Bayesian Inversion Research Articles

Detection of Atmospheric Hydrofluorocarbon-22 with Ground-Based Remote High-Resolution Fourier Transform Spectroscopy over Hefei and an Estimation of Emissions in the Yangtze River Delta

Under the control of the Montreal Protocol and its amendments, hydrofluorocarbons (HCFCs) are used as temporary substitutes for ozone-depleting substances, such as chlorofluorocarbons, and are regulated for consumption and production. China plans to phase out HCFCs by 2030, and HCFC-22 (CHClF2) is currently the most abundant HCFC in the atmosphere. This study measures the vertical profiles and total columns of atmospheric HCFC-22 from January 2017 to December 2022, based on the mid-infrared solar spectra recorded by the ground-based high-resolution Fourier transform infrared (FTIR) spectrometer at the Hefei remote sensing station. The HCFC-22 total columns over Hefei increased from 2017–2018 and gradually decreased in 2018–2022, with an annual variation rate of 5.98% and −1.02% ± 0.02%, respectively. Compared with the ACE-FTS satellite independent dataset, the FTIR data indicate good consistency with the ACE-FTS data at a 5–25 km altitude, with an average relative difference of −4.38 ± 0.83% between the vertical profiles. HCFC-22 emissions in the Yangtze River Delta from 2017 to 2022 are estimated, derived from measured total columns combined with the Lagrangian transport model and the Bayesian inversion technique. In the Yangtze River Delta, HCFC-22 emissions were high in 2017, with a value of 33.3 ± 16.8 kt, and decreased from 2018 to 2022, with a minimum of 27.3 ± 13.6 kt in 2022 during the observations.

Bayesian inversion for modelling 3-D density structures in the eastern margin of Bayan Har block and its tectonic implications

SUMMARY Recently, the eastern margin of the Tibetan plateau has experienced three moderate earthquakes. Deep crustal structure is a critical factor for understanding the seismotectonic environment and deformations in this region. Although several multidisciplinary geophysical approaches have been used to develop crustal structure models for this area, substantial inconsistencies still persist in the results due to the intricate structural properties of crust. In this study, we introduce a novel approach to construct a 3-D crustal model with assimilated density structure (MADS) at a resolution of 0.2° × 0.2° × 5 km. This model is built by integrating data from various source, including multisource gravity anomalies and diverse available crustal structure reference models. We use a model-assimilated gravity inversion process with Bayesian parameter optimization. First, we combine the terrestrial gravity profiles data set with published global gravity field models to create a data set rich in reliable high-frequency anomaly information. Secondly, we incorporate three reference models derived from different seismological methods as prior constraints for our model. These models encompass seismic tomography, surface wave dispersion and receiver function data. We optimize the hyper-parameters of these constraints using the Bayesian criterion. The results demonstrate that the MADS not only captures significant changes in the crustal density but also discerns subtle variations in the upper and middle crust, thereby providing detailed insights into the morphologies of major faults. For instance, the central section of the Longmenshan fault is revealed as a high-angle deep thrust feature, while the frontal section of the Longmenshan fault appears as a low-angle mid-deep thrust feature, and the Xianshuihe fault exhibits a vertical deep subduction feature. Additionally, our findings indicate a correlation between the locations of moderate-to-large earthquakes in this region and the high density-gradient zones or asperities with high density within MADS. We believe that the insights into density characteristics offered by the new MADS model can shed light on the study of asperities associated with recent moderate earthquakes and enhance our understanding of deformation in this region.

Geostatistical and multitemporal InSAR method and elastic deformation model for detailed characterizations of topographic change and magma reservoirs: Application to the Tangkuban Parahu Volcano, Indonesia

This study proposes the entire detection of the surface deformation of a volcanic area using interferometric synthetic aperture radar (InSAR) with geostatistics to specify the locations and shapes of the sources causing the deformation. We selected the Tangkuban Parahu area, West Java, Indonesia, as our study site and used a Sentinel-1 dataset. In this study, we combine persistent scatterer and small baseline subset InSAR with a geostatistical technique, i.e., turning bands simulation. This combination can compensate for undetected displacement pixels and decompose the line-of-sight displacement into vertical and horizontal east–west displacements using both the ascending and descending mode results and the least-squares method. This two-dimensional geostatistics and multitemporal InSAR approach is referred to as 2D GMT-InSAR. A detailed displacement pattern is revealed by 2D GMT-InSAR for undetected pixels in low-coherence areas. Then, the vertical displacement pattern in the study period from 2014 to 2019, mainly uplift with local subsidence, is reproduced via the joint use of the Mogi and Okada models for circular and rectangular parallelepiped sources of the deformation, respectively. Via a Bayesian inversion, one circular source, equivalent to a magma reservoir, and one dyke source are identified. The displacement pattern is likely caused by pressure increases in the magma reservoir, associated with the volcanic activation, and in the dyke, associated with the gas and fluid flows from the reservoir, which induced a phreatic explosion in July 2019. A connection of the dyke with the old Sunda volcanic system is found; this new finding is a result of the caldera collapse during the Sunda volcanic eruption.

Impact of transport model resolution and a priori assumptions on inverse modeling of Swiss F-gas emissions

Abstract. Inverse modeling is a widely used top-down method to infer greenhouse gas (GHG) emissions and their spatial distribution based on atmospheric observations. The errors associated with inverse modeling have multiple sources, such as observations and a priori emission estimates, but they are often dominated by the transport model error. Here, we utilize the Lagrangian particle dispersion model (LPDM) FLEXPART (FLEXible PARTicle Dispersion Model), driven by the meteorological fields of the regional numerical weather prediction model COSMO. The main sources of errors in LPDMs are the turbulence diffusion parameterization and the meteorological fields. The latter are outputs of an Eulerian model. Recently, we introduced an improved parameterization scheme of the turbulence diffusion in FLEXPART, which significantly improves FLEXPART-COSMO simulations at 1 km resolution. We exploit F-gas measurements from two extended field campaigns on the Swiss Plateau (in Beromünster and Sottens), and we conduct both high-resolution (1 km) and low-resolution (7 km) FLEXPART transport simulations that are then used in a Bayesian analytical inversion to estimate spatial emission distributions. Our results for four F-gases (HFC-134a, HFC-125, HFC-32, SF6) indicate that both high-resolution inversions and a dense measurement network significantly improve the ability to estimate spatial distribution of the emissions. Furthermore, the total emission estimates from the high-resolution inversions (351 ± 44 Mg yr−1 for HFC-134a, 101 ± 21 Mg yr−1 for HFC-125, 50 ± 8 Mg yr−1 for HFC-32, 9.0 ± 1.1 Mg yr−1 for SF6) are significantly higher compared to the low-resolution inversions (20 %–40 % increase) and result in total a posteriori emission estimates that are closer to national inventory values as reported to the UNFCCC (10 %–20 % difference between high-resolution inversion estimates and inventory values compared to 30 %–40 % difference between the low-resolution inversion estimates and inventory values). Specifically, we attribute these improvements to a better representation of the atmospheric flow in complex terrain in the high-resolution model, partly induced by the more realistic topography. We further conduct numerous sensitivity inversions, varying different parameters and variables of our Bayesian inversion framework to explore the whole range of uncertainty in the inversion errors (e.g., inversion grid, spatial distribution of a priori emissions, covariance parameters like baseline uncertainty and spatial correlation length, temporal resolution of the assimilated observations, observation network, seasonality of emissions). From the abovementioned parameters, we find that the uncertainty of the mole fraction baseline and the spatial distribution of the a priori emissions have the largest impact on the a posteriori total emission estimates and their spatial distribution. This study is a step towards mitigating the errors associated with the transport models and better characterizing the uncertainty inherent in the inversion error. Improvements in the latter will facilitate the validation and standardization of national GHG emission inventories and support policymakers.

Constraining Sector‐Specific CO2 Fluxes Using Space‐Based XCO2 Observations Over the Los Angeles Basin

AbstractThe concentration of carbon dioxide (CO2) in Earth's atmosphere is increasing due to human activities and the resulting effects on the global climate system have initiated several policy‐driven approaches to reduce emissions of this greenhouse gas. Quantifying the effectiveness of such policies requires both bottom‐up and top‐down approaches to estimate CO2 emissions. This work investigates, for the first time, the potential of using Snapshot Area Map observations from NASA's OCO‐3 instrument to disaggregate sector‐specific emissions from instrument observations. Optimized sector‐specific timeseries were produced using Bayesian inversion techniques and compared to proxy activity data from transportation, commercial maritime, and industrial sectors in the Los Angeles Basin. Results demonstrate that dense space‐based observations of atmospheric CO2 are capable of disentangling sector‐specific CO2 fluxes, paving the way for accurate monitoring of the effects of carbon‐reduction policies and operational carbon monitoring systems.

A tutorial on the Bayesian statistical approach to inverse problems

Inverse problems are ubiquitous in science and engineering. Two categories of inverse problems concerning a physical system are (1) estimate parameters in a model of the system from observed input–output pairs and (2) given a model of the system, reconstruct the input to it that caused some observed output. Applied inverse problems are challenging because a solution may (i) not exist, (ii) not be unique, or (iii) be sensitive to measurement noise contaminating the data. Bayesian statistical inversion (BSI) is an approach to tackle ill-posed and/or ill-conditioned inverse problems. Advantageously, BSI provides a “solution” that (i) quantifies uncertainty by assigning a probability to each possible value of the unknown parameter/input and (ii) incorporates prior information and beliefs about the parameter/input. Herein, we provide a tutorial of BSI for inverse problems by way of illustrative examples dealing with heat transfer from ambient air to a cold lime fruit. First, we use BSI to infer a parameter in a dynamic model of the lime temperature from measurements of the lime temperature over time. Second, we use BSI to reconstruct the initial condition of the lime from a measurement of its temperature later in time. We demonstrate the incorporation of prior information, visualize the posterior distributions of the parameter/initial condition, and show posterior samples of lime temperature trajectories from the model. Our Tutorial aims to reach a wide range of scientists and engineers.

Structure of the crust-uppermost mantle beneath the Ethiopian volcanic province using ambient seismic noise and teleseismic P wave coda autocorrelation

The Ethiopian-Yemen plateaus have been affected by plume-related magmatism for at least 40 My, yet the nature and distribution of intrusive magmas and their relation to subsequent East Africa rifting remain poorly characterized. This paper presents a 3D shear (S) - wave velocity structure of the crust and uppermost mantle beneath the northern sectors of the East African rift and the dynamically-supported Ethiopian Plateau. We apply a Bayesian inversion of group and phase velocity dispersion curves for periods 5–40 s extracted from the ambient noise tomography of data from over 125 broadband seismic stations, and we identify seismic discontinuities using autocorrelation of P-wave coda. The resulting crustal structure affecting much of the Main Ethiopian Rift (MER) indicates a pronounced low S-wave velocity lower crust (∼3.6 km/s) that becomes thinner towards the northeast rising to almost the same depth level (∼20 km) as the base crust beneath the Afar triple junction zone. We also find high velocity features in the crust and uppermost mantle beneath the Afar rift axes, the current locus of strain and volcanism, that may indicate voluminous new basaltic crust. Our Moho-depth map indicates that the entire Afar Depression is underlain by crust thinner than 25 km, whereas the MER and central Ethiopian plateau are underlain by low S-wave velocity crust thicker than 35 km. These patterns suggest active underplating beneath the largely unfaulted plateau, in contrast to the efficient magmatic feeder system supplying a narrow zone of incipient seafloor spreading in the Afar depression. Within the uppermost mantle we report evidence of a localized asthenospheric upwelling beneath the western part of the plateau southeast of Lake Tana, overlying a cooled magma body within the upper crust. A broader low-velocity uppermost mantle underlies the crust beneath the Western Plateau. These observations attest to active mantle upwelling, heating, and melt intrusion at relatively different length scales beneath the plateau in agreement with the ongoing active strains reported away from the rift zones. At 45–60 km depth beneath the rift and its shoulders, we observe a fast lid (4.2–4.4 km/s). Beneath the plateau, upper mantle velocity highs that are at least 5 km below the Moho are observed. These areas have most likely experienced prolonged magma extraction and may mark highly depleted areas.

A Benchmark for the Bayesian Inversion of Coefficients in Partial Differential Equations

A Benchmark for the Bayesian Inversion of Coefficients in Partial Differential Equations

Crustal structure and seismic anisotropy of rift basins in Somaliland

Rift margins provide insights into the processes governing the rupture of the continental lithosphere and the subsequence formation of sedimentary basins. The Proterozoic basement underlying Somaliland has been affected by multiple rifting; however, the crustal structure of these rifted basins remains unknown. This study utilized teleseismic receiver function analysis, Bayesian inversion, common conversion point imaging and 2D forward gravity modelling to examine the crust and upper mantle of Somaliland. The results indicate 36.8–38.2 km of crust in southern Somaliland, while the central and northern regions feature thinned crust (~ 21 km) with 5–6 km thick sediments. The joint analysis of radial and transverse components of receiver functions and shear wave splitting revealed fast axis directions trending to 50–56° in the upper mantle, indicating that azimuthal anisotropy is oriented in the regional Africa-Arabia plate motion. Such orientation may have resulted from lattice preferred orientation of olivine from the asthenospheric flow. Additionally, the fast polarization of the crust in central Somaliland is oriented at − 15°, indicating fossil deformation in the thinned crust related to the NW–SE trending Late Jurassic rift event. Further, the fast polarization for stations near the Gulf of Aden is oriented at 75–80°, suggesting crustal deformation associated with the Oligocene rift event. The crustal anisotropy at southern Somaliland revealed fast polarization oriented at − 85°, indicating a preserved far-field response of the WNW-ESE trending Late Cretaceous rift event. Overall, the study provides for the first-time insight into the rift-related extensional strain fabric in the crust and upper mantle anisotropy induced by asthenospheric flow in Somaliland.

InSAR-observed surface deformation in New Mexico’s Permian Basin shows threats and opportunities presented by leaky injection wells

Knowledge of aquifer dynamics, including groundwater storage changes, is key to effective groundwater resource and reservoir management. Resolving and accurate modeling of these processes requires knowledge of subsurface poroelastic properties and lateral heterogeneity within units of interest. Computationally demanding methods for determining lateral heterogeneity in poroelastic properties exist but remain difficult to practically employ. The InSAR-based detection of uplift over a New Mexico well with a casing breach provides an opportunity to determine poroelastic properties using a tractable 2D analytical plane strain solution for surface uplift created by a pressurized reservoir with overburden. Using a Bayesian inversion framework, we calculate poroelastic properties under deep (depth of well-screen) and shallow (depth of well-breach) conditions. We find that shallow injection is necessary to produce the observed deformation. However, pressure-varying forward solutions for uplift are required to reproduce the temporal evolution of deformation. For this we use realistic shallow poroelastic properties and well dynamics, which reflect the evolving injection conditions at the well breach as the casing further erodes. Analysis of individual interferograms or InSAR time series may provide insights into shallow subsurface heterogeneity or anomalous injection conditions at operating wells more rapidly than scheduled field inspections.

Divide-and-conquer DNN approach for the inverse point source problem using a few single frequency measurements

We consider the inverse problem to determine the number and locations of acoustic point sources from single low-frequency partial data. The problem is particularly challenging in the sense that the data is available only at a few locations which span a small aperture. Integrating the deep neural networks (DNNs) and Bayesian inversion, we propose a divide-and-conquer approach by dividing the inverse problem into three subproblems. The first subproblem is to determine the number of point sources, which is formulated as a common machine learning task—classification. A simple DNN is proposed and trained to predict the numbers of the point sources. The second subproblem is to reconstruct the (approximate) locations of the point sources. We formulate the problem as a nonlinear function with the input being the measured data and the output being a carefully elaborated location vector. Then a second DNN is proposed to learn the mapping and predict the location vector effectively. The location vector is post-processed to provide an indicator (image) function for the (approximate) locations of the point sources. The third subproblem is to improve the accuracy of the location prediction, for which we employ a Bayesian inversion algorithm. This divide-and-conquer approach can effectively treat both phase and phaseless data as demonstrated by various examples.

Petrophysical interpretation of logging-while-drilling borehole measurements in the presence of electrical anisotropy, mud-filtrate invasion, noise, and well deviation effects

Petrophysical interpretation of logging-while-drilling (LWD) borehole measurements in the presence of electrical anisotropy, mud-filtrate invasion, noise, and well deviation effects remains a challenge in formation evaluation. In high-angle and horizontal (HAHZ) wells penetrating electrically anisotropic sandstones, phase and attenuation apparent resistivity logs often exhibit values larger than resistivity parallel to bedding planes. Consequently, traditional interpretation methods often fail to accurately estimate hydrocarbon saturation when using only the long-spacing phase apparent resistivity log (P40H) in petrophysical calculations. We implement two approaches (analytical and Bayesian) to estimate horizontal and vertical resistivities from apparent resistivity measurements. The first analytical approach is based on the numerical simulation of LWD resistivity measurements using synthetic models under various conditions of electrical anisotropy and well inclination to derive analytical models. The relative error of analytical approximations is less than 6%. In the presence of measurement noise and shoulder-bed effects, we implement a Bayesian method for well-log inversion and uncertainty quantification. The relative error of Bayesian inversion is less than 2%. Estimates of horizontal and vertical resistivities then can be used for petrophysical analysis. A challenging set of synthetic and field examples of HAHZ wells penetrating electrically anisotropic formations is selected for examination and verification of the new methods. For radial lengths of invasion less than 20 cm (8 in), sensitivity analysis indicates that the effects of conductive mud-filtrate invasion on long-spacing resistivity logs are negligible. The long-spacing phase (P40H) and attenuation (A40H) apparent resistivities are used to estimate horizontal and vertical resistivities. In the field examples under study, electrical anisotropy is caused by intercalated laminations of coarse- and fine-grained sandstones; the volumetric concentration of shale is negligible. Considering that Archie’s parameters are direction dependent, sensitivity analysis indicates that the effective value of the saturation exponent parallel to bedding planes is less sensitive to the volumetric concentration of fine-grained sandstone layers compared with the saturation exponent perpendicular to bedding planes. Thus, water saturation of grain-laminated sandstones in HAHZ wells can be estimated using horizontal resistivity with Archie’s parameters that are consistent with petrophysical interpretations performed in vertical wells. Estimates of water saturation in the field examples using horizontal resistivity agree with saturation-height models. Compared with conventional interpretation methods that use P40H as the formation resistivity, the new approach improved the estimation of hydrocarbon saturation by 10%.

Astronomical Forcing of Sea‐Level Changes and the History of the Solar System 1,640 Million Years Ago

AbstractThe Paleoproterozoic was an important stage in the evolution of life and the environment during Earth's history. Understanding astronomical rhythms and solar system behavior in the Paleoproterozoic is often challenging. In this study, ∼190 m high‐resolution magnetic susceptibility (MS) and ∼30 m high‐resolution Ba/Al data are used to conduct cyclostratigraphic analyses of the Chuanlinggou Formation in the Yanliao Rift, North China Craton. Spectral analysis indicates significant peaks at wavelengths of 12.1–7.7, 2.8–1.6, 0.58–0.33, and 0.29–0.22 m, which matches well with the astronomical cycles predicted by Waltham for ∼1,640 Ma. A 9.9‐Myr astronomical time scale is constructed by tuning the MS series to the 405‐kyr‐long eccentricity cycle. The geological records show ∼1.56‐Myr very long eccentricity period and ∼1.0‐Myr very long obliquity period (close to 3(s4 − s3) − 2(g4 − g3) = 0) in the Paleoproterozoic. The sea‐level change curve predicted by dynamic noise models reveals a significant ∼1.0‐Myr period, indicating that sea level fluctuation may have been driven by the very long obliquity period. Bayesian inversion is used to further estimate the evolution of the ancient Earth‐Moon orbital parameters, constraining a precession rate of 87.14 ± 0.25 arcsec/year and an Earth‐Moon distance of 341,530 ± 390 km for the Paleoproterozoic Changcheng System. These results indicate that astronomical orbital forcing may have played an important role in climate and sea‐level changes in the Precambrian, increasing the understanding of the fundamentals of global sea level fluctuations, orbitally driven mechanisms and the chaotic behavior of the Precambrian solar system.

A general model for sediment-column structure on the New England Mud Patch from Bayesian geoacoustic inversion of seabed reflection data

Muddy sediments cover significant portions of continental shelves, but their physical properties remain poorly understood compared to sandy sediments. To explore the spatial and frequency dependencies of mud properties, wide-angle seabed reflection coefficients versus grazing angle and frequency were measured on the New England Mud Patch (NEMP) during the 2017 Seabed Characterization Experiment. This paper presents trans-dimensional Bayesian inversion of reflection coefficients within a frequency band of 1–3 kHz and an angular range of ∼15–25° to obtain geoacoustic profiles and associated uncertainties, as well as frequency dependencies of sound speed and attenuation. The estimated geoacoustic profiles are similar to those from previous inversions of reflection-coefficient data at lower frequencies (0.4–1.3 kHz) collected at two different sites on the NEMP. Based on the inversion results at all three sites, a general interpretive model for sediment-column structure and variability is synthesized for the NEMP. This model includes an upper mud layer in which sediment properties change slightly with depth due to near-surface processes, an intermediate mud layer with uniform properties, and a transition layer where properties change rapidly with depth due to increasing sand content in the mud above a sand layer. [Work supported by the Office of Naval Research.]

Geoacoustic inversion of wide-angle reflection-coefficient data to estimate sediment shear properties

This paper considers Bayesian geoacoustic inversion of broadband, wide-angle reflection-coefficient data including shear parameters in the seabed model to investigate the ability to estimate these parameters as well as effects on the estimation of other geoacoustic parameters, particularly compressional-wave attenuation. The seabed parameterization is based on the viscous grain-shearing (VGS) sediment-acoustic model, including the grain-to-grain shear modulus as an unknown parameter. VGS sediment parameters are transformed to density and frequency-dependent compressional- and shear-wave speeds and attenuations. Data prediction involves spherical-wave reflection-coefficient calculations. Trans-dimensional inversion, which samples probabilistically over the number of layers in the seabed model, is applied to combine quantitative model selection with parameter/uncertainty estimation. The inversion is applied to reflection-coefficient data sets collected on the New England Mud Patch, and inversion results are compared to those obtained under the common assumption of negligible shear effects (i.e., inverting for a fluid sediment model).

Passive acoustic glider for marine acoustic environment characterization

Acoustic payload-equipped underwater gliders have great potential for assessing the marine soundscape (oceanic acoustic environment), including characterizing properties of the sound field, of acoustic sources, and of the marine environment (water column and seabed). This talk presents observations and analysis of passive acoustic recordings carried out by gliders during the 2017 Seabed Characterization Experiment (SBCEX17). Two Teledyne Webb Research Slocum gliders equipped with omni-directional hydrophones were deployed as virtual acoustic moorings in 72 m deep water on the New England Mud Patch for time periods of ∼6 days for one glider and ∼3 days for the other. Acoustic recordings collected by the gliders captured the marine soundscape, including natural ambient noise, marine-life sounds, ship noise, and acoustic signals transmitted by the SBCEX17 participants. The acoustic environment in the water column is characterized in terms of the acoustic power spectral density as a function of time, depth, and frequency. As an example of the use of passive acoustic gliders for environmental characterization, Bayesian geoacoustic inversion for seabed properties is presented, making use of recordings of controlled sources associated with SBCEX17. [Work supported by the Office of Naval Research.]

Depth and frequency dependence of geoacoustic properties on the New England Mud Patch from reflection coefficient inversiona).

Muddy sediments cover significant portions of continental shelves, but their physical properties remain poorly understood compared to sandy sediments. This paper presents a generally applicable model for sediment-column structure and variability on the New England Mud Patch (NEMP), based on trans-dimensional Bayesian inversion of wide-angle, broadband reflection-coefficient data in this work and in two previously published reflection-coefficient inversions at different sites on the NEMP. The data considered here include higher frequencies and larger bandwidth and cover lower reflection grazing angles than the previous studies, hence, resulting in geoacoustic profiles with significantly better structural resolution and smaller uncertainties. The general sediment-column structure model includes an upper mud layer in which sediment properties change slightly with depth due to near-surface processes, an intermediate mud layer with nearly uniform properties, and a geoacoustic transition layer where properties change rapidly with depth (porosity decreases and sound speed, density, and attenuation increase) due to increasing sand content in the mud above a sand layer. Over the full frequency band considered in the new and two previous data sets (400-3125 Hz), there is no significant sound-speed dispersion in the mud, and attenuation follows an approximately linear frequency dependence.

A Bayesian inversion for emissions and export productivity across the end-Cretaceous boundary.

The end-Cretaceous mass extinction was marked by both the Chicxulub impact and the ongoing emplacement of the Deccan Traps flood basalt province. To understand the mechanism of extinction, we must disentangle the timing, duration, and intensity of volcanic and meteoritic environmental forcings. In this study, we used a parallel Markov chain Monte Carlo approach to invert for carbon dioxide (CO2) and sulfur dioxide (SO2) emissions, export productivity, and remineralization from 67 to 65 million years ago using the LOSCAR (Long-term Ocean-atmosphere-Sediment CArbon cycle Reservoir) model. Our results closely match observed and proxy data and suggest decoupled CO2 and SO2 emissions, a two-step decline in export productivity with a protracted recovery, and no clear volatile impulse at the boundary. More broadly, our methods provide a potential path forward for efficient parallel inversion of complex Earth system models.

Proxy-based Bayesian inversion of strain tensor data measured during well tests

Recent instrument developments have made it possible to measure the strain tensor caused by injecting or pumping fluid from aquifers or reservoirs, but the full value of these data is limited because the long runtimes of poroelastic forward models makes it impractical to use many inversion schemes. This limits the interpretation of strain data for managing the recovery of resources or storage of wastes in the subsurface. This paper describes a method of inverting deformation data using a poroelastic numerical simulator so the results can be used to manage reservoirs or aquifers. We developed a workflow designed to reduce the number of simulations sufficiently to make it feasible to use DREAMzs, an advanced Bayesian inversion method that translates the uncertainties from different sources into unbiased posterior parameter distributions and uncertainty envelopes around the field data. Using a KNN proxy model for the poroelastic simulator is key to reducing the overall computations, and the workflow includes a strategy for ensuring the proxy model results converge on the results from the simulator. The workflow is tested using an idealized example that verifies the ability to correctly identify parameters and characterize noise used to perturb the data. Field data from an injection test at an oil reservoir near Tulsa, Oklahoma, are also used to evaluate the efficacy of the workflow with a real dataset. The workflow identified 265 history matching solutions out of 1240 total simulation runs (21% acceptance ratio), where the results were used to characterize posterior parameter distribution and evaluate the prediction uncertainty. This workflow is significant because it enables strain tensor, or other geomechanical measurements to be interpreted to guide decision-making during energy and environmental processes in the subsurface.

Seismic structure of the Eastern European crust and upper mantle from probabilistic ambient noise tomography

The Eastern European lithosphere is a natural laboratory to study continental formation and evolution through time, comprising Archean continental remnants, Proterozoic rifts and belts, and younger accreted terranes. We investigate the seismic structure of the East European Craton (EEC) crust and uppermost mantle, and the transition from Precambrian to Phanerozoic Europe across the Trans European Suture Zone (TESZ) using probabilistic transdimensional ambient noise tomography. We cross-correlate noise recorded at broadband seismic stations from Eastern, Northern, and Central Europe, remove earthquake signals using continuous wavelet transform, and extract Rayleigh wave phase velocity dispersion curves. We invert these for the highest resolution shear wave velocity model of the Eastern European lithosphere to date, using Markov chain Monte Carlo Bayesian inversion. Our shear wave velocity model exhibits spatial correlation with major tectonic units and bears similarities with active seismic survey profiles in terms of seismic velocity patterns and main discontinuities. The crust thickens across the TESZ boundary and the mantle is seismically faster than beneath younger terranes, consistent with a less dense Precambrian lithosphere in the EEC. The crust and lithosphere beneath the Pannonian region is hyper-extended but the adjacent Transylvanian basin crust shows significant heterogeneity. The Precambrian building blocks of the EEC exhibit contrasting seismic fabrics. The Baltic orogens of Fennoscandia are underlain by uniform crust with a flat Moho, while Sarmatia shows alternating high and low velocity layers and a regional south-dipping crustal boundary from beneath the Ukrainian Shield towards the Crimean Peninsula. The last observation supports a geodynamic style driven by horizontal rather than vertical tectonics, with fundamental implications for the formation and evolution of early continents.