NDGRI: A Novel Sentinel-2 Normalized Difference Gamma-Radiation Index for Pixel-Level Detection of Elevated Gamma Radiation

Highlights

What are the main findings?

• A novel Sentinel-2 spectral index named Normalized Difference Gamma-Ray Index (NDGRI) that delineates elevated natural gamma radiation zones in semi-arid basins of Mongolia.
• NDGRI was validated against airborne and car-borne spectrometry datasets.

What is the implication of the main finding?

• NDGRI used as a pre-screening tool that supports subsequent airborne and ground-based surveys, helping to reduce their overall cost and focus field efforts more efficiently.

Abstract

This study introduces the Normalized Difference Gamma Ray Index (NDGRI), a novel spectral composite derived from Sentinel 2 imagery for mapping elevated natural gamma radiation in semi-arid and arid basins. We hypothesized that water-sensitive spectral indices correlate with gamma-ray hotspots in arid regions of Mongolia, where natural radionuclide distribution is influenced by hydrological processes. Leveraging historical car-borne gamma spectrometry data collected in 2008 across the Sainshand and Zuunbayan uranium project areas, we evaluated twelve spectral bands and five established moisture-sensitive indices against radiation heatmaps in Naarst and Zuunbayan. Using Pearson and Spearman correlations alongside two percentile-based overlap metrics, indices were weighted to yield a composite performance score. The best performing indices (MI—Moisture Index and NDSII_1—Normalized Difference Snow and Ice Index) guided the derivation of ten new ND constructs incorporating SWIR bands (B11, B12) and visible bands (B4, B8A). The top performer, NDGRI = (B4 − B12)/(B4 + B12) achieved a precision of 62.8% for detecting high gamma-radiation areas and outperformed benchmarks of other indices. We established climatological screening criteria to ensure NDGRI reliability. Validation at two independent sites (Erdene, Khuvsgul) using 2008 airborne gamma ray heatmaps yielded 76.41% and 85.55% spatial overlap accuracy, respectively. Our results demonstrate that NDGRI effectively delineates gamma radiation hotspots where moisture-controlled spectral contrasts prevail. The index’s stringent acquisition constraints, however, limit the temporal availability of usable scenes. NDGRI offers a rapid, cost-effective remote sensing tool to prioritize ground surveys in uranium prospective basins and may be adapted for other radiometric applications in semi-arid and arid regions.

1. Introduction

Mongolia’s uranium potential has been systematically investigated since the 1950s, with Soviet led airborne radiometric surveys evolving into detailed car-borne spectrometry and geochemical investigations by the 1970s–1980s. Over 30 technical reports (1970–1990) documented uranium occurrences, later made public via Mongolia’s Mineral Resources Authority (MRAM) in 2006 [1]. Post-1990, international consortia revitalized exploration, leveraging Mongolia’s geotectonic division into northern (Precambrian–Paleozoic) and southern (Paleozoic–Mesozoic) provinces along the Main Mongolian Lineament, a key suture in the Central Asian Orogenic Belt [1,2]. Uranium mineralization models, notably by Mirnov [3] and Rutherford [4], highlight diverse genetic settings: from magmatic-hosted U⁴⁺ in granites/rhyolites to redox-controlled deposits in Mesozoic–Cenozoic basins.

Geological literature dating back to the 1970s consistently divides Mongolia into two primary geotectonic provinces: a northern and a southern domain [5]. These are delineated by the Main Mongolian Lineament, a major structural boundary that separates Precambrian and Early Paleozoic formations of the northern region from the predominantly Paleozoic to Mesozoic lithological assemblages in the south. This lineament represents a significant tectonic suture and has played a pivotal role in the evolution of the Central Asian Orogenic Belt. Its structural and lithostratigraphic significance forms a fundamental framework for interpreting regional tectonics, magmatism, and mineralization patterns across Mongolia.

Both Mironov [3] and Rutherford [4] categorize Mongolian uranium occurrences based on genetic setting and host environments, though they emphasize different geological controls. Mironov’s classification spans seven types, from fluorine–molybdenum–uranium mineralization in Late Mesozoic volcano-tectonic settings, to uranium in terrigenous Mesozoic and Cenozoic depressions, coal-bearing strata, and weathered leucogranites—emphasizing both magmatic and sedimentary processes across temporal and lithological contexts [3]. Rutherford [4], meanwhile, introduces a threefold model: Type 1 includes uranium in intrusive contacts and shear zones within granitic skarn and pegmatite systems of cratonic terrains—linked to Sn, Th, REE, and other critical elements but deemed economically marginal. Type 2 covers volcanic–intrusive zones of intracratonic settings with modest potential, while Type 3 highlights sediment-hosted uranium in Cretaceous to Neogene rift basins, influenced by redox dynamics and groundwater chemistry. Together, these frameworks underscore Mongolia’s diverse uranium metallogeny, from primary magmatic sources to secondary mobilization in continental sedimentary basins. This layout highlights how Mironov provides a broader spectrum of genetic types—especially those linked to sedimentary environments—while Rutherford zeroes in on tectonic and redox-controlled systems with emphasis on exploration viability [3,4].

Previous efforts to map gamma-radiation anomalies have employed a variety of remote-sensing and geophysical techniques. Ondieki et al. demonstrated that supervised classification of Landsat-8 surface reflectance into vegetation and soil/rock classes could predict thorium-rich outcrops at Mrima Hill, Kenya, with approximately 90% overall accuracy when validated against field gamma-dose measurements [6]. Saepuloh et al. extended this approach by using Sentinel-2 band-ratio composites and a red-edge vegetation stress index (REVI) to identify uranium-bearing hydrothermal alteration in Sulawesi, Indonesia, finding that areas of anomalous REVI values corresponded closely with elevated uranium assays [7]. In Egypt’s Eastern Desert, Assran et al. fused Sentinel-2 false-color composites, principal component analysis, and SWIR band ratios with airborne gamma-spectrometry (K, eU, eTh) to produce integrated radiometric anomaly maps that aligned strongly with known uranium mineralization [8]. Similarly, Ahmed et al. combined eU/eTh ratio maps from airborne data with Landsat and Sentinel alteration signatures to trace uranium migration pathways in the Duwi and Quseir formations, achieving high spatial concordance between spectral alteration and radiometric hotspots [9].

Remote sensing offers a powerful complement to field-based gamma surveys, especially in arid terrains where sparse vegetation and low ambient moisture minimize spectral interference. Our central hypothesis is that moisture-sensitive composite indices, when applied to Sentinel 2 Level 2A imagery acquired under strict climatological constraints, will spatially co-locate with zones of naturally elevated gamma radiation. This alignment reflects the oxidative mobilization of uranium and its moisture-driven transport pathways. By quantitatively evaluating existing indices and developing a new Normalized Difference Gamma Ray Index (NDGRI), we address a critical gap in exploration technology for semi-arid basinal environments.

The primary objective of this study was to develop a purely remote-sensing approach that can precede, and sharply narrow, the scope of traditional uranium exploration in arid and semi-arid basins. Conventional workflows rely on costly airborne and ground spectrometry campaigns, followed by even more expensive drilling and geochemical assays to confirm uranium occurrence. By introducing the NDGRI, computed solely from Sentinel-2 imagery, we aim to delineate prospective uranium-bearing zones without any initial field deployment. This pre-screening step can guide and optimize the placement of airborne surveys, ground radiometric traverses, and drill exploratory holes, thereby reducing the overall survey footprint and delivering substantial economic savings. NDGRI serves as an efficient filter—directing expensive follow-up operations to areas most likely to host elevated gamma radiation and, by proxy, uranium mineralization.

In this study, sedimentary uranium deposits in southeastern Mongolia (Dornogovi region) are examined as the primary focus. As a control framework for the presented methodology concerning anomalous radioactivity phenomena, specific zones are identified where elevated values are directly associated with the presence of granitic and rhyolitic formations. The decay products of these lithologies have been distributed into the surrounding environment, predominantly via horst–graben structural systems. However, areas of increased radioactivity may, but not necessarily, be exclusively linked to granites or rhyolites.

2. Materials and Methods

2.1. Test Areas

For the gamma-radiation analysis, two areas in Dornogovi Province were selected: Naarst (110.55°E–110.65°E, 44.86°N–45.02°N, WGS 84/UTM Zone 49N), hereafter referred to as Area 1, and Zuunbayan (110.16°E–110.34°E, 44.17°N–44.42°N, WGS 84/UTM Zone 49N), hereafter referred to as Area 2 (Figure 1). Raster format heatmaps for these sites, acquired via the car-borne gamma spectrometer survey detailed in Section 2.4, were rendered using three spectral bands (red, green, and blue). To improve comparability, the heatmaps were subjected to two preprocessing workflows prior to analysis.

2.2. Organization of the Database of Anomalies and Zones

As baseline material, for this paper and other purposes, the dataset was compiled from selected Soviet-era geological reports, text excerpts, and scanned map materials, obtained from the MRAM under the official terms in effect between June and September 2006. The acquired materials were integrated into a purpose-built database on uranium and radioactive anomalies across Mongolia, with initial data structuring conducted during 2006–2007. Subsequent revisions and data corrections were implemented in 2012 to enhance spatial accuracy and attribute consistency, ensuring the dataset’s reliability for geospatial analysis and remote sensing validation [11].

A total of 22 Soviet-era reports (No. 2447, 2462, 5251, 2411, 2448, 2449, 2427, 2419, 2520, 2452, 2426, 2442, 2437, 2414, 2453, 2455, 2428, 2429, 2432, 4289, 4358, and 4454) were reviewed and integrated into an Excel-based anomaly and zone database according to the MRAM referencing system [11].

2.3. Regional Geology of Dornogovi and Areas of Interest (Naarst and Zuunbayan)

The regional geology of Dornogovi Province was established through a synthesis of Soviet-era geological surveys [11,12], the national geologic map of Mongolia and its accompanying documentation, as well as direct field observations and satellite imagery analysis [13]. This integrated framework provided a foundational geological context, enabling the identification and interpretation of structurally favorable settings and lithological units relevant to uranium mineralization [13]. It also supported the remote sensing-based delineation of anomalous zones, forming a geospatial baseline for further spectral and radiometric investigations.

The two localities investigated in this study, Naarst and Zuunbayan, are aligned along a NE–SW-trending corridor approximately 75 km in length and lie within the Upper Cretaceous Bainshiren Suite (K2bs). This formation, dated to approximately 98–83 Ma (or alternatively 93–80 Ma), comprises grey sandstones, gravel-rich horizons, and interbedded red and grey clays. The area is structurally complex, marked by uplifted Paleozoic basement blocks and active tectonism, which together foster the development of uranium and associated radioactive anomalies (Figure 2).

2.3.1. Geological Role of Granite in Uranium Mobilization: Case Study from South-Eastern Mongolia

Granitic formations in southeastern Mongolia, particularly those associated with the structures and various granite intrusions, play a critical role in the georadio-logical framework of the region. These Paleozoic granites, emplaced along major fault systems, serve as primary source rocks for uranium, thorium, and potassium—elements of significant radiogenic potential. Their long-term exposure to atmospheric and hydrothermal processes has facilitated the mobilization of uranium from solid-state U(IV) into the soluble uranyl ion U(VI), particularly under oxidizing conditions [15].

The tectonic evolution of southeastern Mongolia has produced a series of uplifted blocks and graben systems, forming continental sedimentary basins that act as geochemical traps. Within these basins, uranium-bearing fluids derived from granite weathering migrate through porous media and precipitate in reducing environments, typically marked by grey to black sediments. This redox-controlled mechanism underpins the formation of sediment-hosted uranium deposits, as observed in the Bayan Shiree (K2bs) formation, where uranium concentrations reach up to 90 ppm in oxidized gravel conglomerates [15].

Historical Soviet exploration (1979–1981) identified multiple radioactive anomalies within the various areas, many of which are spatially and genetically linked to granitic sources. Recent airborne gamma spectrometry and spatial data integration reaffirm the strategic importance of these granites as both carriers and mobilizers of radioactivity. The integration of historical anomaly catalogs, field radiometric assays, and airborne survey data has enabled the construction of a comprehensive geospatial database, facilitating targeted exploration and environmental assessment [15].

In conclusion, granites in southeastern Mongolia are not merely passive lithological units but active geochemical agents in the genesis and redistribution of uranium. Their role as radiogenic reservoirs and mobilizers is central to understanding the region’s uranium metallogeny and informs both resource development and geoconservation strategies [15].

2.3.2. Significance of Particular Sedimentary Formation for Uranium Exploration in Southeast Mongolia

This section examines four major sedimentary formations in southeastern Mongolia (K1dz, K2ss1, K2ss2, and K2bs), highlighting their contrasting lithological features and roles in uranium metallogeny.

The K1dz Formation, a Lower Cretaceous sedimentary unit in southeastern Mongolia, plays a critical stratigraphic role in regional uranium exploration, despite lacking direct mineralization itself. Lithologically, the formation is composed predominantly of fluvial and lacustrine depositgranite intrusions, including fine- to medium-grained sandstones, silt-stones, and claystones, often exhibiting features such as ripple marks, planar bedding, and occasional paleosol horizons. These sediments reflect deposition in relatively stable continental environments, with limited tectonic re-working and subdued redox variability compared to overlying formations [15].

Petrographic analyses indicate a low degree of diagenetic alteration, with minimal cementation and weak development of redox interfaces—conditions that are generally unfavorable for uranium fixation. Geochemically, the K1dz Formation exhibits low uranium mobility and retention capacity, due to the absence of significant organic matter, iron oxides, or clay minerals capable of adsorbing uranyl ions under oxidizing conditions. Consequently, no economic uranium concentrations have been identified within this unit, and it is not considered a metallogenic target [5].

However, the significance of the K1dz Formation lies in its function as a stratigraphic boundary and geochemical baseline. It underlies the uranium-bearing Bainshiren Formation (K2bs), which hosts dispersed uranium in oxidized sandstones and clays. The unconformity or transitional contact between K1dz and K2bs marks a shift in depositional regime, tectonic activity, and redox conditions—factors that collectively enhance uranium mobility and concentration in the overlying strata. This boundary thus serves as a reference horizon in exploration models, delineating the onset of favorable conditions for uranium mineralization [5].

In regional metallogenic mapping, the K1dz Formation is used to constrain the vertical extent of uranium-bearing systems and to differentiate barren stratigraphy from prospective zones. Its consistent absence of mineralization, coupled with its widespread distribution, makes it a reliable lithostratigraphic marker for subsurface correlation and for refining airborne radiometric anomalies. As such, while the K1dz Formation is not a direct source or host of uranium, its role in defining the lower boundary of uranium-enriched sequences is essential for both geological interpretation and targeted exploration in southeastern Mongolia [5].

The sedimentary suites K2ss1 and K2ss2, exposed within the Dornogovi region of southeastern Mongolia, constitute stratigraphic units of the Upper Cretaceous age, deposited in an intracontinental basin characterized by episodic tectonic subsidence and variable hydrodynamic regimes. K2ss1 comprises fine- to medium-grained sandstones interbedded/intercalated with siltstones and claystones, reflecting low-energy fluvio-lacustrine deposition under fluctuating redox conditions. In contrast, K2ss2 is dominated by coarser sandstones and polymictic conglomerates indicative of proximal alluvial fan and braided stream environments, with enhanced porosity and permeability [5].

These suites are critically relevant to uranium metallogenesis in the region. K2ss1 provides reductive microenvironments conducive to uranium precipitation, facilitated by organic-rich interbeds and diagenetic pyrite. K2ss2, with its higher hydraulic conductivity, acts as a conduit for oxidized uranium-bearing fluids, enabling lateral migration and concentration along facies boundaries and structural discontinuities. Mineralization is predominantly epigenetic, with uraninite and coffinite occurring within reduced zones, often in association with carbonaceous material and sulfides [15].

The hologenous framework integrates sedimentological architecture, diagenetic evolution, and uranium geochemistry, emphasizing the systemic interdependence of facies distribution, fluid flow, and redox gradients. Within the Dornogovi basin, these suites exemplify the lithological and geochemical prerequisites for sandstone-hosted uranium deposits, offering a predictive model for exploration and a structural basis for ontological reflection on resource localization [5].

The Bainshiren Formation (K2bs) represents a key Upper Cretaceous continental unit in southern Mongolia, most likely deposited during the Santonian to Campanian stages (~86–72 Ma). It unconformably overlies Jurassic or Lower Cretaceous sediments and is locally capped by younger Cretaceous or Paleocene strata. The formation exhibits pronounced lithological heterogeneity, with dominant medium- to coarse-grained sandstones that are typically reddish, yellowish, or grey-brown in color. These sandstones frequently display sedimentary structures such as cross-bedding, ripple marks, and paleochannels, indicative of fluvial dynamics. Interbedded clays and silts are fine-grained and occasionally laminated, with paleosol horizons suggesting episodic subaerial exposure. Conglomerates, often polymictic and stratified, contain rounded clasts of quartz, volcanic, and metamorphic origin, and are typically concentrated at the base or as intercalations within the sequence [5].

Facies variability is both lateral and vertical, reflecting shifts in depositional environments across alluvial plains, fluvial systems, and lacustrine settings. The sedimentation regime was episodic, influenced by climatic fluctuations and tectonic activity that modulated grain size distribution and facies architecture. Thickness varies locally, with an average range between 300 and 600 m. Fossil content is notable, including vertebrate remains such as theropod, sauropod, and hadrosaur dinosaurs, as well as turtles and fish. Plant fossils—leaves, seeds, and woody fragments—are also present, typically concentrated in fine-grained sediments and paleosol layers [5].

Petrographically, the sandstones exhibit secondary quartz cementation and a weak to moderate degree of diagenesis. Clays contain montmorillonite and kaolinite, with localized iron reduction zones. Conglomerates are polymictic, dominated by quartz and volcanic clasts. The formation is situated within intramontane basins of southern Mongolia, which were tectonically active during the Late Cretaceous. Sedimentation was controlled by fault dynamics and variations in paleorelief, contributing to the complex stratigraphic architecture [5].

Of particular significance is the formation’s role in uranium metallogeny. The Bainshiren Formation provides favorable conditions for uranium accumulation due to its redox-sensitive facies architecture. The juxtaposition of oxidized sandstones and reduced clay-rich horizons facilitates uranium precipitation, especially within paleosol zones and lacustrine facies. Proximity to Paleozoic granitic intrusions—primary sources of uranium—enhances the potential for secondary enrichment through weathering and hydrothermal mobilization. Paleochannels and permeable sandstones enable the migration of uranyl-bearing fluids, while clay-rich layers act as geochemical traps. Historical radiometric surveys, including those conducted in the Suujin Tal structure, have confirmed elevated radioactivity within the Bainshiren Formation, underscoring its strategic relevance for sediment-hosted uranium exploration [15].

In sum, the Bainshiren Formation is a structurally and geochemically favorable unit for uranium accumulation, integrating tectonic activity, sedimentary heterogeneity, and proximity to radiogenic granitic terrains. Its study is essential for reconstructing Cretaceous paleogeography and for advancing resource assessment in southern Mongolia.

2.3.3. The Naarst Area

The Naarst area has undergone extensive uranium exploration, initially by Soviet teams between 1978 and 1981, resulting in over 250 drill holes, and subsequently through additional boreholes drilled between 2006 and 2009 by Western companies. These efforts were triggered by the detection of uranium anomalies in the late 1970s. The region’s current surface geology, dominated by sand, gravel, and locally derived sandstone, reflects its sedimentary context within the Cenomanian–Santonian formations (K2ss2 and K2bs) [11]. Despite post-drilling contamination from radioactive drilling mud pits that hindered auto-gamma surveys, spectrometric data revealed elevated uranium values in both grey (reduction-favoring) and yellowish-to-brownish sandstones (Figure 3). Notably, uranium mineralization appears to concentrate near the convergence of two paleo drainage systems beneath a thin Quaternary cover—features clearly distinguishable via satellite imagery. The area is structurally complex, with active tectonism producing a network of crosscut faults and generating discrete blocks measuring approximately 500–700 × 100–150 m. However, recent investigations have not confirmed the presence of a coherent ore body amenable to in situ leaching [16]. Although the anomalies trace similar structural trends, mineralized intersections occur at variable or excessive depths, in some cases exceeding 400 m.

2.3.4. The Zuunbayan Area

The Zuunbayan area, delineated within the Upper Cretaceous Bainshiren Suite (K2bs), exhibits high uranium potential as evidenced by drilling conducted between 2008 and 2009. Although initial gamma anomalies were identified in the early 1980s, systematic uranium exploration commenced only after 2006 [14]. Spanning approximately 22 km in length and 4–7 km in width, the zone functions as a natural groundwater collector—confirmed by satellite imagery—and is marked by significant subsurface hydrodynamics. Drilling operations frequently triggered spontaneous groundwater upflows, occasionally requiring relocation of rigs to prevent instability. Despite minimal vegetation, the area’s wetland-like conditions and surface instability from unconsolidated sediments rendered access and conventional geological mapping particularly difficult (Figure 4). Nonetheless, auto-gamma surveys corroborated earlier Soviet data, and oxidized brown sandstone outcrops were successfully identified. Subsurface investigations revealed multiple uranium-enriched intersections, typically at depths between 220 and 340 m, with concentrations exceeding 200 ppm [16], suggesting promising potential for the identification of an economically viable ore body in future detailed exploration.

2.4. Car-Borne Gamma Spectrometer Survey

A car-borne gamma spectrometry survey was conducted in 2008 across the Sainshand and Zuunbayan uranium project areas using the RS-700 system [17], a high-resolution, 1024-channel gamma-ray spectrometer developed by Radiation Solutions Inc. (Canada). The system was equipped with a 4-L NaI(Tl) detector mounted on a Toyota Land Cruiser 4×4, with data acquisition and control managed via a Panasonic ToughBook laptop. The RS-700 operates across an energy range of 20 keV to 3 MeV and is capable of handling count rates up to 250,000 cps with less than 20% dead time, ensuring high spectral fidelity even under elevated radiation conditions. Background levels typically remain below 100 cps, while elevated readings in the several hundred cps range may indicate natural enrichment; values exceeding 1000 cps are considered anomalous and may suggest contamination or unexpected radioactive sources. The system’s advanced digital signal processing and automatic gain stabilization enable reliable field performance without the need for radioactive calibration sources [17].

The car-borne gamma heatmaps represent natural gamma dose rates, expressed in total count values (cps). These values were derived from raw counts per second (cps) recorded by the vehicle-mounted spectrometer and corrected for cosmic background, vehicle shielding, and system noise using established calibration constants. On the natural gamma dose map (Figure 5A), blue areas (~4400 cps) correspond to natural background levels, while red and orange areas (~9000–11,900 cps) indicate zones of elevated gamma radiation, approximately two to three times higher than background. This cps-to-dose conversion allows for consistent interpretation across survey blocks and highlights anomalous regions suitable for follow-up exploration. In the Naarst area, the hotspots reach ~9200 cps (Figure 5B), while in the Zuunbayan area they rise to ~11,900 cps (Figure 5C) [16].

In Figure 6, the car-borne uranium count heatmap represents the uranium-specific channel of the spectrometer, expressed in counts per second (cps). Values range from near 0 cps in background areas to ~16.6 cps in anomalous zones. Blue areas correspond to low or background uranium levels, while yellow to red areas indicate progressively elevated counts. In the Naarst area, hotspots reach ~12.5 cps, while in the Zuunbayan area they rise to ~16.6 cps. Hotspots in both the uranium count map and the natural gamma dose map coincide spatially in the Naarst and Zuunbayan areas. This overlap indicates that the elevated total gamma response in these zones is strongly influenced by uranium, rather than being dominated by potassium or thorium contributions. Such correspondence provides greater confidence that the anomalies reflect true uranium enrichment.

2.5. Methodology

As illustrated in Figure 7, our workflow began with the hypothesis that pixels exhibiting high values in water-sensitive composite indices would partially coincide with zones of elevated gamma radiation in semi-arid basinal environments, reflecting the natural distribution of radioactive elements and their mobilization by episodic moisture. To test this, we acquired Level 2A Sentinel 2 imagery and overlaid it on raster heatmaps from a car-borne gamma spectrometer survey of two study areas (Naarst and Zuumbayan). We converted the RGB heatmaps to grayscale using a custom formula. We also applied ISO Cluster classification to the RGB heatmaps before reclassifying the resulting clusters into three gamma radiation classes. A suite of established and newly derived normalized difference composite indices was evaluated against these classes using Pearson and Spearman correlations, two percentile-based overlap metrics, and confusion matrix–derived precision, recall, F1, and overall accuracy. Finally, we combined these metrics into a weighted scoring system to rank and select the top-performing indices for mapping high-gamma radiation hotspots.

To enable direct statistical comparison between the multi-band gamma-ray heatmaps and the single-band composite indices, each RGB heatmap raster was converted into a single-band (grayscale) raster. This transformation collapses the three-color channels into a single intensity value per pixel. The resulting grayscale rasters facilitate scalable data handling, streamline subsequent geospatial processing, and ensure compatibility with one-band index evaluation workflows. Standard RGB-to-grayscale conversion methods include [18]:

• Luminosity Method—This approach accounts for the human eye’s varying sensitivity to different colors by computing the grayscale value as a weighted average of the R, G, and B channels:

$${Gray}_{pixel}=0.2989\times R_{\mathrm{p}\mathrm{i}\mathrm{x}\mathrm{e}\mathrm{l}}+0.5870\times G_{\mathrm{p}\mathrm{i}\mathrm{x}\mathrm{e}\mathrm{l}}+0.1140\times B_{\mathrm{p}\mathrm{i}\mathrm{x}\mathrm{e}\mathrm{l}}$$

(1)

• Arithmetic Mean Method—A simpler technique that calculates the grayscale value as the unweighted average of all three channels:

$${Gray}_{pixel}={\displaystyle \frac{R_{pixel}+G_{pixel}+B_{pixel}}{3}}$$

(2)

where $R_{pixel}$, $G_{pixel}$, and $B_{pixel}$ are the red, green, and blue band values, respectively [18].

However, because our heatmaps’ hotspots are characterized by extremely high red-band values (with green and blue near zero), we adopted a customized formula that accentuates the red channel and de-emphasizes the others [18]:

$${Gray}_{pixel} = 1 \times R_{pixel} - 0.1 \times G_{pixel} - 0.2 \times B_{pixel}$$

(3)

Unlike conventional formulas, whose weights sum to unity to preserve overall brightness, our weights sum to 0.7 in order to maximize contrast between high-gamma-radiation regions and the surrounding background. This specific weighting provided clearer delineation of radiation hotspots and yielded more reliable pixel values for subsequent correlation analyses (Figure 8).

2.6. ISO-Cluster Classification

The original heatmaps were also processed using the ISO-Cluster classifier in ArcGIS Pro, an unsupervised classification method based on the K-means clustering algorithm. Unlike supervised approaches, ISO-Cluster does not require pre-defined training samples. Instead, it automatically partitions pixels into groups according to their spectral similarity. We set the maximum number of clusters to ten, allowing the algorithm to iteratively assign each pixel to the cluster whose mean spectrum most closely matches its own and then update cluster centroids until convergence [19]. This procedure yields a raster in which each pixel is labeled by its spectral class, facilitating the isolation of gamma-ray anomaly zones for subsequent analysis.

Following ISO-Cluster classification, Area 2 yielded ten spectral classes (values 0–9), with class 9 corresponding to the highest gamma-radiation levels and class 0 to the lowest. In Area 1, nine classes (0–8) were produced, where class 8 represented the most intense gamma-radiation zones and class 0 the background. Because the original car-borne heatmaps exhibited three distinct gamma-radiation regimes—high (>8300 cps), medium/low (5500–8300 cps), and negligible (≤5500 cps)—we reclassified the ISO-Cluster outputs into three consolidated classes (Figure 9):

• Class 2 (High gamma radiation): Area 1′s class 8; Area 2′s class 9;
• Class 1 (Medium/Low gamma radiation): Area 1′s class 7; Area 2′s classes 8 and 7;
• Class 0 (Negligible gamma radiation): Area 1′s classes 1–6; Area 2′s classes 1–6.

3. Results

3.1. Composite Index Evaluation

Sentinel 2 Level 2A imagery, acquired on 20 September 2022 under exceptionally favorable conditions (0% cloud cover, 0.007% vegetation cover, 0% snow and ice cover and mean water vapor content of 0.77 g/cm²) was used for composite index evaluation. Ambient surface temperatures during acquisition ranged from 6.3 °C to 19.7 °C, and no rainfall occurred on the acquisition date or in the preceding two weeks.

Based on our initial hypothesis, we evaluated all spectral bands of the Sentinel 2 scene as well as a suite of composite indices sensitive to water-related surface changes. First, each index was visually compared against the spatial distribution of gamma radiation hotspots on the heatmaps, and indices exhibiting substantial mismatches were excluded. Next, we conducted a detailed analysis of spectral bands B1 through B12 and the following composite indices: MI—Moisture Index ((B8A − B11)/(B8A + B11)), NDSI—Normalized Difference Snow Index ((B3 − B11)/(B3 + B11)), NDWI—Normalized Difference Water Index ((B3 − B8)/(B3 + B8)) [20], WRI—Water Ration Index ((B3 + B04)/(B08 + B11)) [21] and NDSII_1—Normalized Difference Snow and Ice Index ((B4 − B11)/(B4 + B11)) [22].

Correlations between each index and the classified gamma radiation zones were quantified using:

• Pearson’s correlation coefficient.
• Spearman’s rank correlation coefficient.
• Two percentile-based comparisons.

3.2. Pearson and Spearman Correlation

In statistics, the Pearson and Spearman coefficients quantify the correlation between two datasets. Pearson’s coefficient evaluates the relationship as a linear function, whereas Spearman’s assesses it as a monotonic function. Both coefficients range from −1 to 1, where 1 denotes a perfect positive correlation, −1 a perfect negative correlation, and 0 no correlation at all. Because they summarize correlation across entire datasets, these metrics are only partially suited for evaluating the relationship between composite indices and gamma radiation—our hypothesis concerns the co-occurrence of hotspots (i.e., pixels with both high index values and high gamma readings), not the overall raster. Consequently, we do not expect extremely high Pearson or Spearman values; nevertheless, they remain valuable evaluation parameters, with their limitations addressed by the subsequent percentile-based comparisons [23].

3.3. Percentile-Based Comparisons

Percentiles are a statistical measure that partition a dataset into 100 equal segments, where each percentile denotes the value below which a specified percentage of observations lie. This approach provides a nuanced view of the data distribution, its concentration, and the relative positioning of particular values within the overall dataset.

We designed two percentile-based comparisons to evaluate the “predictive power” of each composite index, that is, the extent to which the pixels with the highest index values (hotspots) coincide with areas of elevated gamma radiation [24].

In the first comparison, the 95th percentile of each composite index was calculated, and all pixel values below this threshold were discarded, leaving the top 5% of pixels (those with the highest index values) designated as composite hotspots. The 70th percentile of the grayscale gamma-radiation heatmap was then computed, and, by the same criterion, only pixels exceeding this threshold (the top 30% in terms of radiation) were retained. Finally, we determined the proportion of composite-hotspot pixels (above the 95th percentile) that overlapped with the heatmap pixels above the 70th percentile.

The second comparison assessed the fraction of the top 5% of composite-index pixels (those above the 95th percentile) that fell within the Class 2 polygon of the ISO-Cluster classified heatmap, which corresponds to the highest gamma-radiation zones. The outcomes of both comparisons were expressed as values between 0 and 1 (or 0–100%), indicating the predictive alignment of the composite indices with elevated gamma-radiation areas.

3.4. Interpretation of Evaluation Results

In the first step, we calculated the five comparison metrics for each individual spectral band and established composite indices, and the results are presented in

Table 1. Composite and spectral band scores for Sentinel 2.

	Area 2				Area 1				E
	PC	SC	P1	P2	PC	SC	P1	P2
MI	0.34	0.23	0.86	0.4	0.09	0.08	0.29	0.13	36.50%
NDSII_1	0.37	0.25	0.85	0.4	−0.04	−0.12	0.27	0.15	34.60%
WRI	0.31	0.22	0.76	0.45	−0.08	−0.16	0.2	0.11	30.96%
NDSI	0.29	0.2	0.74	0.41	−0.09	−0.17	0.19	0.1	28.86%
NDWI	0.09	0.07	0.55	0.1	−0.12	−0.2	0.12	0.06	13.19%
B01	0.07	0.03	0.62	0.31	0.22	0.1	0.5	0.29	26.52%
B02	0.06	0.04	0.62	0.32	0.19	0.08	0.49	0.24	25.54%
B03	0.05	0.04	0.48	0.3	0.19	0.13	0.51	0.24	23.34%
B04	0.06	0.06	0.36	0.24	0.22	0.16	0.56	0.25	21.57%
B05	0.05	0.06	0.24	0.16	0.25	0.2	0.57	0.27	18.71%
B06	0.03	0.05	0.12	0.07	0.26	0.24	0.54	0.23	14.35%
B07	0.01	0.04	0.09	0.04	0.27	0.26	0.53	0.23	12.92%
B08	−0.01	0.03	0.08	0.02	0.25	0.25	0.5	0.2	10.95%
B08A	−0.02	0.02	0.06	0.01	0.28	0.29	0.5	0.22	10.93%
B11	−0.15	−0.09	0.04	0	0.25	0.28	0.49	0.18	5.43%
B12	−0.16	−0.11	0.04	0	0.2	0.2	0.49	0.16	3.79%

below. We then aggregated these metrics into a single composite score, assigning a greater weight (70%) to the parameters derived from Area 2—owing to its more naturally distributed radiation pattern compared to Area 1 (30%), as discussed earlier. The composite score E (expressed on a 0–1 scale, or 0–100%) was computed using:

$$E=0.3\times {\displaystyle \frac{P{C}_1 +S{C}_{1 }+P{1}_{1 }+P{2}_{1 }}{4}}\hspace{0.25em}+\hspace{0.25em}0.7\times {\displaystyle \frac{P{C}_2+S{C}_2+P{1}_2+P{2}_2}{4}}$$

(4)

In this formula, PC denotes the Pearson correlation coefficient, SC the Spearman correlation coefficient, P1 the result of the first percentile-based comparison, and P2 that of the second. Subscript “1” refers to metrics from Area 1 and subscript “2” to those from Area 2. The final composite scores are listed in Table 1.

Analysis of the results showed markedly better performance in Area 2 compared to Area 1, as expected, since the gamma radiation distribution in Area 2 is naturally controlled, whereas in Area 1 it is influenced by anthropogenic factors. The composite indices MI and NDSII_1 achieved the highest scores, exhibiting the strongest correspondence between their hotspots and zones of elevated gamma radiation. Both indices are defined using normalized difference (ND) formulas and incorporate band B11 (SWIR 1, ~1610 nm) in the denominator, a wavelength at which water absorption is particularly strong.

Moreover, in Area 2 we observed negative Pearson and Spearman correlation values for band B11, as well as for band B12 (SWIR 2, ~2190 nm), deviating from the behavior of other bands (see Table 1). Band B12 also experiences strong water absorption. Consequently, we formulated new theoretical indices, still using ND constructs that employ B11, B12, or both as the subtractive term. Both MI and NDSII_1 include band B4 (red, ~665 nm), another water absorptive wavelength, and band B8A (narrow NIR, ~865 nm), which is highly reflective in healthy vegetation. For the new formulas’ denominators, we also experimented with other visible and NIR bands, motivated by the observed decline in Pearson correlation and overall composite score E in Area 2 as band wavelength increases (see Table 1).

The newly derived indices were evaluated in both areas using the same methodology, and their results (ranked from best to worst) are presented in

Table 2. Scores of the new theoretical composites.

		Area 2				Area 1				E
	Formula	PC	SC	P1	P2	PC	SC	P1	P2
Composite 1	(B4 + B8A − B12)/(B4 + B8A + B12)	0.39	0.26	0.89	0.74	0.17	0.16	0.38	0.16	46.58%
Composite 2	(B5 + B4 + B8A − B11 − B12)/(B4 + B5 + B8A + B11 + B12)	0.41	0.28	0.88	0.71	0.09	0.02	0.37	0.19	44.89%
Composite 3	(B6 + B5 + B4 + B8A − B11 − B12)/(B6 + B4 + B5 + B8A + B11 + B12)	0.41	0.28	0.89	0.72	0.08	0.02	0.35	0.18	44.88%
Composite 4	(B6 + B4 + B8A − B11 − B12)/(B4 + B6 + B8A + B11 + B12)	0.4	0.27	0.88	0.72	0.09	0.04	0.35	0.17	44.78%
Composite 5	(B7 + B4 + B8A − B11 − B12)/(B4 + B7 + B8A + B11 + B12)	0.4	0.27	0.88	0.72	0.09	0.06	0.35	0.16	44.74%
Composite 6	(B4 + B8A − B11 − B12)/(B4 + B8A + B11 + B12)	0.41	0.27	0.88	0.7	0.1	0.05	0.37	0.18	44.72%
Composite 7	(B04 − B12)/(B04 + B12)	0.4	0.26	0.88	0.68	0.08	0	0.39	0.19	43.85%
Composite 8	(B3 + B6 + B5 + B4 + B8A − B11 − B12)/(B3 + B6 + B4 + B5 + B8A + B11 + B12)	0.41	0.29	0.85	0.66	0.05	−0.02	0.33	0.17	42.72%
Composite 9	(B3 + B5 + B4 + B8A − B11 − B12)/(B3 + B4 + B5 + B8A + B11 + B12)	0.41	0.29	0.84	0.64	0.05	−0.03	0.33	0.17	42.01%
Composite 10	(B4 − B11 − B12)/(B4 + B11 + B12)	0.4	0.26	0.87	0.63	0.01	−0.08	0.34	0.18	41.18%
Composite 11	(B4 + B8A − B11)/(B4 + B8A + B11)	0.4	0.28	0.86	0.65	0.01	−0.07	0.29	0.16	41.08%
Composite 12	(B3 + B4 + B8A − B11 − B12)/(B4 + B3 + B8A + B11 + B12)	0.4	0.28	0.82	0.61	0.04	−0.03	0.33	0.16	40.80%
Composite 13	(B4 + B8 − B11)/(B4 + B8 + B11)	0.38	0.26	0.86	0.62	−0.02	−0.09	0.26	0.14	39.15%
Composite 14	(B2 + B4 + B8A − B11 − B12)/(B4 + B2 + B8A + B11 + B12)	0.38	0.27	0.8	0.57	0.02	−0.06	0.3	0.15	38.71%
Composite 15	(B1 + B4 + B8A − B11 − B12)/(B4 + B1 + B8A + B11 + B12)	0.39	0.28	0.8	0.56	0.03	−0.04	0.29	0.15	38.60%
Composite 16	(B1 + B4 − B11 − B12)/(B4 + B1 + B11 + B12)	0.35	0.25	0.76	0.47	−0.05	−0.14	0.24	0.13	33.15%

. These tailored, theoretically grounded composites have met expectations by outperforming the established indices under the specific conditions of gamma radiation comparison.

Subsequently, the ten composites with the highest evaluation scores were classified and are henceforth referred to by their ordinal numbers (Figure 10).

3.5. Classification of Top-Performing Composites

The ten highest scoring composites were classified into three categories: Class 2 (high gamma radiation zones), Class 1 (medium and low gamma radiation zones), and Class 0 (negligible gamma radiation zones). The first step was to determine the pixel value thresholds that would delineate these classes.

Common image segmentation algorithms isolate objects from the background by identifying a critical grayscale threshold. In bimodal images, the histogram exhibits two dominant peaks—one corresponding to object pixels and the other to background pixels—separated by a pronounced valley. The optimal threshold is placed at this minimum to minimize misclassification of pixels between the two groups [25].

We implemented a multi-class extension of this approach as follows:

• Each composite was overlaid with the ISO Cluster classification of Area 2, since Area 2 exhibits a natural gamma radiation distribution (Figure 11).
• Three histograms were generated, each representing the distribution of composite pixel values within the polygon for one of the three heatmap classes.
• The class boundaries for the composite were chosen at the intersections of these overlaid histograms, ensuring that within each composite class the maximum number of pixels coincided with the corresponding heatmap class.

The threshold, or critical value, between each pair of composite classes was set at the intersection of the overlaid histograms. These histograms represent the distribution of composite pixel values within the polygons of the classified heatmap classes. Our goal was to position the boundaries so that, for each composite class, the greatest possible number of pixels fell within the corresponding heatmap class. In ideal conditions, the histogram intersection would lie in the valley between two dominant peaks, although that was not precisely the case here, the desired outcome was still achieved (Figure 12).

The exact pixel values defining the class boundaries for each composite are listed in

Table 3. Class boundary values for each composite, showing the lower boundary first, followed by the upper boundary.

	Composite 1		Composite 2		Composite 3		Composite 4		Composite 5
Class 2	0.26	0.35	0.12	0.19	0.26	0.33	0.12	0.21	0.12	0.21
Class 1	0.25	0.26	0.10	0.12	0.24	0.26	0.10	0.12	0.11	0.12
Class 0	0.14	0.25	−0.04	0.10	0.09	0.24	−0.04	0.10	−0.03	0.11
	Composite 6		Composite 7		Composite 8		Composite 9		Composite 10
Class 2	−0.09	−0.01	−0.11	−0.04	0.33	0.40	0.22	0.29	−0.44	−0.38
Class 1	−0.11	−0.09	−0.13	−0.11	0.32	0.33	0.21	0.22	−0.45	−0.44
Class 0	−0.24	−0.11	−0.29	−0.13	0.19	0.32	0.07	0.21	−0.59	−0.45

. After converting these values into percentiles, we found that the boundary between Class 2 and Class 1 for all composites falls at approximately the 95th percentile, while the boundary between Class 1 and Class 0 is around the 88th percentile. Figure 13 shows the classified heatmap alongside the composites for Area 2.

Subsequently, the composites in Area 1 were classified using the exact pixel-boundary values determined for each class (Figure 14).

3.6. Assessment of Composite Predictive Power

To assess each composite’s predictive power, we compared its three classes (2, 1, and 0) against the three classes of the ISO-Cluster-classified heatmaps for both Area 2 and Area 1. For each area, we first built a confusion matrix in which the reference (target) labels were the classes from the gamma-radiation heatmap, and the predicted labels came from the classified composite. For each class, we then computed [19]:

• True Positive area (TP): the overlap between the predicted class polygon and the reference class polygon—i.e., the area correctly predicted.
• False Positive area (FP): the portion of the predicted class polygon that does not overlap the reference polygon—i.e., overprediction, or “commission error.”
• False Negative area (FN): the portion of the reference class polygon that does not overlap the predicted polygon—i.e., underprediction, or “omission error.”

Using TP, FP, and FN, we derived the following metrics for each class:

1.

Precision:

$$P = {\displaystyle \frac{TP}{\left(TP+FP\right)}}$$

(5)

Precision quantifies the accuracy of predicted areas: the proportion of the predicted class area that is correct. A high precision indicates that most of the predicted region overlaps the reference.

2.

Recall:

$$R= {\displaystyle \frac{TP}{\left(TP+FN\right)}}$$

(6)

Recall measures completeness: the proportion of the reference class area that was correctly predicted. A high recall means that most of the true class area was captured, indicating few omissions.

3.

The F1 score:

$$F1 = {\displaystyle \frac{2\times \left(P\times R\right)}{\left(P+R\right)}}$$

(7)

The F1 score is the harmonic mean of precision and recall, providing a single balance metric between overprediction and underprediction.

4.

Overall Accuracy:

$$OA={\displaystyle \frac{\sum \left(TP\right)}{\sum (TP+FP+FN)}}$$

(8)

Overall Accuracy (OA) is defined as the ratio of the sum of true positive areas across all classes to the total area of all cases across all classes. This metric provides a general measure of classification performance, where a value of 1 indicates perfect agreement between the predicted and reference data.

To quantify the predictive power of each composite index, we computed a score G using the formula:

$$G=\left(0.7\times \left(0.6\times F{2}_2+0.1\times F{1}_2+0.1\times F{0}_2+0.2\times {OA}_2\right)+\left(0.3\times \left(0.6\times P{2}_1+0.1\times P{1}_1+0.1\times P{0}_1+0.2\times {OA}_1\right)\right)\right)\times 10$$

(9)

Here, F2, F1 and F0 are the F₁ scores for classes 2, 1, and 0, respectively; P2, P1 and P0 are their corresponding precision values; and OA is the overall accuracy. The subscript “1” denotes metrics for Area 1, and “2” for Area 2.

When weighting the parameters, we allocated the highest weight (0.6) to class 2, 0.1 to each of classes 1 and 0, and 0.2 to overall accuracy. This is because class 2 represents the high gamma-radiation zone, and the accuracy of predicting this zone is paramount, since the objective is to successfully predict areas with elevated gamma-radiation based on the composites. At the area level, Area 2 was given a weight of 0.7 and Area 1 a weight of 0.3, reflecting the fact that gamma-radiation in Area 2 follows a natural distribution, whereas in Area 1 it is anthropogenically influenced. Moreover, because anthropogenic factors in Area 1 cause class 2 to cover an unnaturally large extent, recall was very poor. This also impacts the F1 score values, and because precision is far more critical than recall for predicting gamma-radiation zones, precision was used as a parameter in the formula. The resulting score was then multiplied by 10 to produce a 0–10 scale (

Table 4. Results of the predictive power evaluation of the composites.

		Area 1				Area 2				G
		P	R	F1	OA	P	R	F1	OA
Composite 1	Class 2	0.72	0.63	0.67	0.75	0.26	0.03	0.06	0.77	5.84
	Class 1	0.52	0.15	0.23		0.07	0.02	0.03
	Class 0	0.77	0.96	0.86		0.81	0.95	0.87
Composite 2	Class 2	0.70	0.58	0.63	0.75	0.40	0.02	0.05	0.80	5.92
	Class 1	0.50	0.15	0.24		0.01	0.00	0.00
	Class 0	0.77	0.96	0.86		0.81	0.98	0.89
Composite 3	Class 2	0.72	0.58	0.64	0.75	0.35	0.02	0.04	0.79	5.88
	Class 1	0.50	0.16	0.24		0.01	0.00	0.00
	Class 0	0.77	0.96	0.86		0.81	0.98	0.89
Composite 4	Class 2	0.71	0.59	0.64	0.75	0.28	0.02	0.05	0.79	5.74
	Class 1	0.50	0.16	0.24		0.02	0.00	0.01
	Class 0	0.77	0.96	0.86		0.81	0.98	0.88
Composite 5	Class 2	0.70	0.61	0.65	0.75	0.25	0.03	0.05	0.79	5.70
	Class 1	0.51	0.14	0.22		0.03	0.00	0.01
	Class 0	0.77	0.96	0.86		0.81	0.98	0.88
Composite 6	Class 2	0.69	0.58	0.63	0.75	0.32	0.03	0.05	0.79	5.77
	Class 1	0.50	0.15	0.23		0.02	0.00	0.01
	Class 0	0.77	0.96	0.86		0.81	0.98	0.89
Composite 7	Class 2	0.69	0.54	0.60	0.75	0.57	0.03	0.06	0.80	6.09
	Class 1	0.50	0.14	0.22		0.02	0.00	0.00
	Class 0	0.77	0.96	0.86		0.81	0.99	0.89
Composite 8	Class 2	0.67	0.53	0.59	0.75	0.34	0.03	0.06	0.79	5.61
	Class 1	0.48	0.15	0.22		0.01	0.00	0.00
	Class 0	0.77	0.96	0.86		0.81	0.98	0.88
Composite 9	Class 2	0.65	0.51	0.57	0.75	0.37	0.03	0.06	0.79	5.58
	Class 1	0.49	0.14	0.22		0.01	0.00	0.00
	Class 0	0.77	0.96	0.85		0.81	0.98	0.88
Composite 10	Class 2	0.69	0.46	0.55	0.74	0.64	0.02	0.04	0.80	5.99
	Class 1	0.47	0.16	0.24		0.01	0.00	0.00
	Class 0	0.77	0.96	0.85		0.81	0.99	0.89

).

The ranking of composites in our evaluation clearly highlights the superior performance of the newly derived indices over established moisture-sensitive metrics. Composite 7 achieved the highest composite score (6.09), closely followed by Composite 10 (5.99), Composite 2 (5.92), Composite 3 (5.88), and Composite 1 (5.84). By contrast, the Moisture Index (MI) scored 4.99 and the Normalized Difference Water Index (NDWI) only 2.78. This performance gap underscores that these explicitly tailored indices can more precisely discriminate gamma-radiation-related moisture anomalies than generalized water-sensitive formulas.

The formula for Composite 7 is NDGRI = (B4 − B12)/(B4 + B12), which we have termed the Normalized Difference Gamma-Ray Index. This index predicts elevated gamma radiation (Class 2) zones with 62.83% precision in Naarst and Zuunbayan, classifying pixels with values between −0.109 to −0.040 as high-radiation areas. It achieves an overall accuracy across all classes of 0.78 in these two areas.

3.7. Validation at Other Explored Areas

We evaluated NDGRI in two additional test sites in Mongolia, both in Dornogovi Province. The first site lies near Erdene (110.99°E–111.35°E, 44.22°N–44.84°N,WGS 84/UTM Zone 49N), and the second near Khuvsgul (109.51°E–110.35°E, 43.53°N–43.67°N, WGS 84/UTM Zone 49N). Sentinel-2 scenes were selected according to the climatological limitations, the Erdene image was acquired on 19 August 2023, and the Khuvsgul image on 30 July 2023. For each site, we identified all pixels with NDGRI values between −0.129 and −0.040 (classes 1 and 2) and calculated the percentage of those pixels overlapping high-gamma-radiation areas delineated from airborne gamma-spectrometry heatmaps.

The heatmaps derive from an airborne gamma-ray survey conducted in 2008 by GEOSAN LLC over the Sainshand uranium project area, flown in a Cessna 208B fixed-wing aircraft equipped with a dual-detector radiometric system comprising two Radiation Solutions RSX-4 spectrometers [26]. Each sensor contains four 4-L NaI(Tl) crystals (16 L per unit, 32 L total) and employs a 1024-channel digital MCA spanning approximately 12 keV to 3 MeV with an energy resolution better than 8.5% FWHM at 662 keV. Each crystal sustained count rates up to 250,000 cps with minimal dead time, ensuring high fidelity even over strongly radioactive targets. Automatic multi-peak gain stabilization—referencing natural isotopes of K, Th, and U—maintained peak drift below 0.5% without the need for onboard calibration sources, although daily pre- and post-flight thorium checks were performed at a fixed airfield position. Data were recorded every second (approximately 75 m along-track at a nominal speed of 75 m/s) as both full 256-channel spectra and five standard energy-window count rates (total count, K-40, Bi-214, Tl-208, and cosmic), then subjected to dead-time correction, background subtraction (aircraft, cosmic, and radon), NASVD noise reduction, Compton stripping, and height-attenuation correction to produce calibrated eU, eTh, K, and total-count data suitable for geological mapping [27]. Calibration was supported by detailed radiometric constants and background corrections. Aircraft and cosmic background levels were quantified as 122.65 cps total count, 28.40 cps K, 2.85 cps U, and 0.93 cps Th, with cosmic scaling factors of 0.6572, 0.0325, 0.0293, and 0.0331, respectively. Compton stripping ratios (α = 0.2505, β = 0.4189, γ = 0.7388, etc.) were derived from calibration pad measurements, ensuring reliable spectral separation of K, U, and Th windows. Daily spectral calibration checks against thorium and uranium reference pads confirmed system stability, with average background-subtracted counts remaining within a narrow range over the survey period. Sensitivity testing on dynamic calibration tracks indicated responses of ~11 cps per ppm eU and ~4.5 cps per ppm Th, validating the robustness of the airborne-to-ground concentration conversion. The heatmaps depict total gamma intensity values ranging from 1434.42 to 6318.4 cps (Figure 15). The red transect lines crossing the maps indicate different research right boundaries, which are not shown on the accompanying detailed survey maps [16].

The original airborne gamma-spectrometry heatmaps were classified in ArcGIS Pro using an ISO Cluster (K-means) classifier and subsequently reclassified into two polygon classes: elevated radiation (>4000 cps) and background (<4000 cps). Pixels within the elevated radiation class were treated as targets, while NDGRI predictions were defined such that class 1 and class 2 pixels represented elevated radiation and class 0 represented background. The resulting confusion matrices are shown in

Table 5. Classification performance metrics (precision, recall, and F1 score) for NDGRI predictions of elevated radiation zones compared with airborne gamma-spectrometry data in the Erdene (Area 1) and Khuvsgul (Area 4) study areas.

		P	R	F1
Erdene	elevated radiation	0.71	0.04	0.08
	background	0.53	0.98	0.68
Khuvsgul	elevated radiation	0.86	0.09	0.16
	background	0.39	0.98	0.55

. Although recall for elevated radiation pixels is relatively low, precision is notably higher, 0.71 at the Erdene site and 0.86 at the Khuvsgul site. These outcomes are encouraging because precision is the most critical factor in this context since false positives would be more problematic than missed detections, whereas low recall mainly lowers the F1 score without undermining NDGRI’s value for delineating elevated gamma-radiation zones (Table 5). The spatial overlap accuracy of pixels with elevated radiation was also calculated: 76.41% of class 1 and 2 pixels coincided with the elevated-radiation polygon in the Erdene site (Figure 14), while in the Khuvsgul site, the overlap was even higher at 85.55% (Figure 16), further supporting the positive performance of the method.

The schematic geological maps of the Erdenet (Figure 16B) and Khuvsgul (Figure 16D) areas illustrate that NDGRI zones with elevated gamma radiation (Figure 16A,C) are spatially associated with intrusive lithologies. In Erdenet, these anomalies coincide with granitic intrusions (red areas with black crosses), while in Khuvsgul they are linked to both granitic intrusions and rhyolite bodies (dark pink areas with short lines). In both cases, the radiation anomalies are interpreted as the result of long-term geological decay within these rocks and their subsequent dispersion into the surrounding formations.

4. Discussion

The ranking of composites in our evaluation clearly highlights the superior performance of the newly derived indices over established moisture-sensitive metrics. Composite 7 achieved the highest composite score (6.09), closely followed by Composite 10 (5.99), Composite 2 (5.92), Composite 3 (5.88), and Composite 1 (5.84). By contrast, the Moisture Index (MI) scored 4.99 and the Normalized Difference Water Index (NDWI) only 2.78. This performance gap underscores that these explicitly tailored indices can more precisely discriminate gamma-radiation-related moisture anomalies than generalized water-sensitive formulas.

The formula for Composite 7 is NDGRI = (B4 − B12)/(B4 + B12), which we have termed the Normalized Difference Gamma-Ray Index. This index predicts elevated gamma radiation (Class 2) zones with 62.83% precision in Naarst and Zuunbayan, classifying pixels with values between −0.109 and −0.040 as high-radiation areas. It achieves an overall accuracy across all classes of 0.78 in these two areas. NDGRI is the normalized difference between the red band (B4), which is sensitive to vegetation pigment and surface brightness, and the short-wave infrared band (B12), which responds strongly to water, moisture, and clay absorption [28,29,30]. According to our analysis, NDGRI anomalies correspond to gamma radiation hotspots in semi-arid basinal environments, where intermittent moisture mobilizes radionuclides and sparse vegetative cover allows spectral detection. B12 (SWIR-2, ~2.19 µm) can sense the Al–OH absorption of clays (illite–muscovite–phengite; kaolinite), whose absorption minima occur at ~2.19–2.22 µm [28,29], while B4 (red, 665 nm) can capture brightness and ferric contrasts typical of semi-arid regolith [31]. White-mica/kaolinite absorptions at 2.19–2.22 µm depress B12 reflectance, while many U-bearing surfaces and ferric-stained calcretes are bright in the red; the normalized difference therefore highlights pixels where clay-associated alteration (often K/Th/U-rich) co-occurs with high red reflectance, consistent with the known association between gamma highs and K-bearing clays and U-fixation [32]. In addition, laboratory spectroscopy demonstrates that several secondary uranium minerals (e.g., carnotite, autunite, uranophane) display distinctive VNIR–SWIR reflectance signatures, combining high visible reflectance with absorption features near 2.2 µm [33], supporting the physical rationale for the band pairing. This provides a robust basis for NDGRI’s empirical overlap with U-count and dose anomalies. In practice, background pixels in the semi-arid terrains of Naarst and Zuunbayan exhibit strongly negative NDGRI values (−0.29 to −0.13), reflecting high SWIR-2 reflectance from barren soils and evaporites. By contrast, anomalous pixels cluster between −0.13 and −0.04, indicating relative suppression of SWIR-2 due to clay absorptions and uranium-associated surfaces. This spectral shift toward less negative NDGRI values underpins the observed spatial coincidence with car-borne uranium anomalies [34,35,36].

We present (Figure 17) and explain (

Table 6. Sentinel-2 band utility for minerals.

Mineral	Primary Absorption Feature	Key Sentinel-2 Bands	Detection Limitations
Illite	~2200 nm (Al-OH)	B12, B11	Broad bandwidth blends subtle features.
Kaolinite	~2160–2200 nm (Al-OH doublet)	B12, B11	Doublet unresolved; may confuse with other clays.
Alunite	~2165 nm (SO4/Al-OH)	B12, B4, B3	Broad bands miss narrow feature; overlaps with clays.
Carnotite	<500 nm (Uranium)	B1, B2, B3	Atmospheric scattering; low spatial resolution (B1).
Autunite	<500 nm + ~1400/1900 nm (H2O)	B1, B2, B9	Water vapor interference (B9); low resolution for B1/B9.

) the representative spectra of minerals illite/kaolinite/alunite and a U-mineral such as carnotite/autunite with Sentinel-2 band centers in order to visually support our described mechanism [37,38,39].

The NDGRI anomalies (classes 1 and 2) show significant spatial overlap with the uranium distribution heatmaps derived from car-borne spectrometry (Figure 18). In the Naarst area, NDGRI anomalies correspond with uranium-specific channel values of up to ~9.2 cps, which are well above background (0–3 cps) but below the local maximum of ~12.5 cps. In the Zuunbayan area, they coincide with values reaching ~16.6 cps, the highest recorded in the survey. This correspondence demonstrates that the zones highlighted by the index are not random spectral artifacts but align with measured uranium channel counts on the ground, reinforcing NDGRI’s value as a screening tool for refining exploration targets.

However, it is important to recognize that Composite 7 may not be universally optimal under all environmental conditions. Composites 10, 2, 3, and 1 also performed strongly and could serve as complementary or alternative indices in regions with different soil types, moisture regimes, or land covers. Future work should therefore extend testing across diverse lithologies, climates, and landscape morphologies to determine whether a single index consistently outperforms the others, or whether an ensemble approach (selecting from a suite of high-scoring composites) yields more reliable exploration targets. Such investigations will clarify whether NDGRI represents a unique solution or one member of a broader family of gamma radiation-sensitive remote sensing indices.

Parallel to these radiometric mapping studies, moisture-sensitive multispectral indices have proven effective at detecting subtle water variations in arid and semi-arid landscapes using Sentinel-2 [40]. It was shown that NDWI, its modified form (mNDWI), and a custom SWIR reflectance ratio reliably flagged soil moisture and episodic flooding in Oman’s desert terrain. Malakhov and Tsychuyeva found that the Normalized Difference Moisture Index (NDMI) outperformed NDVI in correlating with biomass and soil water content in Kazakhstan’s sparse grasslands [41], and Lykhovyd and Sharii reported that seasonal NDMI time series from Sentinel-2 and Landsat-8 tracked maize water stress in Ukraine’s semi-arid steppe (R² ≈ 0.62) [42]. These studies confirm that Sentinel-2-derived moisture indices can capture hydrological contrasts in dry lands, suggesting their utility as proxies for subsurface processes that depend on localized moisture dynamics.

NDGRI integrates both the red band, long employed in vegetation indices to detect plant stress and cover changes, with the SWIR 2 band, which underlies moisture-sensitive indices proven effective in arid and semi-arid settings. By normalizing the difference between these two bands, NDGRI captures both vegetation anomalies, potentially induced by subsurface radionuclide stress, and subtle surface moisture variations that modulate gamma ray movement dynamics. This dual-band strategy represents a unique approach that achieved robust results in our tests over Mongolian desert basins, outperforming conventional moisture. This dual-band strategy represents a unique approach that achieved robust results in our tests over Mongolian desert basins, outperforming conventional indices solely based on moisture or vegetation.

4.1. Climatological Limitations

NDGRI is highly sensitive to both surface moisture and atmospheric water content, which imposes strict constraints on Sentinel-2 image selection. In practice, even minimal cloud or vegetation cover can overwhelm the index, so we require cloud cover below 4% of land pixels—otherwise thin clouds elevate red- and SWIR-band reflectance and distort moisture measurements. Vegetation cover must be under 1%, as green foliage strongly affects the red band and produces spurious NDGRI highs. Similarly, snow and ice cover must remain below 1% because they are highly reflective in the red band and absorb strongly in SWIR. Snow appears bright in visible wavelengths and very dark in SWIR, which would dominate the moisture signature. In addition, the SWIR band used by NDGRI is itself designed to measure soil/vegetation moisture, so high atmospheric water vapor can also distort the signal. Therefore, we restricted granule mean water-vapor content to below 2 g/cm². Finally, we impose meteorological constraints: any scene acquired on the day of rainfall or within the preceding few days (depending on precipitation amount) is excluded, since rain introduces fresh surface moisture that confounds the NDGRI signal. Equally, the minimum daily temperature must remain above 0 °C because subzero nights (followed by warm days) can produce dew or frost that unpredictably wets the surface. Dew formation (when the surface reaches the dew point) can recharge soil moisture, and frost from overnight freezing can similarly add water in ice form; both would confound the NDGRI signal. In summary, these strict limits on clouds, vegetation, snow/ice, atmospheric vapor, recent rainfall, and freezing conditions drastically reduce the number of usable scenes, but they are essential to ensure that NDGRI anomalies reflect gamma-related moisture and not incidental water or reflectance artifacts.

Table 7. Metadata for the example Sentinel-2 scenes deemed usable or unusable for NDGRI screening.

Acquisition Day	10 June 2021	19 August 2023	4 June 2024	14 September 2024	23 August 2024	11 March 2024	6 November 2024
Cloud cover (%)	0.00%	0.00%	65.69%	0.06%	2.34%	0.24%	0.00%
Vegetation cover (%)	0.00%	0.03%	0.00%	0.71%	3.00%	0.00%	0.00%
Snow & Ice (%)	0.00%	0.00%	0.00%	0.00%	0.00%	26.13%	0.00%
Mean water vapor (g/cm2)	0.58	0.97	1.42	0.63	2.51	0.26	0.45
Rain on acquisition day (mm)	-	-	26 mm	-	-	-	-
Rain in prior days (mm)	01.06.—1 mm	10.08.—0.4 mm	-	12.09.—21 mm	22.08.—11 mm	-	20.10.—3 mm
Temp °C (mean/min/max)	26.0/14.5/32.2	24.4/11.4/30.5	21.0/16.0/30.8	9.7/2.1/15.0	22.3/16.8/27.8	−5.5/−13.9/0.4	0.2/−5.6/7.6
Verdict	Usable	Usable	Unusable (heavy rain & clouds)	Unusable (residual moisture)	Unusable (residual moisture)	Unusable (snow & ice)	Unusable (freeze-thaw moisture)

and the accompanying Figure 19 illustrate the key differences between Sentinel-2 scenes that meet our climatological screening criteria and those that are rendered unusable. The example imagery covers a broader region (109.74°E–111.12°E, 44.15°N–45.15°N, WGS 84/UTM Zone 49N) encompassing both the Naarst and Zuunbayan study areas. Cloud cover, vegetation cover, snow/ice cover, and atmospheric water-vapor content were extracted directly from the Sentinel-2 metadata fields CLOUDY_PIXEL_OVER_LAND_PERCENTAGE, VEGETATION_PERCENTAGE, SNOW_ICE_PERCENTAGE, and GRANULE_MEAN_WV. Corresponding meteorological variables—precipitation and air temperature—were obtained from the Meteomaz platform, which aggregates both observed data (via SYNOP and BUFR messages from official weather stations) and forecast products from the GFS and ECMWF global models [43].

4.2. Potential False Positives (Geological Limitations)

Certain geological materials and surface conditions can mimic the spectral response of uranium-associated alteration, resulting in NDGRI anomalies that do not reflect true uranium enrichment. The most common sources of such false positives include water bodies, evaporitic surfaces, and clays, each of which can depress SWIR reflectance in ways that overlap with uranium-related signals.

Pure water bodies have very low reflectance in the SWIR, which drives B12 values toward zero while B4 remains > 0. As a result, NDGRI values for water pixels typically become positive (NDGRI ≥ 0), placing them well outside the anomaly range we defined (−0.13 to −0.04). In practice, this means that pure water pixels are not classified as anomalies. However, shoreline or mixed pixels containing both water and soil can yield NDGRI values closer to zero and, in some cases, slightly negative. To reduce the risk of water-related edge effects being misclassified as anomalies, a water mask could be applied using the Modified Normalized Difference Water Index (MNDWI), defined as (B3 − B11)/(B3 + B11) with Sentinel-2 green and SWIR-1 bands. In semi-arid environments, MNDWI generally performs better than the original NDWI because it suppresses bright soils and salt flats that might otherwise mimic water [44]. Pixels with MNDWI values greater than 0.30 could be identified as water, with the threshold relaxed to 0.20 in cases of shallow or turbid surfaces [45]. A buffer of a few pixels, adjusted according to the spatial resolution, can be applied around mapped water bodies to capture shoreline and mixed pixels, and the same approach can also be extended to other masks. When the MNDWI mask with a five-pixel buffer was applied, no masked pixels appeared in the Zuunbayan and Naarst areas, while only a few small clusters were detected in the Erdene and Khuvsgul areas. This outcome was anticipated given the scarcity of surface water in these arid to semi-arid regions. In the limited cases where masking occurred, the affected NDGRI pixels formed circular patterns outlining the margins of small water bodies. Importantly, NDGRI itself did not classify the open water pixels as anomalies, but it did highlight shoreline zones where mixed soil-water reflectance produced values near the anomaly threshold. The MNDWI mask therefore functioned as intended, selectively removing shoreline effects and helping to improve the reliability of the NDGRI classification (Figure 20).

Additional constraints, such as requiring B12 reflectance > 0.08 and B8 (NIR) > 0.15, may further reduce the inclusion of dark soils or shadows. This follows the findings of Gao [46], who showed that pure water has near-zero reflectance in the NIR and SWIR, whereas soils and other land surfaces retain higher reflectance values. Although Gao’s study focused on wavelengths near 0.86 µm and 1.24 µm, the same principle applies to Sentinel-2′s NIR (B8, 842 nm) and SWIR-2 (B12, 2190 nm) bands. Such a combined thresholding approach would help ensure that not only pure water pixels (which typically yield NDGRI ≥ 0) but also shallow or shoreline mixed pixels are excluded, preventing them from being misclassified within the anomaly range [47]. When these constraints were applied, no pixels were masked in our study areas. This reflects the spectral properties of the semi-arid landscapes we analyzed, where soils and rocks seldom reach the near-zero reflectance in B8 and B12 that is characteristic of pure water. Consequently, the thresholds operated conservatively, preserving genuine land surfaces while still providing a safeguard against potential misclassification, which are more likely in environments with more persistent surface water or shadowed terrain. In these regions, such constraints may play a more significant role by preventing shoreline effects or shadow-related artifacts from being misinterpreted as NDGRI anomalies.

At shorter SWIR wavelengths, however, such as B11 (1.61 µm), these same surfaces retain relatively higher reflectance. This spectral contrast produces characteristically high B11/B12 ratios for evaporites compared to clays, which tend to show more uniform depressions across both bands [35]. By mapping areas with unusually high B11/B12 ratios (≥1.3) in combination with very low absolute reflectance in B12 (<0.2), it becomes possible to distinguish salt flats and evaporitic playas from clay-rich alteration zones, thereby reducing the risk of misclassifying these bright but uranium-poor surfaces as NDGRI anomalies. The ratio condition captured the distinctive spectral behavior of evaporites, which retain relatively high reflectance in B11 but drop sharply in B12, while the low B12 threshold ensured that only surfaces with genuinely dark SWIR-2 signatures were flagged. Applied to our study areas, the mask did not identify any pixels in three out of four cases, while in the Erdene, a relatively small area was flagged (Figure 21). These proved to be minor false positives relative to the overall extent. The absence of widespread masking reflects the semi-arid surfaces of our sites, which typically do not reach the very low B12 reflectance values (<0.2) or extreme B11/B12 ratios (>1.3) characteristic of evaporites. In Erdene, localized soil or mineralogical effects likely mimicked evaporitic behavior, but the spatial extent was minimal, underscoring that the mask is conservative and only activates under unusual spectral conditions. Nonetheless, this safeguard could become more important in regions where evaporitic playas or salt flats are widespread, by helping to minimize false positives in NDGRI applications.

Hydrothermal alteration minerals such as illite, kaolinite, or alunite also produce strong absorptions near 2.2 µm that can elevate NDGRI values independently of uranium enrichment [48]. These Al–OH minerals are widespread in altered volcanic and sedimentary environments, meaning NDGRI anomalies may sometimes reflect hydrothermal clay alteration rather than uranium fixation in these areas.

Further research across different geological settings and continued testing of NDGRI against ground-based gamma-ray data will be needed to determine which types of false positives are most critical to avoid and which masking or validation strategies are most effective.

However, we did not observe clear evidence of these false positives in our study areas. Relatively small or localized anomalies were not the focus of this analysis and were therefore not considered in detail. Instead, in the following section, we examine the larger NDGRI anomalies that might initially appear as false positives and provide the reasoning for why they can most likely be interpreted as genuine positives rather than artifacts.

We divided the apparent false positives in the Zuunbayan area into two groups. Group 1 is shown in Figure 22 (circled). As illustrated in Figure 22B, these anomalies occur on the periphery of the zone delineated by historical Soviet measurements (~20 µrad/h). In addition, Figure 22C shows that they overlap with anomalous uranium-count zones recorded during the 2008 car-borne gamma survey. Group 2 is shown in Figure 23 (circled). The northern anomaly lies in close proximity to the main anomaly, suggesting that the source of gamma radiation may have been redistributed within the sedimentary environment through subsurface structural systems and groundwater. The southern anomaly is located near a historically registered Soviet anomaly (~20 µrad/h) (Figure 23B) and coincides with anomalous radioactivity detected by the 2008 car-borne survey (Figure 23C).

The apparent false positives in the Erdene area are most likely genuine, as they are located in the immediate vicinity of, and directly on, a granitic intrusion, shown as red areas with black crosses in Figure 24B.

The apparent false positives in the Khuvsgul area are also most likely genuine, as they are situated near a granitic intrusion and acidic volcanic rocks (dark pink with dashes; C₃–P age) (Figure 25), which are potential sources of radioactive components, including K-40, uranium, and thorium. Weatheredmaterial [43] derived from these volcanic rocks may have been redistributed into the surrounding sedimentary cover, which is dominated by sandy, silty, siltstone, and clay-rich deposits.

5. Conclusions

We have developed and validated the Normalized Difference Gamma-Ray Index (NDGRI), derived from Sentinel-2 bands B4 (red) and B12 (SWIR2), as a robust remote sensing index that shows strong coincidence with elevated gamma radiation in semi-arid basins. NDGRI outperformed both established moisture indices and other derived composites, achieving a precision of 62.8% for the highest radiation class in the Naarst and Zuunbayan study areas, and demonstrating an 80.98% spatial overlap with elevated radiation zones on airborne heatmaps at the Erdene and Khuvsgul test sites. Our methodology integrates radiometric ground truth, unsupervised classification, and percentile-based statistical metrics, weighted to account for anthropogenic noise. Strict climatological screening (limiting cloud, vegetation, snow/ice, atmospheric vapor, precipitation, and frost) proved essential to isolate moisture signals linked to uranium mobilization rather than incidental water artifacts. While these constraints restrict the number of suitable Sentinel 2 scenes, they ensure NDGRI’s reliability. NDGRI could serve as a cost-effective screening tool to highlight zones of elevated radiation, helping to narrow down areas for follow-up field surveys using car-borne and airborne gamma spectrometry, which are proven but expensive methods. The demonstrated correlation between NDGRI signatures and gamma radiation hotspots invites further exploration of its utility across diverse arid basins and further refinement of its spectral or climatological parameters to enhance its robustness under variable environmental conditions.

Looking ahead, we are expanding NDGRI validation to additional semi-arid regions—most recently with pilot studies in Australia, which have shown encouraging concordance with known uranium anomalies. We are also evaluating advanced classification frameworks, including support vector machines, extreme gradient boosting, logistic regression, quadratic discriminant analysis, and multilayer perceptrons, to automatically delineate high radiation zones from NDGRI and ancillary spectral layers. Early results indicate that these machine and deep learning models can further enhance hotspot detection accuracy. Future work will systematically benchmark these approaches and develop an integrated operational workflow to guide targeted field campaigns toward the most promising exploration targets.