carlo

Geophysical Journal International - Mon, 01/05/2026 - 00:00

SummaryEfficient Markov chain Monte Carlo (MCMC) sampling from posterior distributions remains a central challenge in Bayesian geophysical inversion. Recent developments in computational statistics and optimal transport suggest that MCMC efficiency can be improved by reparameterising the sampling problem – specifically, by learning an invertible mapping that recasts the target distribution onto a simpler reference distribution. Here, we introduce a Metropolis–Hastings framework that leverages transport maps parameterised by invertible neural networks. These maps are trained on preliminary MCMC samples from the target distribution and used to propose new samples in a fixed reference space, where proposal design is independent of the target’s structure. The proposed samples are transformed back to the target space via the inverse map, and accepted or rejected according to a modified Metropolis–Hastings criterion. As sampling proceeds, the transport maps are updated, yielding proposals increasingly well adapted to the shape of the target distribution. Across a suite of numerical tests – including a 2-D Rosenbrock distribution, a 3-D earthquake location problem, and Gaussian mixtures up to 16 dimensions – transport-map-driven samplers consistently outperform standard MCMC, reducing integrated autocorrelation times by factors of 2.5 to over 6 (or equivalently, yielding sample sets 2.5–6 times larger for the same number of forward evaluations). This improvement comes at the non-negligible cost of training one or more transport maps, which we quantify systematically. We also provide a quantitative criterion for weighing training cost against sampling speed-up. This shows that transport-map MCMC is advantageous whenever the forward problem is nontrivial, making it a promising approach for Bayesian sampling in geophysics and beyond.

Which is better: deep-learning or manual seismic arrival-time picking?

Geophysical Journal International - Mon, 01/05/2026 - 00:00

SummaryEarthquake locations and catalogs from routine earthquake monitoring are typically based on manually reviewed arrival-time picks from classical, rule-based automatic pickers. High-performance, deep-learning (DL) pickers can replace this standard approach, rapidly delivering much larger and complete catalogs. A transition to routine monitoring based on DL picks requires that resulting catalogs include all or almost all events identified by current procedures with locations of the same or higher quality. Here we verify these requirements by comparing the performance of DL and manual picking for earthquake relocation and tomographic inversion. We form a reference catalog with a subset of INGV bulletin events and picks from the 2016 Central Italy sequence. This catalog is re-picked using the DL picker PhaseNet trained on the Northern California Earthquake Data Center dataset and on the INSTANCE Italian dataset. We use these three pick sets for high-precision, non-linear earthquake relocation and for 3D tomographic inversion and relocation. Relative to the high-precision relocations using routine picks, those using DL picks show improved organization and clustering, and, in a ground-truth test, smaller hypocenter separation for event pairs with more similar waveforms. The tomographic inversions show statistically better convergence and more organized relocations using the DL picks than with the routine picks. We conclude that DL based monitoring can rapidly produce more consistent picks and higher quality catalogs than standard procedures, while freeing analyst time for improved quality control, assessment, interpretation, and dissemination of information on seismic activity, especially during significant seismic sequences.

The poroelastic stress and pore pressure effects on delayed seismicity based on fully coupled fluid-solid simulations and rate-and-state friction laws

Geophysical Journal International - Mon, 01/05/2026 - 00:00

SummaryFluid injection into the subsurface can trigger moderate-magnitude earthquakes days to months after shut-in, complicating hazard assessment. To investigate the governing mechanics, we implemented a fully coupled hydro–mechanical model that couples Darcy flow, poro-viscoelastic deformation and rate-and-state fault friction on a planar fault, allowing two-way feedbacks between pore pressure, volumetric strain and fault slip and the simulation of both aseismic and seismic transients. Compared with decoupled or one-way approaches, the fully coupled formulation generally yields longer post-injection delays, owing to poroelastic stress contributions and a more realistic evolution of volumetric strain. After shut-in, a slow poroelastic redistribution of volumetric compression broadens and migrates along the fault, constructively overlapping regions of elevated shear and reduced effective normal stress. This causes the nucleation of a delayed rupture away from the well, indicating that the point of peak instantaneous pressure does not necessarily coincide with the location of maximum coseismic slip. By scanning permeability and injection rate we construct an empirical injection-rate (IR)–permeability (k) phase diagram that delineates regimes of immediate, delayed and no induced seismicity; this diagram is offered as a conceptual, physics-informed screening tool that requires site-specific calibration. Our results indicate that two-way hydro-mechanical coupling and fault slip evolution should be considered when assessing post-injection seismic hazard and in the design of spatially distributed monitoring.

Seafloor Topography Predicted from SWOT Gravity Data by Deep Neural Network in the Northwestern Pacific Ocean

Geophysical Journal International - Mon, 01/05/2026 - 00:00

SummaryTraditional seafloor mapping relies on shipborne soundings which have limited spatial coverage. The Surface Water and Ocean Topography (SWOT) wide-swath altimetry satellite holds the potential for predicting more detailed seafloor topography. In this study, we integrate SWOT gravity data with single-beam shipborne depths to construct seafloor topography models in the Northwestern Pacific using the deep neural network (DNN) method. Compared to shipborne depth checkpoints, the root mean square (RMS) error of the differences between topography model predicted by DNN method and shipborne depths is approximately 97.5 m, improving by 19.5% and 9.9% compared to the gravity-geologic (GGM) method and the Smith and Sandwell (SAS) method respectively. Compared to traditional data, the integration of SWOT gravity data universally enhances prediction accuracy. Furthermore, the DNN method effectively demonstrates superior capability in balancing the characterization of overall structures with the retention of authentic topography features, which we demonstrated in the Mariana region of the NW Pacific Ocean. However, limited by spatial heterogeneity and physical mechanisms, accurate prediction of such complex, fine-scale topography using gravity data remains a significant challenge.