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Results for “Mathematical Geosciences”

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USGS2026

Uncertainty quantification of geologic energy storage in depleted gas reservoirs using material balance equations embedded in a hierarchical errors-in-variables model

The storage potential for gas in geologic settings, such as depleted hydrocarbon reservoirs and solution-mined salt caverns, is becoming salient to future energy infrastructure planning. Technologies such as carbon capture, utilization, and storage, carbon dioxide-enhanced oil recovery, and natural gas and hydrogen storage help meet growing energy demands, reduce carbon emissions to meet climate goals, and provide energy security amid geopolitical uncertainties. Therefore, estimates of underground gas storage capacity could be useful for efficiently navigating the energy transitions. Material balance is a fundamental method in reservoir engineering for estimating original gas in place and potential storage capacity at the scale necessary for national assessments of subsurface pore space resources. However, the deterministic method cannot accommodate multiple data sources or quantify uncertainty in predictions. In this study, a method that embeds material balance equations within a hierarchical errors-in-variables model is proposed which allows the estimation of the distributions of reservoir properties needed for assessments. Uncertainties associated with these reservoir properties have traditionally been expert-elicited, whereas the uncertainty estimates from the proposed models are data-driven. Capacity and uncertainty estimates can be used in a probabilistic resource assessment, supplementing information traditionally used by assessors or even replacing this expert elicitation step when data are unavailable. Various regression models are compared in a case study of the Michigan Basin, a large contributor to the United States’ current natural gas storage capacity. In particular, errors-in-variables models help ameliorate regression dilution and can quantify uncertainty in predictions of pressure in addition to storage capacity. Overfitting is addressed by quantifying generalization error and model averaging in simple and stratified cross-validation against reported working gas capacity, representing the varying quality and quantity of available data. Incorporating a statistical framework into existing numerical methods in reservoir engineering can improve the quality of estimation, and in particular, this method brings rigor to uncertainty quantification as part of a larger effort by the U.S. Geological Survey to assess domestic energy gas storage resources in depleted hydrocarbon reservoirs.

Mathematical Geosciences↗

USGS2024

Hypothetical CO2 leakage into, and hydrological plume management within, an underground source of drinking water at a proposed CO2 storage facility, Kemper County, Mississippi, USA

A large Geologic Carbon Sequestration (GCS) hub has been proposed in Kemper County, Mississippi. The target injection interval consists of numerous Cretaceous-aged deep saline aquifers overlain by a competent and extensive regional sealing layer. Above the seal, the deepest Underground Source of Drinking Water (USDW) at the site is the Eutaw aquifer of the Eutaw Group and McShan Formation, undifferentiated. To assess potential risks of leakage from the deep sequestration reservoir, a model of a portion of the Cretaceous Eutaw Group was constructed in this study. Simulations tested various permeabilities, hypothetical leakage rates, and plume mitigation strategies utilizing existing wells. Results suggest that, under the influence of regional groundwater flow fields, leaking CO 2 would effectively bypass the existing wells, and to influence this migration would require very large water extraction rates. Therefore, to ensure plume detection, monitoring for leakage at the injection wells themselves is very important.

Mississippi↗

USGS2026

3D semantic mapping of surface geological features

Semantic mapping in 3D is fundamental to a wide range of geoscientific studies and applications, including geomorphology, hazard assessment, and environmental monitoring. However, automatically segmenting geological features from large-scale photogrammetric datasets remains a significant challenge. We present a methodology to address this gap. Using overlapping images collected over environments of interest, Structure-from-Motion (SfM) produces georeferenced point clouds and estimates camera poses. Existing large vision models, such as Segment Anything Model, segment objects in the images, generating pixel-segmentation associations. To produce pixel-point associations, we project the points back onto the camera image planes. As objects are independently segmented across multiple images with different perspectives, we develop a segmentation mosaicking algorithm to build probabilistic point-segmentation associations that combines the pixel-segmentation associations and pixel-point associations. Our methodology is validated using both synthetic data generated by Kubric and real-world UAV-SfM data. The implementation is designed to be compatible with existing SfM software, including Agisoft and OpenDroneMap, for photogrammetry mapping in geoscience studies. As a case study, we apply our method to the semantic mapping of precariously balanced rocks (PBRs), which provide upper-bound constraints on historical ground motion shaking intensity. To support object-level identification of PBRs, we additionally integrated Grounding DINO, enabling text-prompted segmentation of features of interest within UAV imagery. This case study demonstrates the effectiveness of our method in generating a 3D semantic map of PBRs, enabling spatial distribution of PBR fragility for earthquake hazard analysis.

Computers & Geosciences↗

USGS2025

From critical minerals to food security, the benefits of data collaboration

The volume of data in the public geoscience sphere is rapidly and continually expanding. At Geoscience Australia (GA) we saw an over 500% increase in data points within our relational databases between 2018 and 2024, over the life of the Exploring for the Future (EFTF) program. With the Resourcing Australia’s Prosperity initiative, a continued increase in data quantity will be seen for the next 10 to 35 years. At the same time, a broadening audience for geoscience data is increasing the desire to enhance the diversity of delivery streams. This ranges from data-dense highly technical outputs for geoscience specialists to curated interpretive products for people who are non-geoscientists. Development of these curated outputs has contributed to our awareness of the need for data to be collected and compiled in a way that ensures its reuse, with a focus on quality metadata and data provenance.

Conference Paper↗

USGS2025

Extracting data from maps: Lessons learned from the artificial intelligence for critical mineral assessment competition

The U.S. Geological Survey (USGS), Defense Advanced Projects Research Agency (DARPA), NASA Jet Propulsion Laboratory (JPL), and MITRE ran a 12-week machine learning competition aimed at accelerating development of AI tools for critical mineral assessments. The Artificial Intelligence for Critical Mineral Assessment Competition solicited innovative solutions for two challenges: 1) automated georeferencing of historical maps, and 2) automated feature extraction from historical maps. Competitors used a new dataset of historical map images to train, validate, and evaluate their models. Automated georeferencing pipelines attained a median root-mean square error of 1.1 km. Prompt-based extraction (i.e., with user input) of polygons, polylines, and points from geologic maps yielded median F1-scores of 0.77, 0.56, 0.35, respectively. Geologic maps pose numerous challenges for AI workflows because they vary significantly. However, despite its short duration, the competition yielded promising results that have since spurred further innovation in this area and led to the development of new AI tools to semi-automate key, time-consuming parts of the assessment workflow.

Applied Computing and Geosciences↗

USGS2025

Ambient field seismology in critical zone hydrological sciences

Passive ambient noise monitoring is an emerging tool in environmental seismology, leveraging the ambient seismic field to assess temporal variations in shallow subsurface properties. This review focuses on the potential and challenges of using scattered coda waves from noise correlation functions to monitor critical zone dynamics. The sensitivity of seismic velocities to various environmental factors, including precipitation, snowmelt, atmospheric pressure, and groundwater fluctuations, underscores the method’s versatility. While coda waves excel in detecting subtle changes due to their scattered nature, ballistic waves provide higher spatial resolution, albeit with challenges in source stability. Advances in seismic sensing, including distributed acoustic sensing and low-cost geophone networks, have enabled high-resolution monitoring of hydrological processes, subsurface deformation, and seismic hazards. Integrating seismic data with hydrological models provides insights into water storage, pore pressure changes, and soil moisture dynamics. However, limitations in spatial resolution, calibration with ground truth data, and coupled effects between environmental factors remain key challenges. This review emphasizes the importance of interdisciplinary approaches in refining methodologies, enhancing sensor deployments, and addressing data gaps. Passive seismic monitoring offers opportunities to understand critical zone processes and their broader impacts on seismic hazards and environmental sustainability.

Comptes Rendus. Géoscience↗

USGS2025

Statistical approaches for modeling correlated grade and tonnage distributions and applications for mineral resource assessments

Correlations between grade and tonnage exist in mineral resource data compiled from published reports, but they are not always addressed during quantitative assessment of undiscovered mineral resources. Failure to account for correlated grade and tonnage distributions can result in geologically unrealistic assessment results. Current software tools simulate univariate ore tonnage and multivariate resource grades of undiscovered deposits independently. As a result, analysts are forced to rely on ad-hoc solutions to minimize the correlation issues by: 1) creating subsets of data with restricted criteria; 2) truncating grade and tonnage distributions; and 3) testing model robustness using exploratory data analysis. While these methods represent pragmatic solutions, the statistical solutions presented here provide additional options to address real correlations in grade and tonnage data used for mineral resource assessments. We present a modified version of the MapMark4 package in R that introduces two alternatives for modeling grade and tonnage distributions, consisting of a multivariate solution that accounts for correlations between ore tonnage and metal grades and an empirical solution that utilizes simple random sampling with replacement to reproduce coupled grades and tonnages from the input data. We present simulations for contained ore and metal for three case studies representing tungsten skarn, komatiite-hosted nickel, and sediment-hosted carbonate amagmatic zinc-lead (Mississippi Valley-type) deposits. Employing the methods presented here yields quantitative mineral resource assessment results that more closely reflect the empirical distributions of grades and tonnages observed in nature and expands the applicability of these tools for ongoing critical mineral resource assessments.

Applied Computing and Geosciences↗

USGS2025

Predictive regressive models of recent marsh sediment thickness improve the quantification of coastal marsh sediment budgets

Coastal marsh wetlands experience variations in vertical gains and losses through time, which have allowed them to infill relict topography and record variations in drivers. The stratigraphic unit associated with the development of the marsh also reflects the long-term importance of key ecosystem services supplied by the marsh environment, including carbon storage and storm mitigation. Mapping these coastal wetland sediments and the marsh unit thickness is challenging as traditional coastal geophysical tools are not easily deployable (acoustic methods) or are unreliable in saline-soil environments (e.g., ground-penetrating radar), leaving core-based methods the most viable mapping method. In the present study, we utilized prior information on the geologic architecture of the region to select spatial and physical metrics that likely persisted throughout evolution of the marsh during the late Holocene. We then assessed the individual and collective power of these metrics to predict marsh thickness observed from cores. Employing regressive predictive models powered by these data, we improve the quantification of marsh thickness for a coastal fringing marsh within the Grand Bay estuary in Mississippi and Alabama (USA). The information gained from this approach yields improved estimates of the carbon stocks in this environment. Additionally, the stored sediment masses reflect the past, and potential future, persistence of the Grand Bay marsh under historical and present marsh-estuarine sediment exchange fluxes. Such improvements to both the sediment budget of recent marsh stratigraphic units and the spatial extent provide new resources for comparison with large-scale landscape models, the latter of which may be used, when validated, to predict future change and ecosystem transformations.

Alabama. Mississippi↗

USGS2026

The mineral chemistry networks of tin and tungsten reflect metallogenic eras of the Mesozoic

Continental remobilization is a crucial driver of metallogenesis and the formation of ore deposits. Some of the world’s largest mineral deposits of the economically valuable elements tin (Sn), tungsten (W), gold (Au), copper (Cu), lead (Pb), and zinc (Zn) formed during the Mesozoic Era. Additionally, the chemistry and distribution of the elements Sn and W have been investigated in previous studies to understand planetary formation and differentiation processes. These two elements are largely co-located during certain South China Mesozoic metallogenic events but are not co-located during other time periods in the same regions. Here, we investigated the mineral chemistry network similarities and dissimilarities of Sn and W to understand their mineral formation and distribution during the Mesozoic Era and throughout Earth history. Mineral chemistry network community detection analysis and electronegativity associations among mineral constituent elements of Sn minerals and W minerals indicate that the elements have similar chemistry among their oxide minerals. However, Sn forms a much wider range of minerals that also contain S compared to W, which occurs in a limited number of S-containing minerals. The divergent constituent element interactions among S-containing Sn minerals and W minerals reflect the redox sensitivity and importance of oxygen (O) fugacity in Sn mineral formation. Conversely, extensive W mineral deposits are known to form at both high and low O fugacities. The similarities and differences between the mineral chemistry networks of Sn and W reflect the mineral distribution of the two elements in the Sn-W mineralization event from 160 to 139 Ma vs. the Sn–uranium (U) mineralization event from 125 to 98 million years ago (Ma). The mineral chemistry and distribution of Mesozoic Sn and W deposits illustrate the contrasting importance of redox and O fugacity on the mineral formation of different elements, and the dynamic crustal evolution that took place during this period of Earth history.

Geosciences↗

USGS2007

Divisions of geologic time—Major chronostratigraphic and geochronologic units

Effective communication in the geosciences requires consistent uses of stratigraphic nomenclature, especially divisions of geologic time. A geologic time scale is composed of standard stratigraphic divisions based on rock sequences and calibrated in years. Over the years, the development of new dating methods and refinement of previous ones have stimulated revisions to geologic time scales. Since the mid-1990s, geologists from the U.S. Geological Survey (USGS), State geological surveys, academia, and other organizations have sought a consistent time scale to be used in communicating ages of geologic units in the United States. Many international debates have occurred over names and boundaries of units, and various time scales have been used by the geoscience community. For consistency purposes, the USGS Geologic Names Committee and the Association of American State Geologists developed Divisions of Geologic Time .

Fact Sheet↗

USGS2018

Divisions of geologic time—Major chronostratigraphic and geochronologic units

Introduction Effective communication in the geosciences requires a consistent nomenclature for stratigraphic units and, especially, for divisions of geologic time. A geologic time scale is composed of standard stratigraphic divisions based on rock sequences and is calibrated in years. Geologists from the U.S. Geological Survey (USGS), State geological surveys, academia, and other organizations require a consistent time scale to be used in communicating ages of geologic units in the United States. Many international debates have occurred over names and boundaries of units, and various time scales have been used by the geoscience community. For consistent usage of time terms, the USGS Geologic Names Committee and the Association of American State Geologists developed the Divisions of Geologic Time ; the 2018 update in this fact sheet contains the unit names and boundary age estimates ratified by the International Commission on Stratigraphy in 2018. Scientists may use other published time scales, provided that these are specified and referenced.

Fact Sheet↗

USGS2025

What 25+ years of "Did You Feel It" intensities tell us about shaking in California

“When will the Big One happen?” is a question that people often have for earthquake scientists. But while waiting for the “Big One” to occur, people will usually experience frightening or damaging shaking from multiple relatively smaller‐magnitude earthquakes. Given this context, it raises the question: “Where does most of the damage come from?” Could smaller, yet more frequent, earthquakes account for the majority of reported impactful shaking? To explore this question, we consider reports of earthquake damage and felt shaking experiences from a catalog of community‐collected intensity values from the U.S. Geological Survey’s “Did You Feel It?” system. Comparing these intensities to expectations from a ground‐motion model, we find that earthquakes of magnitudes smaller than expected are responsible for most reported intensities of community decimal intensities (CDI) 4.5 and above (moderate and higher shaking intensity levels). (Here “expected value” is meant in its mathematical sense of the mean or equivalently median shaking intensity.) We also present a regional analysis of observed earthquake shaking for specific areas, detailing the maximum intensity experienced within a predetermined area. We identify several instances of M < 4.5 events that generated maximum intensities of CDI > 5 in regions in California surrounding the cities of Eureka, San Francisco, Los Angeles, and San Diego. Our results motivate the need to include smaller‐magnitude earthquakes in communications about earthquake hazard and risk reduction.

California↗

USGS2025

Beyond optimality: Dryland ecosystems infrequently use water efficiently for carbon gain

Optimality theory assumes plants maximize carbon gain per unit water lost and is often implemented to scale leaf-level carbon gain and water use to regional and global scales. Optimality theory is often mathematically represented by assuming plant water-use efficiency (WUE) scales with VPD k , where k = ½ represents expected optimal behavior. It is unclear, however, if this relationship holds in arid and semi-arid ecosystems that are strongly impacted by soil and atmospheric moisture status. We used data from seven flux tower sites along an aridity gradient in New Mexico to answer: how does the relationship between WUE and VPD compare to expectations based on optimality theory? To address this question, we integrated the Dynamic Evapotranspiration Partitioning Approach for Rapid Timescales with a stochastic antecedent model to estimate ecosystem-level WUE (GPP/T) and the net sensitivity of WUE to VPD, or k Dynamic , which we compare to the theoretical optimal sensitivity of k = ½. Our results show that optimality theory is not always appropriate, and k Dynamic often deviates from ½, especially at some of the more arid sites or during periods of low soil moisture. At less arid, higher elevation sites, k Dynamic is most consistent with optimality theory at moderate VPD levels, but not at high VPD. In general, the sensitivity of WUE to VPD is highly variable such that k Dynamic exhibits notable daily and seasonal variability, suggesting highly dynamic stomatal behavior. These results emphasize that representing plant water-use strategies as dynamic in time and space is critical to improving large-scale estimates of plant water use.

New Mexico↗

USGS2010

Divisions of geologic time—Major chronostratigraphic and geochronologic units

Effective communication in the geosciences requires consistent uses of stratigraphic nomenclature, especially divisions of geologic time. A geologic time scale is composed of standard stratigraphic divisions based on rock sequences and is calibrated in years. Over the years, the development of new dating methods and the refinement of previous methods have stimulated revisions to geologic time scales. Advances in stratigraphy and geochronology require that any time scale be periodically updated. Therefore, Divisions of Geologic Time, which shows the major chronostratigraphic (position) and geochronologic (time) units, is intended to be a dynamic resource that will be modified to include accepted changes of unit names and boundary age estimates. This fact sheet is a modification of USGS Fact Sheet 2007-3015 by the U.S. Geological Survey Geologic Names Committee.

Fact Sheet↗

USGS2026

Bascom Laser Diffraction Sedimentology Laboratory, Reston, Virginia

Introduction At the Bascom Laser Diffraction Sedimentology Laboratory, which is located in the Florence Bascom Geoscience Center at U.S. Geological Survey (USGS) headquarters in Reston, Virginia, scientists use physical sedimentology and particle characterization techniques to conduct detailed sediment characterization. Scientists address research problems in collaboration with other USGS science centers, State geological surveys, commercial industry, universities, and other partners. Laboratory capabilities include laser diffractometry for quantitative particle-size analysis, portable x-ray fluorescence (XRF) analysis for determining elemental abundances in rock or sediment samples, petrographic analysis of geologic media, and mechanical sieve analysis. These methods are used to analyze soil and sediment core material from terrestrial, marine, and lacustrine environments, surface sediments from coastal regions, and calcareous materials. Work done by the laboratory supports geologic mapping, resource assessments, land change studies, and geohazard analyses.

Fact Sheet↗

USGS2025

Invited perspectives: Integrating hydrologic information into the next generation of landslide early warning systems

Although rainfall-triggered landslides are initiated by subsurface hydro-mechanical processes related to the loading, weakening, and eventual failure of slope materials, most landslide early warning systems (LEWS) have relied solely on rainfall event information. In previous decades, several studies demonstrated the value of integrating proxies for subsurface hydrologic information to improve rainfall-based forecasting of shallow landslides. More recently, broader access to commercial sensors and telemetry for real-time data transmission has invigorated new research into hydrometeorological thresholds for LEWS. Given the increasing number of studies across the globe using hydrologic monitoring, mathematical modeling, or both in combination, it is now possible to make some insights into the advantages versus limitations of this approach. The extensive progress demonstrates the value of in situ hydrologic information for reducing both failed and false alarms, through the ability to characterize infiltration during, as well as the drainage and drying processes between major storm events. There are also some areas for caution surrounding the long-term sustainability of subsurface monitoring in landslide-prone terrain, as well as unresolved questions in hillslope hydrologic modeling, which relies heavily on the assumptions of diffuse flow and vertical infiltration but often ignores preferential flow and lateral drainage. Here, we share a collective perspective based on our previous collaborative work across Europe, North America, Africa, and Asia to discuss these challenges and provide some guidelines for integrating knowledge of hydrology and climate into the next generation of LEWS. We propose that the greatest opportunity for improvement is through a measure-and-model approach to develop an understanding of landslide hydro-climatology that accounts for local controls on subsurface storage dynamics. Additionally, new efforts focused on the subsurface hydrology are complementary to existing rainfall-based methods, so leveraging these with near-term precipitation forecasts is a priority for increasing lead times.

Alaska↗

USGS2025

Critical Minerals in Ores (CMiO) database

Critical minerals are commodities essential to modern industrial and strategic technologies and are highly vulnerable to supply chain disruption. The Critical Minerals Mapping Initiative (CMMI) is a collaboration among the U.S. Geological Survey (USGS), the Geological Survey of Canada, and Geoscience Australia that aims to deepen global understanding of where critical minerals are located. A key output of this initiative is the Critical Minerals in Ores (CMiO) database that is advancing our collective understanding of critical minerals distributions. For instance, publicly available data on the concentrations of many critical minerals are sparse because these commodities can only be produced in small, yet essential, quantities compared to the primary commodities like copper and zinc. The CMiO database helps bridge this gap by offering high-quality, multielement geochemical data from a wide variety of critical mineral-bearing deposits around the world. Importantly, it uses a novel consensus deposit environment, group, and type classification scheme developed by the agencies that allows comparisons among ore deposits from different regions. The CMiO database contains geochemical data for more than 20,000 samples from more than 100 deposit types comprising 10 deposit environments.

Fact Sheet↗

USGS2026

USGS Geochron—A database of geochronological and thermochronological dates and data—Technical documentation

Geochronological and thermochronological data are essential for constraining the timing and rates of geological processes, supporting geologic mapping, natural hazard assessment, and resource exploration. The U.S. Geological Survey (USGS) Geochron Database is a centralized, relational database that integrates USGS and State geological survey data in accordance with the National Geologic Mapping Act of 1992 and its reauthorizations. This report documents the structure and development of the database, including its standardized schema, controlled vocabularies, and protocols for compiling legacy and newly published data. The database is designed to adhere to FAIR (Findable, Accessible, Interoperable, and Reusable) data principles and currently (2026) includes data from a wide range of geochronological and thermochronological methods. Public access is provided through the USGS Geochron Database Explorer, a browser-based geographic information system (GIS) interface, and through versioned data releases available on ScienceBase, which provide sample-level summary data and detailed analytical information. The USGS Geochron Database is structured to be extensible, supporting the inclusion of additional methods and data types as they are compiled. This format ensures long-term utility and aligns with the Mapping Act’s directive to create a national archive of geochronological information that adds interpretive value to geologic map data. Its design reflects a commitment to data transparency, scientific reproducibility, and national geoscience priorities.

Data Report↗