The northern Great Plains encompasses two prominent sedimentary basins with contrasting structural styles: the Powder River Basin of Wyoming and Montana, and the Williston Basin which spans South Dakota, North Dakota, and Montana and extends northward into Canada (fig. 3). Although geographically proximate, these basins and the uplifts defining their margins are associated with distinct orogenic events, subsidence histories, and structural styles, which are crucial to consider prior to model construction.

The Williston Basin is a nearly symmetrical intracratonic basin characterized by a thick and nearly continuous record of Phanerozoic sedimentation (Gerhard and others, 1990; fig. 4A, B). The total maximum thickness of the sedimentary package in the Williston Basin is approximately 4,611-m thick, and the maximum depth of the basin reaches approximately 4,200 m below sea level near Williston, North Dakota. Structural dips of the basin limbs are continuous and shallow (less than 2 degrees of dip), making the southern and eastern boundaries of the basin challenging to distinctly define to the south and east, where the crystalline Precambrian rocks rise toward modern-day land surface from the South Dakota Plains onto the Transcontinental Arch (Carlson, 1999; fig. 3).

Subsidence of the Williston Basin occurred episodically from the Middle Ordovician through the Late Mississippian, producing long-wavelength structural relief that is subtle in magnitude but regionally persistent (Crowley and others, 1985; Bader, 2019a). The few structural features in the basin formed during this time, such as the Nesson Anticline, which bisects the center of the basin, and Cedar Creek Anticline, which bounds the basin to the southwest (Gerhard and Anderson, 1988; Kent and Christopher, 2007). Notably, the fault controlling the Cedar Creek Anticline is one of the longest-lived structures in the northern Great Plains, having experienced multiple phases of normal and reverse motion since the Devonian (Clement, 1986).

Pennsylvanian through Late Cretaceous strata show broadly uniform thicknesses across the Williston, indicating relative tectonic stability during much of the Late Paleozoic and Mesozoic (Peterson, 1984; Smith and others, 2004). Far-field Laramide-derived strain is believed to be the penultimate phase of deformation and inversion of the Williston Basin from the Late Cretaceous to the late Paleogene, resulting in reactivation of major structural features to their modern-day configuration (Gelman, 2023). Modern strain is accommodated through structural lineaments, such as the Weldon and Brockton-Froid Fault Zones, which outcrop at the surface and offset Quaternary tills yet remain enigmatic in their origin (Wheeler, 1999). From a modeling perspective, the primary challenge in the Williston Basin is its low structural relief, where shallow dips and unconformities allow even minor geometric errors to propagate through the stratigraphic sequence over long distances.

In contrast to the structural symmetry of the Williston Basin, the Powder River Basin is classified as an “asymmetric broken foreland basin” formed during the Laramide orogeny (DeCelles, 2004; Yonkee and Weil, 2015; Horton and others, 2022; fig. 3). Sedimentary fill within the Powder River Basin spans the entire Phanerozoic but features a thin Paleozoic section relative to thick overlying Cretaceous and early Cenozoic strata (Glass, 1993; fig. 4A). The basin axis trends south–southeast and is flanked by a steep western limb defined by the Bighorn Uplift, Casper Arch, and Piney Creek Thrust Fault (fig. 3). The eastern limb of the basin shallows eastward at approximately 1 degree of dip until it meets the Black Hills Monocline and Miles City Arch. Stratal thicknesses exceeding 5,182 m are recorded along the basin axis, which reaches a maximum depth of approximately 4,177 m below sea level to the north of Casper, Wyoming (Blackstone, 1993). A subtle northeast-trending upwarp known as the Belle Fourche Arch bisects the basin axis (Blackstone, 1993).

Flexural subsidence of the Powder River Basin likely initiated due east–northeast oriented shortening in the Late Cretaceous (Yonkee and Weil, 2015; Carrapa and others, 2019). Continued northeast-directed shortening through the Paleocene and early Eocene activated low-angle, basement-involved fault networks and resulted in a series of basement uplifts and arches that define the western and southern margins of the Powder River Basin (Stone, 1993; DeCelles, 2004; fig. 3). The Piney Creek Thrust Fault is a classic example of Laramide basement faulting, exposing Precambrian crystalline rocks at the land surface due to as much as 4,100 m of vertical displacement along the Bighorn Uplift (Stone, 1993, 2003).

Despite the general east–northeast shortening trend, a series of en-echelon thrust faults bound the southern extent of the Powder River Basin against the Laramie Mountains and Hartville Uplift (Blackstone, 1988; Stone, 2002; fig. 3). The geometry of the faulted basin margin can be complex; local nuances in the geology result in an anastomosing network of subsurface faults and folds, transferring displacement along strike of the uplift (Hoy and Ridgway, 1997). Many of these features (such as the Northern Bounding Fault) are obscured by late Cenozoic basin fill and do not outcrop directly at the surface, but can be inferred from the geometry of preorogenic sedimentary units and seismic survey lines (Stone 1993; Blackstone, 1996; Hoy and Ridgway, 1997; Caylor and others, 2023). From a modeling perspective, the primary structural consideration in the Powder River Basin is accurately representing fault geometry and displacement while honoring detailed surface mapping in areas where subsurface data are sparse, legacy, or unevenly distributed.

Laramide intraplate stress activated low-angle basement-cored thrust faults as far east as the Black Hills Uplift, which is the eastern limit of the Cordilleran strain front (DeCelles, 2004). The Black Hills Uplift is a shallow broken foreland-type uplift that forms an elongate basement-cored antiform, exposing crystalline Precambrian rocks at the surface (Erslev and others, 2001; Erslev, 2005; Horton and others, 2022; fig. 2). Numerous north–south trending faults have been mapped through the Black Hills at the surface (for example, Redden and DeWitt, 2008) and in the subsurface (for example, Lisenbee, 1978), which offset the crystalline Precambrian basement (fig. 3). These faults lose displacement vertically up section and form structural folds in more ductile Cretaceous strata evident in surface outcrop patterns. These outcrop patterns present a unique opportunity to asses how effectively surface mapping can produce accurate geologic structure in the 3D GFM. Eastward of the Black Hills, strata gently dip to the east where structural complexity decreases across the South Dakota plains.

Temporally related to uplift of the Black Hills, a northwest-striking trend of alkalic and carbonatite intrusive rocks were emplaced through the crystalline Precambrian rocks and the overlying sedimentary succession as dikes, sills, laccoliths, and small stocks (Redden and DeWitt, 2008; fig. 2). Intrusives occasionally form prominent topographic features where they crop out at surface such as Devils Tower National Monument, Sundance Mountain, or Tinton Dome (DeWitt and others, 1986). Intrusive activity began between 62 and 50 mega-annum (Ma), followed by a second magmatic pulse around 39 Ma (Lisenbee and DeWitt, 1993).

Phanerozoic sedimentary rocks in the northern Great Plains range in age from Cambrian to Holocene, and unconformably overlie Precambrian crystalline basement rock throughout the study area (Anna, 1986). Stratigraphic relations are summarized in figure 5, relative to a generalized Phanerozoic sea-level curve, which represents the primary allogenic control on basin-scale sedimentation trends in conjunction with regional tectonic (Sloss, 1963; Algeo and others, 2014; Marcilly and others, 2022). A strong understanding of these allogenic controls is crucial for appropriately capturing stratigraphic thickness trends, lateral extents, and unconformities within the 3D GFM.

Cambrian sandstones of the Deadwood Formation form the basal sedimentary unit of the GFM and are overlain by laterally extensive Ordovician carbonate and shale units, including the Winnipeg Group and Red River Formation. These laterally continuous units were deposited across the entire study area during a period of rising global sea level and relative tectonic quiescence (Martin and others, 2004; fig. 5). From a modeling perspective, these units can be treated as regionally conformable layers that largely follow basement structure because most deformation affecting their geometry postdates deposition.

Elevated sea levels and episodic subsidence in the Williston Basin from the Late Ordovician through Early Mississippian restricted sedimentary units, such as the Interlake Dolomite, Three Forks Shale, and Bakken Formation, to the north of the study area (Gerhard and Anderson, 1988; fig. 4B). Nondeposition or erosion to the south and west resulted in regional pinch-out of these units. Accurate modeling of this interval needs careful representation of low-angle unconformities and subtle thickness variations, which exert strong control on stratigraphic architecture over long distances.

Falling sea level during the Mississippian was accompanied by widespread carbonate deposition across much of the study area, recorded by units, such as the Madison and Big Snowy Groups (Sonnenfeld, 1996; fig. 5). Mississippian carbonates thin southward and crop out along major uplifts, which requires careful integration of subsurface and surface constraints to retain lateral continuity in structurally deformed areas (Kent and Christopher, 2007; Anna, Pollastro, and Gaswirth, 2013).

Upper Paleozoic and early Mesozoic strata, including the Minnelusa and Spearfish Formations, lie unconformably on the Mississippian section and thin northward and eastward across the study area (Downey, 1986). These rocks show pronounced lateral and vertical lithologic heterogeneity due to deposition in restricted marine, sabkha, lacustrine, and eolian environments during prolonged global sea-level lowstand and relative tectonic quiescence (Carr-Crabaugh and Dunn, 1995; Anna, 2010; Fryberger and Hern, 2014; fig. 5).

Overlying Triassic and Jurassic units, including the Sundance, Gypsum Spring, and Morrison Formations, are internally heterogeneous and less laterally continuous than older Paleozoic units. (Vuke and others, 2007; Syzdek and others, 2019). These strata are bound by widespread unconformities and are locally truncated or entirely absent beneath the Cretaceous Inyan Kara Group (Anna 1986; Downey, 1986; fig. 5). Modeling of Triassic–Jurassic units needs to account for highly variable thicknesses, local nondeposition, and incision from overlying units.

Lower Cretaceous shales and fine sandstones blanket much of the post-Jurassic northern Great Plains and record a deepening-upward sequence from the predominantly nonmarine Inyan Kara Group to the open marine Mowry Shale (Anna, 1986, 2010; Vuke and others, 2007). This deepening-upward sequence records episodic sea level rise and transgression of the Western Interior Seaway during global greenhouse climate conditions (Anna and Cook, 2008; Marcilly and others, 2022; fig. 5). These units are laterally continuous across the study area and can be modeled in a layer-cake fashion, with attention to subtle subsidence-related thickness changes in the Powder River Basin.

Upper Cretaceous strata consist predominantly of shales and sandstones, including the Niobrara Formation and Pierre Shale, which span much of the study area and record low-amplitude transgressive–regressive cycles during global sea-level high stand (Love and others, 1993; Farenbach and others, 2007; Lynds and Slattery, 2017; fig. 5). Locally developed sandstone bodies, such as the informal Turner and Teckla sandstones, are confined to the southwestern Powder River Basin and are most appropriately modeled as eastward-thinning clastic wedges encased within regionally extensive shale units (Lichtner and others, 2020; fig. 4A).

The latest Cretaceous Fox Hills, Lance, and Hell Creek Formations, which cap the Mesozoic section record a fall from sea-level high stand, and regression of the Western Interior Seaway (Lynds and Slattery, 2017; Marcilly and others, 2022; fig.5). Late Cretaceous sandstone intervals additionally record incipient tectonic activity in the northern Great Plains, including elevated clastic sediment supply from the advancing Sevier fold-thrust belt, and increased accommodation space from early subsidence of the Powder River Basin (Yonkee and Weil, 2015; fig. 5). The primary consideration for modeling these units is accurately capturing their subsurface geometry in the west of the model in the Powder River Basin while seamlessly transitioning northeastward to discontinuous outcrop and subcrop in the South Dakota plains and Williston Basin.

Consolidated Cenozoic sedimentary rocks from the Fort Union Group at the base through the Thin Elk Formation at the top (undifferentiated in this study) exceed 1,500 m in thickness in the western Powder River Basin and thin eastward across the South Dakota plains (Love and others, 1993; Martin and others, 2004; Murphy and others; 2009; fig. 5). These strata include sandstones, claystones, conglomerates, lignite, and coal deposited in fluvial, lacustrine, alluvial-plain, and swamp environments (Vuke and others, 2007; Murphy and others 2009; Osmonson and others, 2011). Westward thickening reflects increased sediment supply from Laramide uplifts and rapid flexural subsidence along the basin axis into the Eocene (Fan and Carrapa, 2014; fig. 4A). In contrast, these consolidated units are thin or absent in the Williston Basin and eastern plains, likely owing to early Eocene basin inversion and erosion, with subsequent removal of section during later Cenozoic drainage reorganization (Caylor and others, 2023; Gelman, 2023; fig. 4B).

Poorly or unconsolidated Cenozoic deposits consist of gravels, silts, and muds that overlie a deeply incised unconformity cut into consolidated bedrock, particularly in the northern and eastern parts of the study area (Soller and Garrity, 2018). These deposits record glaciofluvial, lacustrine, and alluvial sedimentation during advance of the Laurentide Ice Sheet in the Pleistocene (Murphy and others, 2009; Naylor and others, 2021; fig. 5). These deposits are not a primary focus of the model and remain undifferentiated in this study.

Digital elevation data for this study were extracted from the USGS 3D Elevation Program (3DEP) 1/3 arc-second Digital Elevation Model (DEM; USGS, 2021a) into an ASCII elevation grid. The 1-arc-second grid was resampled to 100 m to remain within software memory limits for the regional mesh. The ASCII file was then gridded using a standard triangular mesh routine in the Leapfrog Geo 2021.2 (Seequent, 2021) 3D modeling software. The DEM data were used to define land surface elevation and to add elevation values to 2D surficial data used as model inputs (fig. 6A–E).

Surficial geologic contacts and structural surface exposures were compiled across the study area from a combination of digital vector data and scanned images. A generalized digital geologic map was compiled in a GIS by merging the following four datasets:

Source data were given a common map projection (North American Datum of 1983; Contiguous USA Albers, EPSG 5070), and correlative geologic units from each source map were merged in a GIS. Several inconsistencies exist in mapped contacts and stratigraphic nomenclature across State boundaries, but mapping discrepancies were not rectified in this study. Vector polylines delineating stratigraphic contacts of interest and surface expressions of structural features were isolated from the generalized geologic map, resulting in a dataset of 6,834 vectors, which were then draped on the DEM or top bedrock surface as explicit inputs for modeling stratigraphic horizons and structural planes (fig. 6B). Sometimes, minor mapped details or intricate contact polylines were manually simplified to eliminate conflicts between the true ground surface and lower-resolution DEM used in this model. This conflict is a known source of error that may deviate from true ground conditions.

Mapping at a 1:500,000 scale was locally supplemented by scanned and vector 1:100,000-scale geologic maps in the Black Hills (McLaughlin and Ver Ploeg, 2006; Sutherland, 2007, 2008; Johnson and Micale, 2008; Redden and DeWitt, 2008), eastern Montana (Vuke and others, 2001, 2003), the Bighorn Mountains (Lopez, 2000; Vuke and others, 2000; Ver Ploeg and Boyd, 2002, 2003; Ver Ploeg and others, 2004; Wittke, 2007) and the southern Powder River Basin (Hallberg and Case, 2001; Hunter and others, 2005; McLaughlin and Harris, 2005; McLaughlin and Ver Ploeg, 2008; McLaughlin and others, 2011) among others. In GIS software, 1:100,000-scale geologic maps were manually georeferenced and draped on the topographic surface as images. These maps served as general guides and provided implicit information about local portions of the model (for example, local strike and dip values).

Incorporating previously published geological models into regional subsurface compilations is an efficient way of adding local expertise and potentially higher-quality data and presents an opportunity for immediate comparison with model outputs constructed by this study.

Fourteen stratigraphic horizons in the northwestern part of the model were derived from a USGS petroleum systems model of the Williston Basin (Gelman and Johnson, 2023; fig. 6E); associated descriptions of modeled stratigraphic horizons, 148,000 formation top picks, and notes on horizon creation are in Gelman (2023). Additionally, horizon grids of six stratigraphic horizons were constructed from 28,000 wells and their associated logs as part of a dissertation examining geologic heterogeneity related to carbon sequestration in the Powder River Basin (Melick, 2013). Grids were extracted, converted to a standardized format, reprojected, and released as a USGS data release for use in this study (Spangler and others, 2023). Grids of Lower Cretaceous aquifers (Stanton, 2015) were used for comparison, but were not applied in this study.

The location of 146,904 hydrocarbon well collars were compiled from tabular databases provided by the South Dakota Geological Survey’s Oil and Gas Permits Digital Database (South Dakota Geological Survey, undated), Wyoming Oil and Gas Conservation Commission (WYOGCC; WYOGCC, undated), North Dakota Department of Mineral Resources (North Dakota Department of Mineral Resources, undated), and Montana Board of Oil and Gas Conservation (MBOGC; MBOGC, undated). Ground elevation data were extracted from the USGS 3DEP 1m dataset (USGS, 2021b) to all wells missing collar or kelly bushing elevations. Such extracted elevation data deviated from provided collar values by a mean of 0.7 m, which was deemed acceptable for this application.

Throughout the northern Great Plains, historical oil and gas fields are delineated by high-density well placement (160-acre spacing) along linear structural and stratigraphic hydrocarbon accumulations, such as the Cedar Creek Anticline, whereas modern well collars for unconventional development follow a broader grid-defined spacing (1,150-acre spacing), such as in northwestern North Dakota. Exploratory and wildcat wells drilled away from known oil and gas fields are spaced widely and irregularly, which provides particular value to this study as datapoints in poorly tested parts of the study area (fig. 6C).

Borehole deviation surveys or telemetry data were incorporated into this study where available. Boreholes lacking this information were assumed to be vertical with a dip of 90 degrees and a dip direction of 180 degrees.

A total of 288,892 stratigraphic formation tops of interest were selected from the four State databases. After compiling and standardizing names for this study, stratigraphic tops were plotted in 3D space by correlating unit American Petroleum Institute (API) number with well collar, survey, and stratigraphic top. Each data point was plotted on the respective borehole trace at the given depth (in meters) for use as explicit model inputs (fig. 6C).

The locations of 1,024 water wells in the eastern Black Hills were re-released as digital point data (Spangler and Sweetkind, 2022) after Carter (1999) compiled data from water well scout tickets. Collar elevation information was not provided; therefore, elevation data were extracted from the USGS 3DEP 1m dataset (USGS, 2021b) to all wells. Wells were assumed to be entirely vertical with a dip of 90 degrees and a dip direction of 180 degrees because well deviation data were not provided. Collar elevations and well deviations are known sources of error deemed acceptable for this modeling application because stratigraphic horizon elevations from water well information were consistent with nearby oil and gas tops. Data were displayed along proper borehole traces by correlating unique well identification numbers and depth along the borehole survey. Water well data were used as an explicit input for gridding.

Structure contours are lines of constant elevation of a geologic surface. They are interpretive products that interpolate between discrete data points, such as stratigraphic formation tops in wells. The 3D GFM incorporates 10,781 individual structure contour lines from several maps of local and regional extent to define stratigraphic horizons and the subsurface expression of faults (fig. 6D).

In the South Dakota region, vector-format structure contours of the Precambrian basement (McCormick, 2010) served as the primary reference for the geometry of the basement horizon. Structure contours of the Cambrian Deadwood Formation, Mississippian Madison Limestone, Pennsylvanian-Permain Minnelusa Formation, Permian Minnekahta Limestone, and Early Cretaceous Inyan Kara Group in the Black Hills by Williamson and others (2000) were digitized and re-released by Spangler and Sweetkind (2022) for use in this study. Contours on the top of bedrock in eastern South Dakota (Tomhave and Schulz, 2004); the tops of the Late Cretaceous Fox Hills, Hell Creek, and Paleocene Fort Union Formations near the South Dakota border (Thamke and others, 2014); and the base of the Miocene Ogallala Group in southern South Dakota (Peterson, 2016) were imported into GIS software, reprojected, and converted to meters. Scanned Portable Document Format (PDF) contours of the top Deadwood Formation, Madison Group, Minnelusa Formation, and Inyan Kara Group were digitized and applied to areas northeast of the Black Hills (Hocking, 2013a, b, c, d).

Contours for the top of the Precambrian basement horizon provided by the Wyoming State Geological Survey (2022) were foundational for establishing a structural framework of the Powder River Basin margin. In the Williston Basin, contours on the top basement horizon were sourced from Anderson (2009). A set of 825 structure contours mapping Cretaceous strata in the Wyoming part of the Powder River Basin by Lichtner and others (2020) were applied to the top Lower Cretaceous Mowry Shale, Upper Cretaceous Belle Fourche Shale, Greenhorn Formation, Turner Sandy Member of the Carlile Shale, Carlile Shale, Niobrara Formation, Red Bird Silty Member of Pierre Shale and Parkman Sandstone Member of the Mesaverde Formation, Teapot Member of Mesaverde Formation, Tekla Sandstone Member of Lewis Shale, and Fox Hills Formation horizons. These contours cover a substantial part of the Powder River Basin study area and were generally regarded as high-quality data inputs because they were generated using hand-picked formation tops from geophysical logs in more than 2,200 wells. Contours depicting the complex structure of the eastern Black Hills provided valuable detail where well data are sparse (Lisenbee, 1985). Contours mapping the top of the Minnelusa Formation, Minnekahta Limestone, Goose Egg Formation, and Fox Hills Formation by Fox and Higley (1996) were digitized and released by Goldberg and Sweetkind (2022). However, the level of detail of these contours was insufficient for use in the 3D GFM. Thamke and others (2014) released a series of structure contours that define a 3D GFM of the uppermost principal aquifer system in the Williston and Powder River Basins. These contours delineate the top of the Fox Hills Formation, upper and lower parts of the Hell Creek Formation, and three members of the Fort Union Formation. This dataset was essential in the Powder River and Williston Basins and was enhanced with local detail from additional contours delineating the top of the Fort Union Formation in the coal-rich parts of the Powder River Basin (Jones and others, 2003). Finally, contours of the upper bedrock horizon from Soller and Garrity (2018) and Naylor and others (2021) were used to construct an upper bedrock horizon in the glaciated parts of Montana, North Dakota, and South Dakota.

Contour datasets were manually preprocessed by removing redundant data or contours that ignored fault offset. Datasets were then uploaded to 3D modeling software for use as explicit inputs for constraining the geometry of horizons defining the upper boundary of stratigraphic model units.

Published cross sections, depth-converted 2D seismic lines, gravity, and aeromagnetic maps were used to serve as guidelines in areas where drilling is sparse, and better constrain mesoscale structural features not evident in other data types.

Sixteen stratigraphic cross sections from wireline geophysical well logs in South Dakota by Fox and others (2009) were consulted to constrain regional stratigraphic architecture and provided evidence of key stratigraphic pinch-outs and unconformities not immediately evident in the explicit input data. Additional stratigraphic cross sections consulted for this study include Gregory (1997), De Bruin (1998), Anderson (2012), and Nesheim (2016).

Three 2D depth-converted seismic lines were published by Stone (2003) which run approximately west–southwest–east-northeast from the Bighorn Mountains to the axis of the Powder River Basin. These data and their accompanying interpretations were incorporated to constrain the geometry of the Piney Creek Thrust and Granite Ridge tear faults along the western margin of the Powder River Basin. Tagged Imaged File Format (TIFF) images of seismic sections were adjusted to a one-to-one aspect ratio, georeferenced in a GIS, and imported to the modeling software as planar surfaces on which control points were added. Geologic context was added to these lines by three Wyoming Geological Survey cross sections by Wendell and others (1976) and Stone (1987), which were added to the modeling software using a similar method. Additional cross sections were consulted for individual 1:250,000- and 1:100,000-scale quadrangles around the margin of the Powder River Basin and in the Black Hills, but not used as explicit input data given that these were drafted by extrapolating surface mapping into the subsurface using geological first principles (for example, law of superposition, lateral continuity, and so forth) and professional expertise instead of subsurface data (Lopez, 2000; Vuke and others, 2000, 2003; Redden and DeWitt, 2008).

Georeferenced gravity and aeromagnetic maps were used as implicit data. Interpretations of these data by Redden and DeWitt (2008) and McCormick (2010) in South Dakota, Robbins (1994) and Anna (2010) in the Powder River Basin, and Bader (2019a) in the Williston Basin region were applied to identify deep-rooted faults that penetrate the Precambrian basement. Isostatic and Bouguer gravity anomaly data, as well as magnetic anomaly maps, for the conterminous United States were sourced from the USGS Mineral Resources Online Spatial Database (Phillips and others, 1993; Bankey and others, 2002). Subsurface geometries of igneous intrusions were interpreted directly from cross sections, gravity, and magnetic maps where available.

Selected stratigraphic horizons were interpolated using input data from well tops, structure contours, and surface contacts, among other data types mentioned in this study. These surfaces are composed of triangular elements with a resolution of 250 square meters that are calculated using Leapfrog’s FastRBF. Gridding resolution does not necessarily convey model confidence.

Initial grid construction involved simple triangulation among all available explicit inputs for each stratigraphic horizon. Following this initial calculation, horizons were then ordered chronologically to enforce the law of superposition and establish relative timing relations. Further refinement involved classifying horizons as either “depositional” or “erosional,” which governs their crosscutting relations within the modeling software. Depositional horizons are truncated by younger units, whereas erosional horizons may incise both underlying and overlying strata. This configuration allows regional unconformities, such as the base of the Inyan Kara Group, to bevel underlying stratigraphy where appropriate. Intrusive bodies were included within the stratigraphic framework because they crosscut and deform older sedimentary units into which they intrude.

Substantial variation in data density among stratigraphic horizons resulted in locally inconsistent geometries where poorly constrained surfaces deviated unrealistically from adjacent units. To address this issue, horizons with sparse input data were reconstructed as offset surfaces derived from better-constrained “anchor surfaces.” Anchor surfaces were defined as horizons with the highest data density and most reliable subsurface control, such as the Interlake Dolomite horizon, Madison Group horizon, Minnelusa Formation horizon, Inyan Kara Group horizon, Greenhorn Formation horizon, and Pierre Shale horizon. Adjacent low-data horizons were regenerated as offset facsimiles of anchor surfaces using minimum and maximum vertical offset constraints. Available data for low-data horizons were still honored where present. Offset surfaces are considered more uncertain than anchor surfaces.

Forty-seven faults were modeled as planar surfaces that offset stratigraphy and subdivide the 3D GFM into computational fault blocks. Surface traces of selected faults were identified from 1:500,000-scale geologic mapping draped over a DEM and served as primary inputs for constructing fault surfaces (Horton and others, 2017). Complex fault zones or swarms were simplified into representative master faults where appropriate, such as in the Brockton–Froid Fault Zone of Montana and North Dakota (fig. 8A).

For concealed faults that do not propagate to the surface but were identifiable in other data types, representative synthetic control points containing basic structural orientations (for example, dip and dip direction) were placed in space as the primary input. Georeferenced one-to-one geologic cross sections, depth-converted seismic lines, and gravity or magnetics maps served as guides for placing synthetic control points and modifying fault attitudes. Faults with unspecified orientations were modeled with a 90-degree dip, representing structures with a high degree of positional uncertainty. These faults were included because they likely exist, but their orientation, slip sense, and timing of deformation are not well understood.

Fault chronology was defined manually to establish crosscutting relations among intersecting faults. This process required interpretation of relative fault timing, including whether one fault truncates or offsets another, or whether faults intersect with minimal interaction. The resulting fault network was interpolated using Delaunay triangulation at a resolution of 500 m (fig. 8A).

Refined stratigraphic and fault frameworks were combined into a single 3D GFM subdivided into fault-bounded volumes, referred to here as “fault blocks” (fig. 8B). Global modeling parameters, such as grid resolution, were applied consistently across all fault blocks, whereas region-specific settings were applied selectively. For example, in the hanging wall of the Piney Creek Thrust (fault block named “PRB 13”; fig. 8B), well data were filtered to exclude footwall wells from RBF interpolation. In this same fault block, stratigraphic horizons were forced to honor mapped surface contacts, which represent the most reliable and abundant data type in that area.

To ensure that model grids reflect geologically plausible geometries, additional adjustments were made using 2,803 synthetic control points. In the Black Hills region, synthetic points were placed hundreds of meters above the modern land surface to reconstruct pre-erosional stratigraphic configurations, resulting in more realistic dips and surface contacts around the uplift (fig. 9A). Moreover, additional synthetic control points were added when RBF-interpolated horizons “warp” in a sinusoidal pattern where data are sparse (fig. 9B). These artifacts were mitigated using wireframe control points to stabilize surface curvature.

Detailed documentation of stratigraphic hierarchy and horizon-specific modeling parameters is provided in the data releases accompanying this report (Spangler, 2024a, b). Plates showing the elevation from sea level for the uppermost horizon of the Precambrian rock (pl. 1), Interlake Dolomite (pl. 2), Madison Group (pl. 3), Minnelusa Formation and Tensleep Sandstone (pl. 4), Inya Kara Group (pl. 5), Greenhorn Formation (pl. 6), and Pierre Shale (pl. 7) that served as anchor surfaces in this study are available at http://doi.org/10.3133/sir20265127.

Given the regional scale and heterogeneity of input datasets, this study applied a systematic and conservative data-screening workflow to identify and remove anomalous values while preserving genuine geologic variability. This approach balances model fidelity with realistic representation of the subsurface, particularly in data-poor areas where overcorrection could obscure meaningful structural or stratigraphic features.

In well data, inaccuracies were most apparent when erroneous stratigraphic picks resulted in a “spike” that conflicted with surrounding data (fig. 9C). Smoothing functions were avoided so that legitimate geologic variability was not removed; only clear outliers were excluded. A conservative approach to eliminating well data is especially important in areas where well data density is low because isolated data points exert a much stronger control and bear higher relative importance on the shape of a mesh than points in high-density areas.

Interpretive datasets incorporated into this study, such as structure contour maps or model grids, may not always represent the best possible interpretation. Because structure-contour maps may conflict with well data or adjacent horizons, contours were clipped where inconsistent with better-constrained inputs (fig. 9C). Similarly, model grids that conflicted with other data inputs were eliminated where significant discrepancies made subsurface geometries highly unrealistic.

Z-residual values were plotted within the study area and on top of the surfaces they were derived from to visualize their spatial distribution. This visualization serves as a qualitative proxy to communicate uncertainty to the end user. Where dense clusters of low Z-residual values exist, interpretation uncertainty is low. Where clusters of high Z-residual values exist, interpretation uncertainty is high.

When examining the Z-residual distribution of the upper Madison horizon, model results closely honor tightly spaced wells in the eastern Powder River Basin, Cedar Creek Anticline, and Williston Basin (fig. 10E). Isolated outliers in these low Z-residual regions likely indicate issues with input data, such as a bad pick or a wellbore lacking deviation information. Similarly, sporadic well picks in the Lance and Hell Creek horizons led to high Z-residual values because well data for this unit conflicted significantly with structure contour datasets used in grid calculations (fig. 10A).

Clusters of high Z-residuals convey high uncertainty. For example, in the upper Mowry horizon (fig. 10B), high Z-residual clusters near the Black Hills Monocline indicate the presence of small structural features that were not adequately captured by this study. Similar trends occur in the southwestern Powder River Basin near the Hartville Uplift (fig. 10B), where complex fault relations unresolved in this model result in high Z-residual values and uncertainty. Regions with interspersed high and low Z-residual values additionally convey relatively high uncertainty, although the source of uncertainty may be a combination of complex subsurface geology, uncertain input data, and (or) other factors leading to a mismatch between inputs and outputs. This pattern is exemplified by the interspersed high and low Z-residuals for the Mowry Shale near the Casper Arch (fig. 10B).

Z-residuals are not a perfect proxy for uncertainty. For example, many subsurface modeling packages have the capability to match grids exactly to all inputs, which would result in Z-residuals of zero even where obvious outliers exist (for example, fig. 9C). Another factor that affects an uncertainty metric is the data density. It is reasonable to assume that regions with few inputs, or isolated clusters of data, such as the top Precambrian basement horizon (fig. 10F), have an inherently elevated uncertainty even if the Z-residuals are low.

From a perspective view of the Powder River Basin part of the northern Great Plains, the shape of the basin itself and the surrounding uplifts are clearly defined (fig. 11). The northern extent of the model contains relatively flat-lying strata, gently deformed by broad folds and upwarps in the crystalline basement, such as Porcupine Dome and the Ashland Syncline (fig. 3; Vuke and others, 2009). Silurian–Mississippian strata are thickest to the northeast, and thin on top of more isopachous and regionally continuous Cambrian–Ordovician strata to the southwest in the core of the Powder River Basin (Peterson, 1988). The basin axis is modeled in the footwall of the Piney Creek Thrust, which was simplified in this study as a single low-angle master thrust with a shallow back-thrust dipping to the east (fig. 11A; Erslev, 1993; Stone, 1993, 2003). The east–west oriented strike-slip faults referred to as the “Shell Lineament and Granite Ridge Tear Faults” (fig. 8A) probably occurred synchronously with major slip of the Piney Creek Thrust and resulted in a small laterally offset anomaly of exposed Precambrian rocks near Granite Ridge (fig. 11A; Hoy and Ridgway, 1997; Stone, 2003). Seismic, surface mapping, and wells that drilled through the overthrust Precambrian hangingwall into the underlying Paleozoic sedimentary footwall (for example, Gulf Granite Ridge 9–1–2D) were used to constrain the geometry of this part of the Powder River Basin; however, more detailed interpretations of Stone (2003) may be more appropriate for subregional investigations in this area.

Thick accumulations of Fort Union Formation rocks are modeled clearly in the footwall of the Piney Creek Thrust, although the calculated geometry of each individual member within the Fort Union is speculative in this area (Love and Christiansen, 1985). The modeled Tullock Member of the Fort Union Formation is shown to drastically thicken directly adjacent to Granite Ridge; however, the model may overstate the thickness of the Tullock and understate the thickness of the overlying Lebo and Tongue River Members in the footwall syncline, which is truncated by the thrust system in its current configuration (fig. 11A). Furthermore, structural overthickening of these units could have occurred due to propagation of local lower-angle or blind thrust splays in the footwall growth syncline not recognized for more than a few kilometers of strike length. Fort Union rocks are overlain by the Wasatch Formation, which is another synorogenic deposit situated in the footwall syncline of the Piney Creek Thrust that records peak Laramide contraction along the system in the Eocene (Fan and Carrapa, 2014). Roll-front uranium deposits have been identified in Forth Union and Wasatch strata from the Piney Creek Thrust to the Casper Arch, which are possibly related to the weathering of uplifted granites proximal to reducing groundwater in the greater Tullock or Tongue River aquifers.

Eastward-thinning Upper Cretaceous sand bodies, such as the Turner, Teapot, and Tekla sandstone model units, are shown within a thick section of shales near the basin axis (fig. 11A; Lynds and Slattery, 2017). However, the thickness of these units is highly variable in the 3D GFM because of conflict between publicly available well data and published contour maps of these units (Merewether, 1996). Detailed modeling of these sandstones would be more appropriately conducted using original picks from wireline logs and a sequence stratigraphic modelling approach.

A simplified representation of the eastern Powder River Basin and Black Hills Monocline is shown in figure 11B. Many interpretations have been made in this region to define the structure of the uplift (for example, Lisenbee, 1978, 1988; Lisenbee and DeWitt, 1993; Fox and Higley, 1996; Driscoll and others, 2002). This study simplified the uplift to a single eastward-dipping master fault with maximum displacement to the north of the Black Hills Uplift, similar to Marshak and others (2000). However, many small but densely drilled oil fields in the downthrown side of the structure (with significant residual offset in the 3D GFM) indicate more structural complexity. It is likely that a single fault is a significant oversimplification of this region which is better represented by many small-offset faults and “in-line lenses” or “terraces” of Lisenbee (1988). Low-angle faults that were not explicitly modeled may be expressed in the 3D GFM as small undulations in stratigraphic horizons instead of with proper stratigraphic offset (fig. 11B; table 1.1). A highly interpretive rendering of the Bear Lodge intrusive complex and other intrusive bodies in this region were constructed using surface mapping, published cross sections, gravity and magnetic anomalies, and by interpreting intrusives to have uplifted Paleozoic sedimentary rocks where they outcrop at surface outside of the regional structural trend. Although these features have received considerable attention from geologists as natural attractions and a possible source of rare-earth elements, limited subsurface data on these intrusives have been made public (DeWitt and others, 1986; Moore and others, 2015). Additional publicly available data, including high-resolution gravity and magnetic anomaly surveys, geochemical sampling, and drilling, could better constrain interpretations beyond surface mapping and conceptual hand-drawn sketches of these complex but increasingly relevant intrusives.

Complex folding and faulting in the Casper Arch is well documented and evident in well picks and outcrop patterns (for example, Baker, 1957; Love and Christiansen, 1985; Melick, 2013). Major structures, such as the Salt Creek Anticline and Teapot Dome, are shown in the perspective view of the 3D GFM, in addition to smaller faults and folds that crosscut the uplift (fig. 11). The vintage of wells and lack of publicly available seismic data in this region contribute significantly to the level of uncertainty in the Casper Arch despite a well distributed well dataset. Although modeled as throughgoing fault planes in the 3D GFM, it is more probable that faults lose displacement in ductile strata overlying the Madison Group and tip out up section as folds, such as in the fold of Teapot Dome (Baker, 1957; Roberts and others, 2022). Faults bounding the southern margin of the Powder River Basin and Casper Arch, such as the Deer Creek, Casper Mountain, and Northern Bounding Faults, were modeled as en-echelon, low-angle thrust faults similar to interpretations of Blackstone (1996; 1988), Stone (2002), and Bader (2021; fig. 11C). Slip on these faults likely occurred into the Eocene and truncate older faults exposed at surface in the Hartville Uplift and Laramie Mountains, such as the Laramie Peak Shear Zone and Orin Junction Fault. In the footwall of the Deer Creek and Northern Bounding Faults, stratal thicknesses became challenging to rectify, resulting in thickness anomalies in Paleozoic strata, such as the Madison Group, or overthickening in the Fox Hills Formation (fig. 11C). Notable in this area is an overthickened Lance and Hell Creek model unit, the geometry of which is supported by WOGCC well picks and structure contours from wireline log interpretation (Thamke and others, 2014). Relevant to subsurface workers in this region, anomalously high heat flow is observed in Upper Cretaceous strata near the Salt Creek Anticline (150 milliwatts per square meter [mW/m²]) and Teapot Dome (225 mW/m²) (McPherson and Chapman, 1996). Anomalous heat flow values could be attributed to advection by a regional-scale groundwater system, which charges in the Black Hills, sweeps heat from the deeper parts of the basin, and discharges near the fracture-porosity enhanced anticlines of the Casper Arch (McPherson and Cole, 2000; fig. 11C). This thermal regime, coupled with numerous interlayered reservoir and seal intervals and a well-established hydrocarbon industry, could make the southern Powder River Basin an attractive locality for potential future enhanced geothermal exploration or carbon capture use and storage infrastructure development.

A perspective view of the Williston Basin region of the 3D GFM illustrates the subtlety of structural features in the northern extent of the northern Great Plains, such as Nesson Anticline and Poplar Dome (fig. 12; Nesheim, 2016). However, the most important consideration in this part of the 3D GFM was the numerous unconformities between sedimentary units, such as the erosional unconformity at the base of the Cretaceous Inyan Kara Group (Gerhard and Anderson, 1988). Occasionally, attempts to model these unconformities using Leapfrog’s RBF results in thin slivers of sedimentary section (less than 5–10 meters) that may not actually exist in the subsurface. An example of this phenomenon is the Jurassic Morrison Formation, which is shown in the 3D GFM as a thin remnant unit at the base of the Cretaceous unconformity despite the Morrison not generally being recognized in the Williston Basin (Murphy and others, 2009). Similarly, the true extents of units may not be appropriately captured in the GFM, but were left as is to ensure stratal horizons were fully interlocking. For example, the true limits of the Bakken Formation may be improved by eliminating any section in the 3D GFM with a vertical thickness under 2 m because the vertical resolution of this work is not fine enough to capture such granular detail.

Near the top of the sedimentary basin fill, an erosional unconformity at the top of consolidated bedrock is shown scouring into sediments as old as the Late Cretaceous, forming significant relief between channels and ridges in the subglacial till topography (fig. 12A; Soller and Garrity, 2018; Naylor and others, 2021). In this view, as much as 90 m of undifferentiated sedimentary deposits (mostly consisting of glacial till) have been stripped away for illustrative purposes. Details of the shallow bedrock and glacial geology most applicable to groundwater resources or contaminant assessments are likely lost because of the scale of the 3D GFM cannot capture geologic heterogeneity at this scale. A framework model focused exclusively on the uppermost Cretaceous and Cenozoic sedimentary section similar to Thamke and others (2014) or Peterson (2016) could be most appropriate to improve on the synthesis presented in this report.

The Cedar Creek Anticline is one of the most prominent structural features in the Williston Basin region and has long been a focus of hydrocarbon producers with more than 100 wells delineating the structure along strike. High subsurface data density, combined with interpretations from Gelman and Johnson (2023) could make rigorous modeling of the structure relatively straightforward, however geologic problems at the field-scale are still observed on the 3D GFM results (fig. 12B). In lower Paleozoic strata, such as the Interlake Dolomite or Winnipegosis Formations, potentially unrealistic thickening and thinning are observed directly adjacent to the structure. Because the Cedar Creek Anticline has been active since the Late Devonian (Clement, 1986), these relations could certainly be real. However, even slight errors in input data or interpolation settings could dramatically affect the thickness of these units. Similarly, thickness variations in Mississippian and Permian units across the fault are corroborated by well data compiled for this study; however, it would be challenging to identify a convincing natural mechanism for this observation. These thickness issues compound up section, leading to potentially exaggerated vertical offset on the structure in Upper Cretaceous units, such as the Pierre Shale (fig. 12B). Outcropping Upper Cretaceous units are mapped along the strike of the Cedar Creek Anticline (Vuke and others, 2009) and are shown to outcrop correspondingly in the 3D GFM.

A perspective view of the western South Dakota part of the 3D GFM captures the major structural elements in the region, including the Transcontinental Arch, southern margin of the Williston Basin, and Black Hills Uplift (fig. 13). Lower Paleozoic rocks, such as the Deadwood Formation and Red River Formation, are preserved in the southern extent of South Dakota; however, these units thicken to the northeast where they dip into the Williston Basin (fig. 13A; Peterson, 1988). Mesozoic rocks are relatively isopachous compared to the lower Paleozoic section, which corroborates the hypothesis that the Williston Basin was tectonically quiescent (inactive) throughout much of this period (Kent and Christopher, 2007; Gelman, 2023). Multiple unconformity surfaces, such as at the top of the Madison Group, base of the Sundance Formation, or base of the Inyan Kara Group, intersect near the southeastern extent of the northern Great Plains and create a complex and challenging to parse stratigraphic framework near the South Dakota–Nebraska border. These relations were approximated using stratigraphic sections of Fox and others (2009). Similarly, unconformity surfaces resulted in apparent thickness anomalies in the Sundance Formation and Morrison Formation on the eastern margins of the Black Hills Uplift (Anna, 1986; Williamson and others, 2000). Although these thickness anomalies are supported by well data and theoretical knowledge of the region, further explanation is needed to confirm the existence of excess thickness in Jurassic units (fig. 13).

Faults below the scale of this model unit are on the margin of the Black Hills as small linear undulations in the crystalline Precambrian basement model unit (fig. 13A). These faults deform the overlying sedimentary rocks in the 3D GFM, which is corroborated by water well data and structure contour mapping by Carter (1999) and Carter and others (2003). It is probable that these faults offset the crystalline Precambrian basement and lose displacement up section in more ductile sediments, which causes these structures to crop out at the surface as folds. Intrusion of laccoliths and small stocks, such as the Bear Buttes stock postdate layered bedrock, and deformation associated with their intrusion is captured in the 3D GFM (fig. 13A). The geometry of the Bear Buttes stock was interpreted from cross sections by Redden and DeWitt (2008), however the geometry is only slightly less speculative than other intrusive bodies in this study.

In addition to challenges with unconformity relations, faults in southern South Dakota near the Nebraska border were noted in this study. Well intercepts of basement rock indicate the presence of some structural features where the Slim Butte Anticline, Pine Ridge Anticline, and an unknown fault are modeled in the 3D GFM. Linear gravity anomalies with a similar west–northwest orientation were noted by McCormick (2010) and could possibly be the northern extent of the Chadron Arch, which predominantly underlies Nebraska. The Slim Butte Anticline is the most prominent of these features, which is modeled in the 3D GFM with basement offset down to the northeast approximately 289 m inferred from wells Amerada #1 Red Eagle and Integrity #1 Pine Ridge. Dip on the fault associated with the Slim Butte Anticline is modeled as a reverse fault of 35 degrees; however, this structure could be high angle with a complex fault history similar to the Cedar Creek Anticline, with phases of normal and reverse activation. Notably, Cambrian Deadwood Formation is not explicitly picked in the public well records on the upthrown side of this fault. While modeled as a thin remnant unit in the 3D GFM, it is possible that this structure was active as early as the Cambrian or was activated shortly thereafter, eroding Deadwood strata from the hangingwall. Up section, a similar challenge to the stratal thickness problems encountered near the Cedar Creek Anticline was observed, where a lack of well picks on the footwall side of the structure results in stratal modeled thickness problems across the fault. As these stratal thickness changes compound up section, the vertical displacement of the fault might become exaggerated in the 3D GFM (fig. 13B). The Niobrara Formation is mapped at the surface of the Slim Butte Anticline and does appropriately crop out in the 3D GFM (fig. 13B); however, these interpretations only provide one rendering of the geology in a region of sparse drilling. The Pine Ridge Anticline and Unknown fault were included in this model because of strong linear magnetic anomalies adjacent to wells English #1 Eucks and KG&S #1 Farley, which required some structural discordance to exist to maintain probable Cretaceous stratigraphic thicknesses. Remarkably low magnetic anomalies are observed on the southwest sides of the structures; and regional values increase gradually to the northeast. These structures were modeled with basement offset down to the northeast at 90 degrees of dip because their slip history is likely similar to the kinematics of the Slim Butte Anticline, but remains uncertain.

National-scale maps of geothermal potential have shown that the region southeast of the Black Hills near the Slim Butte and Pine Ridge faults is highly prospective for hidden sedimentary geothermal resources (Roberts, 2018) Local thermal gradients are as high as 127 degrees Celsius per kilometer (Schoon and McGregor, 1974), which could make characterization of these faults significantly more relevant to subsurface explorers, local communities, and land managers than they historically have been. The Slim Butte, Pine Ridge, and “unknown” faults included in this study are a starting point; however, 4–5 colinear magnetic anomalies trending northwest–southeast may be the source or conduit for anomalously hot fluids in southern South Dakota and have even been postulated to be related to a series of deeply buried volcanic centers (McCormick, 2010).

Fault modeling in the Black Hills region of the northern Great Plains 3D GFM is shown to have been highly simplified on the western margin near the Black Hills Monocline and to the east, where the uplift transitions to the South Dakota plains (figs. 11B and 13A). The geometry of basement-cored faults in this model is similar to large offset, range-bounding Laramide faults, such as the Piney Creek Thrust on the western margin of the Powder River Basin (Lisenbee and DeWitt, 1993). However, many subtle anticlines and probable faults are in the sedimentary units in cross section view through the Black Hills region of the 3D GFM, which are not accounted for by this structural model (fig. 14). Although the results presented in this report are likely adequate for many 3D modeling applications, a significantly more complex fault geometry similar to a shallow broken foreland-type uplift of Erslev (2005) or Horton and others (2022) may be more appropriate in this region. The inline lenses and terraces of Lisenbee (1988) to the west of the Black Hills Monocline corroborated by drilling and modeling in this study would likely be accounted for by nearly horizontal subthrust splay anticlines (fig. 14). Contractional structures in the Wyoming part (or forelimb) of the Black Hills Uplift could be accounted for by west-dipping backthrust-tip anticlines, and small-scale faulting on the east side of the Back Hills (backlimb) would likely be caused by backlimb-tightening anticlines (figs. 13 and 14; Horton and others, 2022).