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The stratum can be modelled as a horizontal transversely isotropic medium when a single set of vertically parallel fractures embedded in an isotropic background medium, which facilitates efficient study for fractured reservoirs. Elastic parameters and fracture weaknesses are important parameters to describe the characteristics of fractured reservoirs, and seismic inversion plays a significant role in parameters estimation. The commonly used deterministic inversion methods do not fully utilize the prior information and fails to present the uncertainty analysis of inversion results. To address these shortcomings, we propose a Bayesian linearized amplitude variation with offset and azimuth inversion method tailored for horizontal transversely isotropic media, enabling a more robust analysis of uncertainty. Within the framework of Bayesian inversion, the proposed method successfully derives analytical expressions for the posterior mean and covariance of both elastic parameters and fracture weaknesses. The response characteristics of the anisotropic reflection coefficient are analysed, and it is found that the perturbations of elastic parameters have a greater effect on reflection coefficient compared to fracture weaknesses. Synthetic data examples confirm that the accuracy of estimated P‐ and S‐wave velocities and density surpasses that of fracture weaknesses, and the proposed method still performs well for the case of moderate noise. A field data example demonstrates that the inverted profiles agree well with the logging curve, and the estimated fracture weaknesses display significantly high values in the reservoir area. The estimated reservoir parameters not only contribute to a more accurate representation of the fractured gas‐bearing reservoir but also provide insights into the target gas reservoir through its posterior distribution. Both synthetic and field data examples demonstrate the stability and reliability of the proposed method in characterizing fractured reservoirs. We determine that the proposed method provides an available tool for nuanced evaluation of uncertainty for the inversion results, and it is helpful for the fine description of fractured hydrocarbon‐bearing reservoirs. [ABSTRACT FROM AUTHOR]

Prior model construction is a fundamental component in geophysical inversion, especially Bayesian inversion. The prior model, usually derived from available geological information, can reduce the uncertainty of model characteristics during the inversion. However, the prior geological data for inferring a prior distribution model are often limited in real cases. Our work presents a novel framework to create 3D geophysical prior models using soil geochemistry and borehole rock sample measurements. We focus on the Bayesian inversion, which enables encoding of knowledge and multiple non-geophysical data into the prior. The new framework developed in our research comprises three main parts, namely correlation analysis, prior model reconstruction, and Bayesian inversion. We investigate the correlations between surface and subsurface geochemical features, as well as the correlation between geochemistry and geophysics, using canonical correlation analysis for the surface and borehole geochemistry. Based on the resulting correlations, we construct the prior susceptibility model. The informed prior model is then tested using geophysical forward modeling and outlier detection methods. In this test, we aim to falsify the prior model, which happens when the model cannot predict the field geophysical observation. To obtain the posterior models, the reliable prior models are incorporated into a Bayesian inversion framework. Using a real case of exploration in the Central African Copperbelt, we illustrate the workflow of constructing the high-resolution 3D stratigraphic model conditioned on soil geochemistry, borehole data, and airborne geophysics. [ABSTRACT FROM AUTHOR]

The Southwestern United States experiences active deformation, seismicity, and magmatism, remarkable in an intraplate setting. The Basin and Range and Colorado Plateau (CP) are inferred to differ in lithospheric thickness, but modeling geophysical properties of the lithosphere, in particular the depth of the Lithosphere‐Asthenosphere Boundary (LAB), across the entirety of the region, has proved challenging. Here, we introduce a new model of 1‐D depth profiles in shear wavespeed, determined through a probabilistic joint inversion of information from Sp receiver functions and Rayleigh wave phase velocity. From these profiles we quantify the locations and Vs contrast of wavespeed gradients that represent boundaries such as the Moho, the LAB, and intralithospheric discontinuities. We infer a lithosphere that is thinner and lower in Vs in the Basin and Range. In the CP and farther north, the LAB is more gradual, deeper, and intermittently observed. We also observe Mid‐Lithospheric Discontinuities (MLDs) near the boundaries between the CP, Wyoming Craton, and Northern Basin and Range, as well as within the Craton. When both an MLD and LAB are observed, the Vs gradient associated with the LAB is narrower than expected. Finally, we image Positive Velocity Gradients beneath areas of thinner lithosphere, which are consistent with recent global observations that have been attributed to the base of a partially molten zone below the lithosphere. Overall, the picture of the lithosphere‐asthenosphere system that emerges is one of considerable structural complexity with a strong dependency on tectonic regime and geological history. Plain Language Summary: We examine the properties of, and processes that shape, the lithosphere—the rigid outermost layer of the Earth, which participates in plate tectonics. Our focus is the southwestern United States where in fact the lithosphere does not behave like a simple, homogeneous, plate. Instead, in the Basin and Range Province, widespread deformation, frequent earthquakes, and recent volcanic activity are observed, all of which are rare for a location removed from plate boundaries. In the neighboring Colorado Plateau and the regions north and west of it, the lithosphere behaves more rigidly but volcanism is also observed. To understand how the lithosphere and mantle below vary, we produce a model of seismic wavespeed using data from surface waves, which travel along the Earth's surface, and converted body waves, which interact with interior boundaries such as the bottom of the lithosphere. This model enables us to find the depths of major boundaries and understand how the speed of seismic waves changes across them. We consistently observe decreases in seismic wavespeed that we associate with the bottom of the lithosphere or structures within the lithosphere. We also note wavespeed increases below the lithosphere that might indicate partial melting of rocks deep within the Earth. Key Points: We perform a joint inversion for Vs in the upper mantle of the Southwestern U.S., using data from body wave scattering and surface wavesThe lithosphere varies regionally: it is flat and thin in the Basin and Range, thicker in the Colorado Plateau, and complex in cratonic regionsMid‐Lithospheric Discontinuities are observed in cratonic regions, associated with sharp Vs gradients at the base of the lithosphere [ABSTRACT FROM AUTHOR]

The complexity of the active tectonic system in East Indonesia has influenced various types of seismicity in the Seram Sea, resulting in several significant earthquakes. In the last decade, there were two devastating earthquakes, Mw 6.2 (October 31, 2017) occurred with the thrust mechanism as typical of active subduction while Mw 6.5 (September 26, 2019) occurred with a left-lateral mechanism due to the unknown active fault in the Seram Island and its surroundings. In the present study, we analyzed the current seismicity for 8-years (2015–2022) by using Bayesian moment tensor inversion for the two largest earthquakes and multivariate hypocenter clustering in the spatial-time-distance-magnitude (STDM) domain using an earthquake catalog. The Bayesian inversion was applied by using bootstrapping chain analysis with the regional seismic network with a distance of up to 4000 km to figure out the earthquake source mechanism. The inversion results show that both earthquakes have different mechanisms. The October 2017 event occurred in the actual plane with strike 262°, dip 21° and rake 68°, suggesting an active subduction with a steep dipping angle of 20°–25° towards the north direction. However, the September 2019 occurred with strike 346°, dip 85°, and rake −140°, indicating an offshore unidentified fault with rupture propagation towards the N–S direction and pure reverse slip. The grid search of the centroid location shows a converged solution with small shifting of 10–15 km to the east and 10 km to the south while the depth is consistent at 7–10 km. The obtained focal mechanism shows an uncertainty with 70–80% confidence intervals and a percentage of Double-Couple (DC) component > 90% that evidences the tectonic process. To support the earthquake mechanism results, earthquake clustering analysis was performed based on nearest-neighborhood distance with its components in STDM. The notable breaks in the STDM time series due to the Mw 6.2 (2017) and Mw 6.5 (2019) earthquakes are discussed, supported by a Multitaper spectral analysis for effective visualization of STDM spectral peaks. Finally, the relation between STDM time series is studied by magnitude-squared coherence with 95% confidence intervals. As a result, we found that although the magnitude of coherence was not high, they are weakly related to each other. This implies that the occurrence of future seismicity somehow depends upon these parameters. The comprehensive results of this study may support the existence of the South Seram subduction system that can be used to update the mitigation plan for different earthquake characteristics shortly. [ABSTRACT FROM AUTHOR]

The knowledge of fracture properties and its geometrical patterns is often required for the analysis of mechanical and flow properties in fractured reservoirs, as fracture characterization plays a critical role in the optimization of hydrocarbon production or estimation of storage capacity of subsurface reservoirs. A stochastic method based on a Markov chain Monte Carlo (MCMC) algorithm is proposed to estimate fracture properties using a rock physics model for fractured rocks. Two implementations are presented: a Metropolis algorithm based on a Gaussian prior distribution and an extended Metropolis algorithm with an informative prior obtained from multiple-point statistics simulations. The results are compared to a Bayesian analytical approach where the solution is based on a linearized approximation of the rock physics model. The novelty of the proposed approach is the use of a training image, that is, a conceptual geological model, to account for the spatial distribution of the fractures. Two fracture properties are considered, namely fracture density and aspect ratio, and the spatial distribution and geometrical characteristics of fractures are also investigated to understand the connectivity patterns that control fluid flow. The MCMC approach with a training image is more computationally demanding but provides geometrical models of the spatial distribution of fractures. The inversion results show that the prediction accuracy of fracture density and aspect ratio obtained by the MCMC methods is similar to the one obtained with the analytical approach, and that the MCMC methods provide a reliable assessment of the posterior uncertainty as well. [ABSTRACT FROM AUTHOR]

In this paper, we consider the travel time tomography problem for conformal metrics on a bounded domain, which seeks to determine the conformal factor of the metric from the lengths of geodesics joining boundary points. We establish forward and inverse stability estimates for simple conformal metrics under some a priori conditions. We then apply the stability estimates to show the consistency of a Bayesian statistical inversion technique for travel time tomography with discrete, noisy measurements. [ABSTRACT FROM AUTHOR]

In evaluating the safety of rock slopes engineering, it is imperative to account for rheological effects. These effects can lead to significant deformations that may adversely impact the overall structural integrity. Consequently, accurate determination of the rheological mechanical parameters of slope rocks is essential. However, the application of rheological parameters obtained from laboratory tests encounters limitations due to the rock's inherent heterogeneity, scale effects, and inevitable sample dispersion. By contrast, on-site monitoring data serve as critical assets for real-time calibration and risk assessment in the evaluation of rheological parameters and prediction of slope deformation. To integrate on-site monitoring data with rheological mechanical mechanisms, this study introduces a probabilistic inverse model for evaluating rock slope rheological parameters, grounded in Bayesian theory, and incorporating a No-U-Turn Sampler (NUTS) based on Markov Chain Monte Carlo (MCMC) sampling algorithm. In terms of methodological efficiency, we compared the NUTS method with the traditional Metropolis–Hastings (M-H) approach, demonstrating the superior efficiency of the former. Additionally, sensitivity analysis of rheological parameters was conducted using the Burgers constitutive model. By combining the NUTS-based MCMC method with this model, the uncertainty of creep parameters was successfully evaluated. Utilizing these updated posterior parameters, up to 3-year deformation forecast for the slope was executed, the findings demonstrate that the deformation on the left bank slope is slight, indicating a state of safety. This study integrates monitoring data with rheological mechanics to establish a physical-data-driven rheological safety assessment mechanism. It offers a scientifically robust and effective approach for the uncertainty evaluation of rheological parameters and deformation prediction, providing significant support for the safety assessment of the left bank slope of the Baihetan hydropower station, China. [ABSTRACT FROM AUTHOR]

Objective In geothermal exploration, a clay cap is a typical hydrothermal geothermal system, and its depth and distribution range can provide crucial information for delineating the scope of geothermal resources and determining the location of geothermal drilling. Clay caps are usually composed of a clay layer formed through hydrothermal reactions and are characterized by low resistance. The low-resistivity cap can be effectively imaged using the audio-frequency magnetotelluric method. To obtain uncertainty information about the distribution of clay cap layers and imaging results, this paper employs the 1D trans-dimensional Bayesian inversion method to investigate the detection capabilities of low-resistance cap layers in geothermal areas through audio electromagnetic data. Methods In this paper, a model test is first carried out to establish a geoelectric model of a typical geothermal system.Subsequently, a 1D trans-dimensional Bayesian algorithm is used to invert the synthetic data to obtain the uncertainty information of the subsurface electrical structure and interface position. Then, the method was applied to the processing of measured audio frequency magnetotelluric data in the Yanggao geothermal area of Shanxi Province. Results This method has relatively accurate identification ability for low-resistivity clay caps, and the obtained uncertainty analysis results of the upper and lower interfaces of low-resistivity caps are also relatively reliable according to numerical tests. It was found that this method has a good ability to identify shallow low-resistivity caps and can provide an uncertainty evaluation of the clay cap interface position via field data tests. The 2D inversion results of this survey line verify the reliability of the 1D inversion. Conclusion This method has relatively accurate imaging capabilities and uncertainty analysis capabilities for shallow geothermal clay caprocks and has strong application prospects in geothermal detection.

Using a Bayesian approach we compare anecdotal tsunami runup observations from the 29 December 1820 Flores Sea earthquake with close to 200 000 tsunami simulations to determine the most probable earthquake parameters causing the tsunami. Using a dual hypothesis of the source earthquake either originating from the Flores Thrust or the Walanae/Selayar Fault, we found that neither source perfectly matches the observational data, particularly while satisfying seismic constraints of the region. Instead both posteriors have shifted to the edge of the prior indicating that the actual earthquake may have run along both faults. [ABSTRACT FROM AUTHOR]

Frequent water injection and oil extraction can potentially lead to changes in reservoir pressure, burst or collapse of casings, and corresponding variations on the ground surface. Attention should be focused on developing the strategies to monitor and mitigate the adverse consequences of oilfield operations. Here, the distributed scatterer InSAR (DS-InSAR) technique is applied to estimate the surface deformation of Daqing oil field with the surveillance period from 2015 to 2019. Furthermore, Bayesian method with three models, including Mogi, prolate spheroid, and Okada, are implemented to obtain parameters related to underground cavities, using cumulative deformation recorded between June and December 2015 and May and December 2016 as input. Inversion validation measurements were carried out by comparing the results with field data in the area of interest. Our findings demonstrate that, in comparison to other models, the prolate spheroid could recover both reservoir pressure and surface deformation, offering compelling evidence in favor of mitigating shear failure-related issues. A dual-source prolate spheroid model is also used to simulate large-scale deformation on the surface of oilfield. Its characteristics are nearly in line with variations in reservoir pressure and casing depth, which may minimize the negative consequences of casing failures and guarantee the stability of oil production.

The phenomenon of differential rotation of the Earth's inner core relative to the mantle is a subject of interest in geodynamo modeling that has been validated by seismological observations, mainly via the earthquake‐doublets method. Although recent studies converge on the time‐varying differential rotation of the inner core relative to the mantle, favoring a decadal variation, the inferred models significantly differ. Here, considering the data selection, the observed data structure, and the subjective model parameterizations, which we avoid by employing a Bayesian transdimensional approach, we show that the recent best‐fit model by Yang and Song (2023, https://doi.org/10.1038/s41561‐022‐01112‐z) featuring the 70‐year decadal variation is not obtained when all available data are considered. Namely, including only a small number of discarded earthquake doublets (<10%) changes the period of the inner‐core differential rotation fluctuation to 20–30 years. More earthquake‐doublet data are required to address the non‐uniqueness of the inversion problem. Plain Language Summary: Seismologists use repetitive earthquakes (earthquake doublets) and their waves' fixed paths through the Earth's inner core to measure the rate of the inner core spinning relative to the mantle. A recent study in Nature Geoscience (Yang & Song, 2023, https://doi.org/10.1038/s41561‐022‐01112‐z) based on 31 selected earthquake doublets derived a 70‐year decadal cycle of the inner core spinning rate relative to the mantle. We show that the made selective choices change the data structure and possibly miss the inner core 20–30 year periodicity in the earlier times. Key Points: We revisit the problem of the differential rotation of the inner core relative to the mantle from the existing earthquake‐doublet dataThe data selection, the data structure, and the data‐model relationship are critical in inverting the inner core differential rotationConsequently, the model derived by Yang and Song (2023, https://doi.org/10.1038/s41561‐022‐01112‐z) is not a unique model of the inner core's differential rotation [ABSTRACT FROM AUTHOR]

In this paper, we use the Bayesian inversion approach to study the data assimilation problem for a family of tumor growth models described by porous-medium type equations. The models contain uncertain parameters and are indexed by a physical parameter m, which characterizes the constitutive relation between density and pressure. Based on these models, we employ the Bayesian inversion framework to infer parametric and nonparametric unknowns that affect tumor growth from noisy observations of tumor cell density. We establish the well-posedness and the stability theories for the Bayesian inversion problem and further prove the convergence of the posterior distribution in the so-called incompressible limit, m → ∞. Since the posterior distribution across the index regime m ∈ [2, ∞) can thus be treated in a unified manner, such theoretical results also guide the design of the numerical inference for the unknown. We propose a generic computational framework for such inverse problems, which consists of a typical sampling algorithm and an asymptotic preserving solver for the forward problem. With extensive numerical tests, we demonstrate that the proposed method achieves satisfactory accuracy in the Bayesian inference of the tumor growth models, which is uniform with respect to the constitutive relation. [ABSTRACT FROM AUTHOR]

Seismic inversion is the primary way to obtain subsurface models, lithologic and stratigraphic information. However, seismic elastic parameters inversion and 'discrete lithofacies' identification for complex volcanic reservoirs are usually independent during the whole inversion process. Also, the influence of reservoir lithology on elastic parameters is not always considered directly before lithofacies prediction. This paper proposes a probabilistic pre-stack seismic inversion method for lithofacies and elastic parameters of volcanic reservoirs. Under the framework of Bayesian inversion, considering that the prior probability distribution of elastic parameters of volcanic reservoirs is affected by volcanic lithofacies, a posteriori probability distribution characterized by a mixed probability model is first derived. Then, a single-point-direct sequential simulation stochastic algorithm with simultaneous optimization of multiple solutions is used to simulate the posterior probability distribution of elastic parameters and lithofacies of volcanic reservoirs, which improves the resolution of lithofacies prediction results of volcanic reservoirs. The feasibility and stability of our method are ensured through synthetic and field applications. The prediction results highly agree with logging curves and lithology logging interpretation data. We have improved the resolution of volcanic rock reservoir lithofacies prediction results. In one-dimensional tests, we achieved the prediction of lithofacies and elastic parameters for three types of volcanic lithofacies. The error compared to prior information is no higher than 15%, thereby verifying the method's good noise resistance. [ABSTRACT FROM AUTHOR]

The study of offshore freshened groundwater (OFG) is gaining importance due to population growth and environmental pressure on coastal water resources. Marine controlled source electromagnetic (CSEM) methods can effectively map the spatial extent of OFG systems using electrical resistivity as a proxy. Integrating these resistivity models with sub‐surface properties, such as host‐rock porosity, allows for estimates of pore‐water salinity. However, evaluating the uncertainty in pore‐water salinity using resistivity models obtained from deterministic inversion approaches presents challenges, as they provide only one best‐fit model, with no associated estimate of uncertainty. To address this limitation, we employ trans‐dimensional Markov‐Chain Monte‐Carlo inversion on marine time‐domain CSEM data, acquired in the Canterbury Bight, New Zealand. We integrate resistivity posterior probability distributions with borehole and seismic reflection data to estimate pore‐water salinity with corresponding uncertainty estimates. The results highlight a low‐salinity groundwater body in the center of the survey area, hosted by consecutive silty‐ and fine‐sand layers approximately 20–60 km from the coast. The posterior probability distribution of resistivity models indicates freshening of the OFG body toward the shoreline within a permeable, coarse‐sand layer 40–150 m beneath the seafloor, suggesting an active connection between the OFG body and the terrestrial groundwater system. The approach demonstrates how Bayesian inversion constrains the uncertainties in resistivity models and subsequently in pore‐water salinity estimates. Our findings highlight the potential of Bayesian inversion to enhance our understanding of OFG systems and provide uncertainty constraints for hydrogeological modeling, thereby contributing to sustainable water resource development. Plain Language Summary: Geophysical methods that measure the electromagnetic properties of the Earth are effective in investigating freshwater sources beneath the seafloor. By combining the geophysical and geological information, we can better assess the quality of this groundwater. In this study, we develop a workflow that uses statistical methods to integrate electromagnetic observations with borehole and acoustic measurements along the eastern coast of the South Island of New Zealand. We aim to improve our understanding of the groundwater quality beneath the seafloor. Our research confirms the presence of freshened groundwater within the sandy seafloor up to 60 km from the coastline. Importantly, our observations indicate that the groundwater quality increases toward the coast. These findings are significant as they enhance the hydrogeological modeling of the groundwater system and suggest its potential as a source of freshwater. Key Points: A Bayesian workflow is employed to evaluate uncertainty in pore‐water salinity estimatesOffshore groundwater in Canterbury Bight stores freshened pore‐water in fine‐grained sediments, likely extending from the onshore aquiferCorrelation between pore‐water salinities and seismic‐derived stratigraphy provides boundary conditions for hydrogeological modeling [ABSTRACT FROM AUTHOR]

Inconsistencies between observations from long and short period seismic waves and geochemical data mean craton formation and evolution remains enigmatic. Specifically, internal layering and radial anisotropy are poorly constrained. Here, we show that these inconsistencies can be reconciled by inverting cratonic Rayleigh and Love surface wave dispersion curves for shear‐wave velocity and radial anisotropy using a flexible Bayesian scheme. This approach requires no explicit vertical smoothing and only adds anisotropy to layers where required by the data. We show that all cratonic lithospheres are comprised of a positively radially anisotropic upper layer, best explained by Archean underplating, and an isotropic layer beneath, indicative of two‐stage formation. Within the positively radially anisotropic upper layer, we find a variable amplitude low velocity zone within 9 of 12 cratons studied, that is well correlated with observed Mid‐Lithospheric Discontinuities (MLDs). The MLD is best explained by metasomatism after craton formation. Plain Language Summary: The ancient cores of the continents, or cratons, are a treasure‐trove of >2.5 billion years of Earth's history. However, scientists disagree on the processes that led to their formation, or whether they have evolved significantly through time. This is because the geological and geophysical methods used to investigate cratons often yield conflicting results. By capitalizing on an up‐to‐date global long‐wavelength seismic data set, we image the cores of 12 cratons using an advanced statistical method, Bayesian inference. The flexible method requires few choices to be made a priori, is driven by the quality of the data itself and measures uncertainties on results. By detecting velocity differences between horizontally and vertically vibrating seismic waves, we show that all cratons likely comprise an upper layer formed during the hot early Earth, by a process that strongly aligns the constituent minerals of the rocks in the horizontal plane. Below this ∼125 km thick upper layer, a lower layer (∼150 km thick) shows no clear alignment of minerals and so was likely formed by a different process, at a later time. Variable slow wavespeed zones exist within the upper layer that match previous results from short‐wavelength seismic data. Key Points: Bayesian surface wave inversion reconciles existing differences between seismic images of craton structure from long and short period dataCratons show a shallow low velocity zone (LVZ) within a layer of positive radial anisotropy and a high velocity isotropic layer beneathCratons are formed in two stages shown by anisotropic structure and are later modified producing a LVZ and mid lithosphere discontinuities [ABSTRACT FROM AUTHOR]

Quantifying sector‐resolved methane fluxes in complex emissions environments is challenging yet necessary to improve emissions inventories and guide policy. Here, we separate energy and agriculture sector emissions using a dynamic linear model analysis of methane, ethane, and ammonia data measured at a Northern Colorado site from November 2021 to January 2022. By combining these sector‐apportioned observations with spatially resolved inventories and Bayesian inverse methods, energy and agriculture methane fluxes are optimized across the study's ∼850 km2 sensitivity area. Energy sector fluxes are synthesized with previous literature to evaluate trends in energy sector methane emissions. Optimized agriculture fluxes in the study area were 3.5× larger than inventory estimates; we demonstrate this discrepancy is consistent with differences in the modeled versus real‐world spatial distribution of agricultural sources. These results highlight how sector‐apportioned methane observations can yield multi‐sector inventory optimizations in complex environments. Plain Language Summary: Improving our knowledge of the locations, magnitudes, and types of methane sources is important for implementing effective emissions mitigation technologies and regulations. Methane emissions are often challenging to quantify because a wide variety of sources can emit methane, and these disparate sources are often intermingled. We demonstrate how a dynamic linear model can use multi‐month time series of two tracer gases, ethane and ammonia, to effectively separate methane emissions from the energy and agriculture sectors. Incorporating these data into a Bayesian inverse analysis refines the magnitude and distribution of methane fluxes from each sector. Our analysis reveals that methane from agriculture is several times higher than inventory estimates. While this is in part due to the spatial distribution of sources, more monitoring is needed to improve agriculture emissions factors. Energy sector emissions factors optimized in this work are consistent with other regional studies of energy sector methane emissions. A synthesis of these works demonstrates a regional decline in energy sector emissions despite a concomitant increase in oil and gas extraction; however, current emissions are similar to 2008 estimates. Key Points: A dynamic linear model apportions energy and agriculture methane emissions from multi‐month trace gas measurements in Northern ColoradoAn estimated 0.4 ± 0.2 kg CH4 are emitted per barrel of oil equivalent produced, yielding a Wattenberg Field emission rate of 15 Mg CH4/hrOptimized agriculture methane emissions are higher than inventory predictions, in part due to mislocated fluxes in the inventory [ABSTRACT FROM AUTHOR]

Until the Mw 6.6 Luding earthquake ruptured the Moxi section of the Xianshuihe fault (XSHF) on 5 September 2022, the region had not experienced an Mw >6 earthquake since instrumental records began. We used Global Positioning System (GPS) and Sentinel-1 interferometric synthetic aperture radar (InSAR) observations to image the coseismic deformation and constrain the location and geometry of the seismogenic fault using a Bayesian method We then present a distributed slip model of the 2022 Mw6.6 Luding earthquake, a left-lateral strike-slip earthquake that occurred on the Moxi section of the Xianshuihe fault in the southwest Sichuan basin, China. Two tracks (T26 and T135) of the InSAR data captured a part of the coseismic surface deformation with the line-of-sight displacements range from ∼−0.16 m to ~0.14 m in the ascending track and from ~−0.12 m to ~0.10 m in the descending track. The inverted best-fitting fault model shows a pure sinistral strike-slip motion on a west-dipping fault plane with a strike of 164.3°. We adopt a variational Bayesian approach and account for the uncertainties in the fault geometry to retrieve the distributed slip model. The inverted result shows that the maximum slip of ~1.82 m occurred at a depth of 5.3 km, with the major slip concentrated within depths ranging from 0.9–11 km. The InSAR-determined moment is 1.3 × 1019 Nm, with a shear modulus of 30 GPa, equivalent to Mw 6.7. The published coseismic slip models of the 2022 Luding earthquake show apparent differences despite the use of similar geodetic or seismic observations. These variations underscore the uncertainty associated with routinely performed source inversions and their interpretations for the underlying fault model. [ABSTRACT FROM AUTHOR]

Data assimilation is an important tool in many geophysical applications. One of many key elements of data assimilation algorithms is the measurement error that determines the weighting of the data in the cost function to be minimized. Although the algorithms used for data assimilation treat the measurement uncertainty as known, it is in many cases estimated or set based on some expert opinion. Here we treat the measurement uncertainty as a hyperparameter in a fully Bayesian hierarchical model and derive a new class of iterative ensemble methods for data assimilation where the measurement uncertainty is integrated out. The proposed algorithms are compared with the standard iterative ensemble smoother on a 2D synthetic reservoir model. [ABSTRACT FROM AUTHOR]

To investigate the thermal structure of central Te Riu a Māui/Zealandia continent we estimate the depth to base of magnetic sources (DBMS), using an updated compilation of magnetic data. We calculate thousands of power spectral density estimates and solve an analytic solution for the fractal distribution of magnetization using a Bayesian method constrained by a sediment thickness model. Our DBMS results are broadly similar to a global model yet show complex relationships with independent models of crust and elastic thicknesses, and depth to base of seismicity (D90). Across central Zealandia, DBMS occurs above, coincident with, and below the Moho reflecting that factors additional to temperature influence DBMS. Away from subduction zones crustal thickness likely modulates DBMS while plate margins show varying influence dependent on margin characteristics. In the Taupō Volcanic Zone we interpret DBMS to reflect Curie point temperature at an average depth of 9–11 km. Error analysis shows that the choice of prior influences the posterior standard deviation and can result in counter intuitive error versus DBMS relationships. We use the DBMS as a basal temperature isotherm in heat flow models to compare with heat flow derived from borehole temperature measurements. Using the standard Curie point temperature of 580°C we find that DBMS derived heat flow models over estimate heat flow in areas underlain by plutonic rocks. We propose this reflects a higher titanomagnetite content in these rocks, although detailed studies of the magnetic mineralogy of Zealandia's plutonic rocks are required. Plain Language Summary: Knowledge of the thermal structure of the crust is fundamental for understanding many geologic processes. Here we have analyzed a new compilation of magnetic data over central Zealandia continent, including onland New Zealand, and calculated the depth to base of magnetic sources (DBMS) which often reflects the 580°C isotherm, known as the Curie point temperature. We find complex relationships between DBMS and markers such as the crust and elastic thickness and depth to which earthquakes occur, reflecting a range of processes additional to temperature influence DBMS. We use the depth to base of magnetic sources to generate heat flow models based on the assumption that magnetization in rocks vanishes at the Curie point temperature. In our study we find that this assumption may be incorrect in some regions dominated by plutonic igneous rocks as the derived heat flow is too high compared to heat flow derived from borehole temperature measurements. A Curie temperature of 500°C better fits observed data. One explanation is that magnetite in these rocks has a higher titanium content which acts to lower the Curie point temperature. Key Points: Depth to base of magnetic sources (DBMS) is shallower, coincident with, and in places deeper than Moho across Zealandia while plate margin style has variable impact on DBMSTo match borehole observations DBMS derived heatflow models require transient properties and a spatially variable Curie temperatureChoice of model prior influences error distribution in Bayesian DBMS determinations and can lead to counter intuitive results [ABSTRACT FROM AUTHOR]

A non-destructive testing (NDT) application of X-ray computed tomography (CT) is inspection of subsea pipes in operation via 2D cross-sectional scans. Data acquisition is time-consuming and costly due to the challenging subsea environment. While reducing the number of projections in a CT scan yields time and cost savings, this compromises the reconstruction quality when conventional reconstruction methods are used. To address this issue we take a Bayesian approach to CT reconstruction and focus on designing an effective prior that introduces additional information to the problem. We propose a new class of structural Gaussian priors to enforce expected material properties in different regions of the reconstructed image based on available a-priori information about the pipe's layered structure. The prior is composed from Gaussian distributions, and we utilize this to propose an efficient computational strategy to sample the resulting posterior distribution. This is essential in practical NDT applications for fast processing of the large-scale data we see in CT. Numerical experiments with synthetic and real data show that the proposed structural Gaussian prior reduces artifacts and enhances contrast in the reconstruction, compared to using only a conventional Gaussian Markov random field prior or no prior information at all. Furthermore, we obtain uncertainty estimates that indicate the certainty of the reconstructions increase when more prior information is added. [ABSTRACT FROM AUTHOR]

Seismic anisotropy beneath eastern North America, as expressed in shear wave splitting observations, has been attributed to plate motion‐parallel shear in the asthenosphere, resulting in fast axes aligned with the plate motion. However, deviations of fast axes from plate motion directions are observed near major tectonic boundaries of the Appalachians, indicating contributions from lithospheric anisotropy associated with past tectonic processes. In this study, we conduct anisotropic receiver function (RF) analysis using data from a dense seismic array traversing the New England Appalachians in Connecticut to examine anisotropic layers in the crust and upper mantle and correlate them with past tectonic processes as well as present‐day mantle flow. We use the harmonic decomposition method to separate directionally‐dependent variations of RFs and focus on features with the same harmonic signals observed across multiple stations. Within the crust, there are multiple features that may be correlated with stratification in the Hartford Basin, faults in the Taconic thrust belt, shear zones formed during Salinic/Acadian terrane accretion events, and orogen‐parallel crustal flow in the Acadian orogenic plateau. We apply a Bayesian inversion method to obtain quantitative constraints on the direction and strength of intra‐crustal anisotropy beneath the Hartford Basin. In the upper mantle, we identify a fossil shear zone possibly formed during oblique subduction of Rheic Ocean lithosphere. We also find evidence for a plate motion‐parallel flow zone in the asthenosphere that is likely disturbed by mantle upwelling near the southern margin of the Northern Appalachian Anomaly in the eastern part of the study area. Plain Language Summary: Seismic waves with different propagation and oscillation directions can exhibit different velocities when going through a medium with some directional properties; this phenomenon is called seismic anisotropy. Seismic anisotropy observed beneath eastern North America is often attributed to present‐day flow in the upper mantle. The mantle flow causes shear waves oscillating in the direction of flow (e.g., in the direction of North America plate motion) to travel faster than those that travel in other directions. However, this pattern does not hold true for some regions in the Appalachian Mountains, suggesting that past tectonic events can result in long‐lived, "frozen‐in" anisotropy in the lithosphere, which modifies the predicted anisotropic behavior beneath these regions. In this study, we investigate sources of seismic anisotropy beneath southern New England using a method based on directionally dependent variations of P‐wave to S‐wave conversions at interfaces with contrasts in anisotropy. This method can separate signals caused by different anisotropic features and constrain the depth distribution of anisotropy. We identify various anisotropic layers in the crust and upper mantle and correlate them with Appalachian mountain‐building events and complex present‐day flow in the upper mantle. Key Points: Anisotropic receiver function analysis reveals multiple anisotropic layers in the crust and upper mantle beneath southern New EnglandAnisotropic geometries at <10 km depth resolved by Bayesian inversion imply contributions from sediment layering and Paleozoic deformationArray‐wide anisotropic interfaces in the upper mantle show plate motion parallel flow distorted by localized mantle upwelling [ABSTRACT FROM AUTHOR]

Gas-hydrate saturation and porosity are the most crucial reservoir parameters for gashydrate resource assessment. Numerous academics have put forward elastic and electrical petrophysical models for calculating the saturation and porosity of gas-hydrate. However, owing to the limitations of a single petrophysical model, the estimation of gas-hydrate saturation and porosity using single elastic or electrical measurement data appears to be inconsistent and uncertain. In this study, the sonic wave velocity, density and resistivity well log data are combined with a Bayesian linear inversion method for the simultaneous estimation of gas-hydrate saturation and porosity. The sonic wave velocity, density and resistivity data of the Shenhu area in the South China Sea are used to estimate the gas-hydrate saturation and porosity. To validate the accuracy of this method, the estimation results are compared with the saturation obtained from pore water chemistry and porosity obtained from density logs. The well log data examples show that the joint estimation method not only provides a rapid estimation of the gas-hydrate reservoir parameters but also improves the accuracy of results and determines their uncertainty. [ABSTRACT FROM AUTHOR]

Conservation laws of the generic form c t + f (c) x = 0 play a central role in the mathematical description of various engineering related processes. Identification of an unknown flux function f(c) from observation data in space and time is challenging due to the fact that the solution c(x, t) develops discontinuities in finite time. We explore a Bayesian type of method based on representing the unknown flux f(c) as a Gaussian random process (parameter vector) combined with an iterative ensemble Kalman filter (EnKF) approach to learn the unknown, nonlinear flux function. As a testing ground, we consider displacement of two fluids in a vertical domain where the nonlinear dynamics is a result of a competition between gravity and viscous forces. This process is described by a multidimensional Navier–Stokes model. Subject to appropriate scaling and simplification constraints, a 1D nonlinear scalar conservation law c t + f (c) x = 0 can be derived with an explicit expression for f(c) for the volume fraction c(x, t). We consider small (noisy) observation data sets in terms of time series extracted at a few fixed positions in space. The proposed identification method is explored for a range of different displacement conditions ranging from pure concave to highly non-convex f(c). No a priori information about the sought flux function is given except a sound choice of smoothness for the a priori flux ensemble. It is demonstrated that the method possesses a strong ability to identify the unknown flux function. The role played by the choice of initial data c 0 (x) as well various types of observation data is highlighted. [ABSTRACT FROM AUTHOR]

Abstract The phenomenon of differential rotation of the Earth's inner core relative to the mantle is a subject of interest in geodynamo modeling that has been validated by seismological observations, mainly via the earthquake‐doublets method. Although recent studies converge on the time‐varying differential rotation of the inner core relative to the mantle, favoring a decadal variation, the inferred models significantly differ. Here, considering the data selection, the observed data structure, and the subjective model parameterizations, which we avoid by employing a Bayesian transdimensional approach, we show that the recent best‐fit model by Yang and Song (2023, https://doi.org/10.1038/s41561‐022‐01112‐z) featuring the 70‐year decadal variation is not obtained when all available data are considered. Namely, including only a small number of discarded earthquake doublets (

Abstract Inconsistencies between observations from long and short period seismic waves and geochemical data mean craton formation and evolution remains enigmatic. Specifically, internal layering and radial anisotropy are poorly constrained. Here, we show that these inconsistencies can be reconciled by inverting cratonic Rayleigh and Love surface wave dispersion curves for shear‐wave velocity and radial anisotropy using a flexible Bayesian scheme. This approach requires no explicit vertical smoothing and only adds anisotropy to layers where required by the data. We show that all cratonic lithospheres are comprised of a positively radially anisotropic upper layer, best explained by Archean underplating, and an isotropic layer beneath, indicative of two‐stage formation. Within the positively radially anisotropic upper layer, we find a variable amplitude low velocity zone within 9 of 12 cratons studied, that is well correlated with observed Mid‐Lithospheric Discontinuities (MLDs). The MLD is best explained by metasomatism after craton formation.

The Gulf of Aqaba earthquake occurred on 22 November 1995 in the Northern Red Sea and is the largest instrumentally recorded earthquake in the region to date. The event was extensively studied during the initial years following its occurrence. However, it remained unclear which of the many faults in the gulf were activated during the earthquake. We present results from multi-array back projection that we use to inform Bayesian kinematic rupture models constrained by geodetic and teleseismic data. Our results indicate that most of the moment release was on the Aragonese fault via left-lateral strike slip and shallow normal faulting that may have been dynamically triggered by an early rupture phase on the Arnona fault. We also identified a predominantly normal fault-segment on the eastern shore of the gulf that was activated in the event. We dismiss the previously proposed hypothesis of a co-seismic sub-event on the western shore of the gulf and confirm that observed deformation can be rather attributed to post-seismic activity. In conclusion, the gulf shows many signs of active tectonic extension. Therefore, more events close to the shorelines are to be expected in the future and should be considered conducting infrastructure projects in the region.

Abstract Quantifying sector‐resolved methane fluxes in complex emissions environments is challenging yet necessary to improve emissions inventories and guide policy. Here, we separate energy and agriculture sector emissions using a dynamic linear model analysis of methane, ethane, and ammonia data measured at a Northern Colorado site from November 2021 to January 2022. By combining these sector‐apportioned observations with spatially resolved inventories and Bayesian inverse methods, energy and agriculture methane fluxes are optimized across the study's ∼850 km2 sensitivity area. Energy sector fluxes are synthesized with previous literature to evaluate trends in energy sector methane emissions. Optimized agriculture fluxes in the study area were 3.5× larger than inventory estimates; we demonstrate this discrepancy is consistent with differences in the modeled versus real‐world spatial distribution of agricultural sources. These results highlight how sector‐apportioned methane observations can yield multi‐sector inventory optimizations in complex environments.

Abstract The source imaging for offshore earthquakes using terrestrial geodetic data has a limited estimation performance due to the low data resolution. One approach to overcome this limitation is the use of seafloor geodetic data. In this study, we focus on tsunami-source data, which is the spatial distribution of vertical crustal displacements above the source area and can be derived from tsunami waveform records. We evaluate how the use of this spatial seafloor geodetic data improves the estimation of a rectangular fault model. Here, the fault model of the 2016 off-Fukushima earthquake in Japan, which was a shallow intraplate earthquake (M w 7.0), was estimated by three inversions: terrestrial Global Navigation Satellite System (GNSS) data only, tsunami-source data only, and a combination of the GNSS data and tsunami-source data. A Bayesian inversion approach was used to understand the distribution of the estimated fault parameters and their relationship. The results indicated that the terrestrial GNSS data have a low resolution for the analysis of the offshore earthquake, which resulted in a biased solution with large uncertainty. Conversely, the use of tsunami-source data significantly improved the resolution and reliability of source imaging and reduced the dependency among fault parameters. These results suggested that the high-spatial-resolution information of tsunami source is a powerful tool in source imaging of offshore shallow earthquakes. Moreover, the combined use of the two different geodetic data leads to a more robust estimation of fault parameters. We believe that the use of tsunami-source data is useful, not only for the post hoc source analysis, but also for estimating an earthquake rupture area just after a large earthquake, where GNSS data are currently used. Graphical Abstract

Abstract Modern geomagnetic field models are constructed from satellite and observatory data, while models on the millennial timescale are constructed from indirect records of thermoremanent and sedimentary origin. An intermediate period, spanning the last four centuries, is covered by historical survey data and ship-logs, which is strongly dominated by geomagnetic declination information. We apply a sequentialized, Gaussian process-based modeling technique to this dataset and propose a new field model for this era. In order to investigate the information gained from declination records from ship-logs, we separate the dataset and construct a second model, where unpaired declination records (i.e., measurements where only declinations are reported and the rest of the field vector is missing) are removed. The availability of more records helps notably to constrain global field properties like the dipole moment. It also allows to resolve some detailed field structures more accurately. Based on the model constructed from the full dataset, we perform an analysis of the South Atlantic Anomaly and regions of low field intensity in general. We extend a recent analysis of center of mass movement and area evolution of the South Atlantic Anomaly further back in time and confirm the findings of its non-monotonous growth. Graphical Abstract

Abstract Seismic anisotropy beneath eastern North America, as expressed in shear wave splitting observations, has been attributed to plate motion‐parallel shear in the asthenosphere, resulting in fast axes aligned with the plate motion. However, deviations of fast axes from plate motion directions are observed near major tectonic boundaries of the Appalachians, indicating contributions from lithospheric anisotropy associated with past tectonic processes. In this study, we conduct anisotropic receiver function (RF) analysis using data from a dense seismic array traversing the New England Appalachians in Connecticut to examine anisotropic layers in the crust and upper mantle and correlate them with past tectonic processes as well as present‐day mantle flow. We use the harmonic decomposition method to separate directionally‐dependent variations of RFs and focus on features with the same harmonic signals observed across multiple stations. Within the crust, there are multiple features that may be correlated with stratification in the Hartford Basin, faults in the Taconic thrust belt, shear zones formed during Salinic/Acadian terrane accretion events, and orogen‐parallel crustal flow in the Acadian orogenic plateau. We apply a Bayesian inversion method to obtain quantitative constraints on the direction and strength of intra‐crustal anisotropy beneath the Hartford Basin. In the upper mantle, we identify a fossil shear zone possibly formed during oblique subduction of Rheic Ocean lithosphere. We also find evidence for a plate motion‐parallel flow zone in the asthenosphere that is likely disturbed by mantle upwelling near the southern margin of the Northern Appalachian Anomaly in the eastern part of the study area.

A non-destructive testing (NDT) application of X-ray computed tomography (CT) is inspection of subsea pipes in operation via 2D cross-sectional scans. Data acquisition is time-consuming and costly due to the challenging subsea environment. While reducing the number of projections in a CT scan yields time and cost savings, this compromises the reconstruction quality when conventional reconstruction methods are used. To address this issue we take a Bayesian approach to CT reconstruction and focus on designing an effective prior that introduces additional information to the problem. We propose a new class of structural Gaussian priors to enforce expected material properties in different regions of the reconstructed image based on available a-priori information about the pipe's layered structure. The prior is composed from Gaussian distributions, and we utilize this to propose an efficient computational strategy to sample the resulting posterior distribution. This is essential in practical NDT applications for fast processing of the large-scale data we see in CT. Numerical experiments with synthetic and real data show that the proposed structural Gaussian prior reduces artifacts and enhances contrast in the reconstruction, compared to using only a conventional Gaussian Markov random field prior or no prior information at all. Furthermore, we obtain uncertainty estimates that indicate the certainty of the reconstructions increase when more prior information is added.

Camera calibration is necessary for many machine vision applications. The calibration methods are based on linear or non-linear optimization techniques that aim to find the best estimate of the camera parameters. One of the most commonly used methods in computer vision for the calibration of intrinsic camera parameters and lens distortion (interior orientation) is Zhang's method. Additionally, the uncertainty of the camera parameters is normally estimated by assuming that their variability can be explained by the images of the different poses of a checkerboard. However, the degree of reliability for both the best parameter values and their associated uncertainties has not yet been verified. Inaccurate estimates of intrinsic and extrinsic parameters during camera calibration may introduce additional biases in post-processing. This is why we propose a novel Bayesian inference-based approach that has allowed us to evaluate the degree of certainty of Zhang's camera calibration procedure. For this purpose, the a prioriprobability was assumed to be the one estimated by Zhang, and the intrinsic parameters were recalibrated by Bayesian inversion. The uncertainty of the intrinsic parameters was found to differ from the ones estimated with Zhang's method. However, the major source of inaccuracy is caused by the procedure for calculating the extrinsic parameters. The procedure used in the novel Bayesian inference-based approach significantly improves the reliability of the predictions of the image points, as it optimizes the extrinsic parameters. [ABSTRACT FROM AUTHOR]

The source imaging for offshore earthquakes using terrestrial geodetic data has a limited estimation performance due to the low data resolution. One approach to overcome this limitation is the use of seafloor geodetic data. In this study, we focus on tsunami-source data, which is the spatial distribution of vertical crustal displacements above the source area and can be derived from tsunami waveform records. We evaluate how the use of this spatial seafloor geodetic data improves the estimation of a rectangular fault model. Here, the fault model of the 2016 off-Fukushima earthquake in Japan, which was a shallow intraplate earthquake (Mw 7.0), was estimated by three inversions: terrestrial Global Navigation Satellite System (GNSS) data only, tsunami-source data only, and a combination of the GNSS data and tsunami-source data. A Bayesian inversion approach was used to understand the distribution of the estimated fault parameters and their relationship. The results indicated that the terrestrial GNSS data have a low resolution for the analysis of the offshore earthquake, which resulted in a biased solution with large uncertainty. Conversely, the use of tsunami-source data significantly improved the resolution and reliability of source imaging and reduced the dependency among fault parameters. These results suggested that the high-spatial-resolution information of tsunami source is a powerful tool in source imaging of offshore shallow earthquakes. Moreover, the combined use of the two different geodetic data leads to a more robust estimation of fault parameters. We believe that the use of tsunami-source data is useful, not only for the post hoc source analysis, but also for estimating an earthquake rupture area just after a large earthquake, where GNSS data are currently used. [ABSTRACT FROM AUTHOR]

Nepal is an actively deforming region due to its tectonic setting that hosts destructive earthquakes including the recent 2015 Mw 7.8 Gorkha earthquake. To better understand the physics of earthquakes and better assess the seismic hazard in the region, a highly resolved 3‐D structure of the crust is essential. This study presents a new 3‐D S‐wave velocity structure of the crust using ambient noise tomography (ANT). In relation to the 2015 earthquake, we show that the lateral variation of S‐wave velocity likely controls the rupture propagation and arrest. This study further constrains crustal discontinuities beneath Nepal including the Main Himalayan Thrust (MHT) using teleseismic P‐wave coda autocorrelation. The MHT geometry correlates well with sizeable low S‐wave velocity zones obtained from the ANT and separated by two ramps. The southernmost first ramp is where the 2015 Gorkha earthquake nucleated that we map up to the source model of the 1934 historical earthquake in Eastern Nepal. The northernmost second ramp is adjacent to the mid‐crustal low velocity zone beneath south Tibet. In between the two ramps, we interpret the horizontal low velocity zone as the interseismic creeping patch of the MHT with down‐dip extent of 50–70 km length and 90–100 km in correspondence with the Mw 7.8 2015 and 8.4 1934 source models, respectively. A systematic mapping of the low‐velocity zones in relation to the MHT integrated with GPS geodesy along with the respective slip from individual past earthquake ruptures can help decipher the paradox of maximum Himalayan earthquake magnitudes. Plain Language Summary: Nepal is located near the plate boundaries between the Indian and Eurasian plates, resulting in damaging earthquakes in the region. However, we do not know exactly what controls the earthquake processes beneath Himalaya Nepal due to its complex geological settings and lack of detailed seismic properties beneath this region. Here we present the detailed shear (S)‐wave velocity image up to 60 km depth beneath Himalaya Nepal that shows how fast/slow the S‐wave propagates, relating to the material properties in crust beneath Himalaya. We used data extracted from recordings of noise coming from, for example, ocean and atmosphere. We also utilized the conversion and reverberation of compressional waves that are sensitive to the sharp transition of material properties. The estimated S‐wave velocity near surface is consistent with material found on the surface of the crust. Here, we show that MHT can be described as a system of low‐velocity zones connected by two ramps. The first ramp is located near the hypocenter of 2015 Gorkha earthquake and second beneath South Tibet. The low velocity between two ramps is considered as interseismic creeping patch. A systematic mapping of such low‐velocity zone beneath all the Himalaya may allow a better understanding of the earthquake hazard. Key Points: Main Himalayan Thrust (MHT) as a system of sizeable low‐velocity zones connected by rampsInferred MHT interseismic patches with different length scales in correspondence of the 2015 and 1934 earthquakesLateral variations of S‐wave velocity across MHT likely control the rupture of the 2015 Gorkha earthquakes [ABSTRACT FROM AUTHOR]

The bathymetry is the most superficial layer of the Earth's crust on which it is possible to perform direct measurements. However, it is also well known that water covers more than 70% of the Earth's surface, so an enormous expenditure of acquisition campaigns should be performed to produce a high-resolution map of this layer. Currently exploiting mainly commercial navigation routes, the sea floor coverage with shipborne sounding is only at 11%, and the remaining part is currently modeled by classical interpolation techniques or satellite-based gravity inversion methods. In the present work, a new method to refine bathymetry modeling based on the exploitation of global gravity field models is presented. In the proposed solution, once modeled and removed from the observed gravity field, the gravitational signals related to the deepest structures, a 3D Bayesian inversion algorithm is used to improve the actual knowledge of bathymetry. The proposed inversion method also enables limiting the solution to shipborne sounding measurements in such a way as to improve the seafloor grid where no local, high-quality information is available. Two test cases are discussed in the Mediterranean Sea region. Promising results are presented, opening the possibility of applying an analogous method to refine the bathymetry modeling at larger scales up to the global one. [ABSTRACT FROM AUTHOR]

In this paper, we consider a Bayesian inverse problem modeled by elliptic partial differential equations (PDEs). Specifically, we propose a data-driven and model-based approach to accelerate the Hamiltonian Monte Carlo (HMC) method in solving large-scale Bayesian inverse problems. The key idea is to exploit (model-based) and construct (data-based) intrinsic approximate low-dimensional structure of the underlying problem which consists of two components—a training component that computes a set of data-driven basis to achieve significant dimension reduction in the solution space, and a fast solving component that computes the solution and its derivatives for a newly sampled elliptic PDE with the constructed data-driven basis. Hence we develop an effective data and model-based approach for the Bayesian inverse problem and overcome the typical computational bottleneck of HMC—repeated evaluation of the Hamiltonian involving the solution (and its derivatives) modeled by a complex system, a multiscale elliptic PDE in our case. Finally, we present numerical examples to demonstrate the accuracy and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

When building 3D models of the subsurface, reconciling several geological and geophysical data of diverse nature, resolutions, coverage, or sensitivity, is challenging, both numerically and petrophysically. In this work, we propose a workflow for mapping selected geological features and characterise their uncertainty using a Bayesian Estimate Fusion algorithm. Different datasets such as 1D probabilistic models derived from geophysical data, drillholes and geological data are combined to produce probabilistic maps of selected geological boundaries, relying on petrophysical and geological assumptions. Leveraging large, high-quality geophysical datasets acquired in the eastern Gawler Craton in South Australia, we demonstrate the applicability of our approach with two examples: (1) we map in 3D the top of a stratigraphic unit in the cover, the Tregolana Shale, using 1D magnetotelluric (MT) and 1D Airborne Electromagnetic (AEM) probabilistic models, drill holes and surface geology; (2) we map the depth to basement using 1D probabilistic MT models, drill holes and interpreted structural information. Our results show that the different resolution, data sampling, depth of investigation and reliability of the utilised datasets can be combined in a complementary fashion, overcoming their respective limitations, to find solutions/models that satisfy all the datasets. We show that probabilistic workflows permit characterisation and reduce uncertainty when mapping the location of features of interest, but also permit the testing of geological hypotheses against other geophysical and geological data. These types of models are valuable to better characterise, interpret, and conceptualise the subsurface, enabling better exploration targeting and supporting efforts to discover new mineral deposits. [ABSTRACT FROM AUTHOR]

Modern geomagnetic field models are constructed from satellite and observatory data, while models on the millennial timescale are constructed from indirect records of thermoremanent and sedimentary origin. An intermediate period, spanning the last four centuries, is covered by historical survey data and ship-logs, which is strongly dominated by geomagnetic declination information. We apply a sequentialized, Gaussian process-based modeling technique to this dataset and propose a new field model for this era. In order to investigate the information gained from declination records from ship-logs, we separate the dataset and construct a second model, where unpaired declination records (i.e., measurements where only declinations are reported and the rest of the field vector is missing) are removed. The availability of more records helps notably to constrain global field properties like the dipole moment. It also allows to resolve some detailed field structures more accurately. Based on the model constructed from the full dataset, we perform an analysis of the South Atlantic Anomaly and regions of low field intensity in general. We extend a recent analysis of center of mass movement and area evolution of the South Atlantic Anomaly further back in time and confirm the findings of its non-monotonous growth. [ABSTRACT FROM AUTHOR]

The Ocean Color—Simultaneous Marine and Aerosol Retrieval Tool (OC-SMART) is a robust data processing platform utilizing scientific machine learning (SciML) in conjunction with comprehensive radiative transfer computations to provide accurate remote sensing reflectances ( R rs estimates), aerosol optical depths, and inherent optical properties. This paper expands the capability of OC-SMART by quantifying uncertainties in ocean color retrievals. Bayesian inversion is used to relate measured top of atmosphere radiances and a priori data to estimate posterior probability density functions and associated uncertainties. A framework of the methodology and implementation strategy is presented and uncertainty estimates for R rs retrievals are provided to demonstrate the approach by applying it to MODIS, OLCI Sentinel-3, and VIIRS sensor data. [ABSTRACT FROM AUTHOR]

The Community Long‐term Infrared Microwave Combined Atmospheric Product System (CLIMCAPS) spans more than two decades of soundings from infrared and microwave instrument pairs on Aqua, Suomi‐NPP, and NOAA‐20. CLIMCAPS builds on three decades of research within the National Aeronautics and Space Administration Atmospheric Infrared Sounder Science Team (AST) to retrieve profiles of atmospheric temperature, water vapor, ozone, and many other trace gases as well as cloud and surface properties. In this paper, we highlight four innovative aspects of the AST retrieval methodology that allows the CLIMCAPS record (2002 to present) to bridge technology differences, maintain global coverage and stay updated with fast reprocessing times. CLIMCAPS improves on the AST method with rigorous optimal estimation uncertainty quantification for improved understanding of the signal‐to‐noise in sounding retrievals to allow their use in scientific research. Plain Language Summary: The Atmospheric Infrared Sounder (AIRS) was the first instrument of its kind in space. It has been making measurements daily at ∼1:30 a.m./p.m. since 2002. The Community Long‐term Infrared Microwave Combined Atmospheric Product System (CLIMCAPS) uses AIRS measurements to retrieve variables that characterize the thermodynamic and chemical state of the atmosphere. National Aeronautics and Space Administration is funding CLIMCAPS to continue the AIRS record with retrievals from the Cross‐track Infrared Sounder launched on three satellites in similar orbits since 2014 and scheduled for launch on two additional satellites in future. Accurate, consistent, long‐term records of observations are critically important for our understanding of an evolving Earth system. Key Points: Community Long‐term Infrared Microwave Combined Atmospheric Product System (CLIMCAPS) extends the Atmospheric Infrared Sounder (AIRS) + Atmospheric Microwave Sounding Unit record with sounding retrievals from Cross‐track Infrared Sounder + Advanced Technology Microwave SounderKey aspects of the AIRS Science Team retrieval methodology are embedded in the CLIMCAPS algorithm to help bridge technology differencesThe CLIMCAPS algorithm design enables an atmospheric sounding product with global coverage in clear and partly cloudy conditions [ABSTRACT FROM AUTHOR]

Groundwater flow modeling is commonly used to calculate groundwater heads, estimate groundwater flow paths and travel times, and provide insights into solute transport processes within an aquifer. However, the values of input parameters that drive groundwater flow models are often highly uncertain due to subsurface heterogeneity and geologic complexity in combination with lack of measurements/unreliable measurements. This uncertainty affects the accuracy and reliability of model outputs. Therefore, parameters' uncertainty must be quantified before adopting the model as an engineering tool. In this study, we model the uncertain parameters as random variables and use a Bayesian inversion approach to obtain a posterior, data-informed, probability density function (pdf) for them: in particular, the likelihood function we consider takes into account both well measurements and our prior knowledge about the extent of the springs in the domain under study. To keep the modelistic and computational complexities under control, we assume Gaussianity of the posterior pdf of the parameters. To corroborate this assumption, we run an identifiability analysis of the model: we apply the inversion procedure to several sets of synthetic data polluted by increasing levels of noise, and we determine at which levels of noise we can effectively recover the "true value" of the parameters. We then move to real well data (coming from the Ticino River basin, in northern Italy, and spanning a month in summer 2014), and use the posterior pdf of the parameters as a starting point to perform an uncertainty quantification analysis on groundwater travel-time distributions. [ABSTRACT FROM AUTHOR]

Predator–prey dynamics have been suggested as simplified models of stratocumulus clouds, with rain acting as a predator of the clouds. We describe a mathematical and computational framework for estimating the parameters of a simplified model from a large eddy simulation (LES). In our method, we extract cycles of cloud growth and decay from the LES and then search for parameters of the simplified model that lead to similar cycles. We implement our method via Markov chain Monte Carlo. Required error models are constructed based on variations of the LES cloud cycles. This computational framework allows us to test the robustness of our overall approach and various assumptions, which is essential for the simplified model to be useful. Our main conclusion is that it is indeed possible to calibrate a predator–prey model so that it becomes a reliable, robust, but simplified representation of selected aspects of a LES. In the future, such models may then be used as a quantitative tool for investigating important questions in cloud microphysics.

Predator–prey dynamics have been suggested as simplified models of stratocumulus clouds, with rain acting as a predator of the clouds. We describe a mathematical and computational framework for estimating the parameters of a simplified model from a large eddy simulation (LES). In our method, we extract cycles of cloud growth and decay from the LES and then search for parameters of the simplified model that lead to similar cycles. We implement our method via Markov chain Monte Carlo. Required error models are constructed based on variations of the LES cloud cycles. This computational framework allows us to test the robustness of our overall approach and various assumptions, which is essential for the simplified model to be useful. Our main conclusion is that it is indeed possible to calibrate a predator–prey model so that it becomes a reliable, robust, but simplified representation of selected aspects of a LES. In the future, such models may then be used as a quantitative tool for investigating important questions in cloud microphysics.