This study is part of a national initiative in South Guangdong, China, focused on deep subsurface exploration, including groundwater resource assessment and infrastructure development such as the Jiangmen Underground Neutrino Observatory (JUNO) (Hasan et al., 2025). These actions contribute to China's national agenda toward sustainable deep-earth resource utilization. This research was conducted in the Jinji region, a geologically complex area prioritized for deep groundwater exploration (Fig. 1a). The region lies within a subtropical monsoonal climate zone, receiving ∼ 1981 mm of annual rainfall. Topography ranges from low hills to mountainous terrain (39–539.9 m elevation), with dense vegetation and varied slopes. The northern part is relatively flat, while the south includes prominent features such as the Dashishan and Qilongding Mountains. Surface drainage is primarily controlled by the Yongkouwei River in the northeast.

Geologically, the Jinji area has evolved through successive tectono-magmatic processes linked to the Yanshanian, Indosinian, and Caledonian mountain-building phases, resulting in a lithologically diverse landscape of granite, sandstone, and hornstone (Qin, 2017). Granite intrusions reflect deep crustal magmatism, while hornstone indicates contact metamorphism. Overlying Paleogene sediments record later basin development. Tectonic structuring in the area is largely influenced by the Kaiping fault-fold complex, which includes reverse, thrust, and strike-slip faults formed under prolonged crustal compression and later modified by strike-slip tectonics. These northeast-trending structures govern subsurface architecture and groundwater flow pathways (Yang et al., 2021). Fractures and joints are widespread in granite, sandstone, and hornstone, varying by lithology and tectonic history. These brittle features act as primary conduits for groundwater, with their alignment along major faults highlighting the tight coupling between structural geology and hydrogeology.

This study focuses on the vertical stratification of aquifer-bearing formations. Productive groundwater is mainly stored in deep, fractured sandstone units, overlain by low-permeability granite that limits vertical recharge. An intermediate hornstone layer separates the two, with moderate hydraulic properties and limited connectivity. This configuration isolates the deep aquifer from surface influences, rendering shallow investigations ineffective. Deep-targeted exploration is thus essential for identifying and managing these concealed high-potential groundwater resources in a structurally complex hard rock setting.

Table 2 summarizes the integrated dataset from 6 drills and 6 geophysical profiles to resolve the spatial structure of the subsurface into three distinctive hydrogeological units, based on variations in electrical resistivity and corresponding k values. The development of these subsurface models mainly depends on borehole data, CSAMT-derived resistivity measurements, and the regional geological framework. The stratigraphy was categorized into three primary lithologies: sandstone, hornstone, and granite. Classification criteria were established as follows: sandstone was defined by resistivity values below 350 Ωm and a k range of 10–20 mD; hornstone exhibited resistivity values between 350 and 700 Ωm with a k range of 5–10 mD; and granite was characterized by resistivity values exceeding 700 Ωm and k values ranging from 0 to 5 mD. Based on our evaluations of the subsurface hydrogeological model's aquifer potential zones, we found that sandstone contains the high potential aquifer (HPA), hornstone contains medium potential aquifer (MPA), and granite has low potential aquifer (LPA). Aquifers with the largest yields or the best water-bearing capacity are indicated by sandstone, whereas aquifers with the lowest yields or the worst water-bearing capacities are denoted by granite. Groundwater development is best facilitated by sandstone in the study area, whereas groundwater extraction is most hindered by granite.

Using geophysical-borehole correlation as its basis, Eq. (3) efficiently converts 2D CSAMT models (Fig. 3) into 2D k models (Fig. 6). The interpreted 2D k models shown in Fig. 7, in comparison with the limited borehole experiments, allow for a comprehensive assessment of the groundwater resources in hard rock across the whole research area, from 0 to 1300 m deep.

The integrated 2D k models (Fig. 8) and their interpretations (Fig. 9) provide a detailed evaluation of groundwater potential across complex geological settings of sandstone, hornstone, and granite. Profile 1 reveals a high-potential sandstone aquifer (85–305 m thick) between 245–380 m distances at 205–400 m depth. Medium-potential hornstone aquifers are found from 0–525 and 1185–1445 m distance down to 1300 m. Low-potential granite aquifers appear at 0–285 m (290–790 m depth), 385–1185 m (full depth), and 1305–1450 m (390–745 m depth). Profile 2 shows a medium-potential hornstone aquifer with 140–380 m thickness (490–1105 m depth) between 145–215 and 290–645 m distance. No high-potential sandstone aquifers are present. Granite dominates (0–700 m distance, 0–1300 m depth) the profile with low yield except in hornstone zones. Profile 3 contains both high-potential sandstone (0–250, 905–1065, and 1040–1390 m distances at respective depths of 0–1190, 0–205, and 490–1305 m) and medium-potential hornstone aquifers (full depth with 0–1400 m distance) across the entire surveyed line. Granite aquifers are assessed at 80–1015 m (0–590 m depth), 395–845 m (915–1300 m depth), and 1100–1300 m (200–500 m depth). Profile 4 features medium-potential hornstone at 0–105 m (0–340 m depth), 340–645 m (0 to 1300 m depth), 595–790 m (0–300 m depth), and 1015–1145 m (0–345 m depth). No high-potential sandstone is observed. Granite aquifers of low potential dominate (0–1145 m distance between 0–1300 m depth), except in hornstone zones. Profile 5 shows medium-potential hornstone (190–845 m distance, 390–1300 m depth) and two small high-yield sandstone patches (290 m at 790–960 m depth and 815 m at 1045–1135 m depth). Low-potential granite appears at distance 0–190 m (0–1300 m depth) and 790–815 m (0–1025 m depth). Profile 6 includes high-potential sandstone zones at 0–190 m (0–490 m depth) and 1245–1345 m (215–1225 m depth). Low-potential granite is present at 0–690 m (390–1300 m depth) and 790–1360 m (0–1190 m depth), while hornstone with medium potential dominates the remainder. Overall, the southeastern and northwestern zones host abundant medium- to high-potential aquifers, while central regions show limited or poor groundwater prospects.

The 3D k (outer view) visualization (Fig. 10a, b) provides a comprehensive assessment of the water-bearing capacity of the rock mass. Low-potential granite aquifers are found at the surface along: line 1 (85–215, 385–1175 m), line 2 (0–655 m), line 3 (0–45, 95–175, 265–585, 605–845, 1145–1315 m), line 4 (90–390, 490–615, 745–1115 m), line 5 (0–815 m), and line 6 (1045–1345 m). Medium-potential hornstone aquifers appear along: line 1 (0–95, 190–260, 295–415, 1185–1425 m), line 3 (40–105, 215–275, 580–605, 850–910, 1010–1155, 1310–1410 m), line 4 (45–90, 390–490, 590–685, 1115–1185 m), and line 6 (90–190, 215–275, 315–485, 505–605, 635–1045 m). High-potential sandstone aquifers are identified in: line 1 (265–310 m), line 3 (235–255, 915–1010 m), line 4 (0–45 m), and line 6 (0–90, 210–225, 275–305, 515–525, 605–635 m), Overall, Fig. 10a, b shows that higher-yield aquifers are mainly concentrated in the southern portion of the investigated site.

Figure 11a, b shows a 3D internal view of aquifer potential at 1300 m depth. Low-yield granite aquifers are identified along: surveyed line 1 (515–1215 m), line 2 (0–290 m), line 3 (390–690 m), line 4 (0–1145 m), line 5 (0–195, 565–595 m), and line 6 (0–690, 1075–1115 m). Medium-potential hornstone aquifers are found along: profile 1 (0–540, 1215–1445 m), profile 2 (295–675 m), profile 3 (175–395, 445–815, 915–1035 m), profile 5 (205–565, 610–815 m), profile 6 (685–1080, 1110–1355 m). High-potential sandstone aquifers appear along: profile 3 (0–205, 1010–1400 m) and profile 5 (810–815 m). Overall, medium to high potential aquifers are mainly distributed in the southeastern and northwestern regions, while central areas are dominated by low-yield granite. The aerial 3D k model enhances visualization of aquifer distribution, supporting accurate groundwater assessment.

Due to limited borehole data, direct estimation of k below 200 m is not feasible. However, by integrating borehole and CSAMT data, k values could be reliably estimated down to 1300 m. This approach enabled efficient and detailed evaluation of hard rock aquifers using both 2D and 3D models (Fig. 12), with k values extracted at depths of 0, 200, 600, 1000, and 1300 m. At 1300 m, over 42 % of the subsurface in the southwest and northeast comprised low-yield granite. Hornstone accounted for 40 % (medium yield) near granite zones in the northwest and southeast, while high-yield sandstone made up 18 % in the east. At 1000 m, sandstone (15 %) was concentrated in the southeast (high yield), hornstone (38 %) in the southeast and northwest (medium yield), and granite (47 %) dominated the central and boundary zones (low yield). At 600 m, the subsurface was 55 % granite (central and northern zones, low yield), 32 % hornstone (western region, medium yield), and 13 % sandstone (southeast, high yield). At 200 m, granite dominated 64 % of the center and north (low yield), hornstone made up 26 % in the south (medium yield), and sandstone (10 %) in the west was associated with high yield. At 0 m, 73 % of the central area comprised low-yield granite, 20 % of the southwest was hornstone (medium yield), and 7 % sandstone (high yield) was concentrated in the southwest.

Overall, Fig. 12 shows a decrease in low-yield granite thickness with depth. Groundwater potential is lowest around 600–700 m depth, while deeper zones (> 700 m) in the northwest, southeast, and southwest show more favorable aquifer conditions.

Groundwater evaluation was greatly improved by systematic CSAMT-based k estimation using Eq. (3). As shown in Figs. 6–12, granite dominates the central, northeastern, and southwestern zones; hornstone occurs mainly in the southeast, west, and northwest; and sandstone is prevalent in the east. Borehole-based assessments are limited by inconsistent subsurface mapping. While k values align near 200 m depth, broader extrapolation remains uncertain, highlighting the limitations of sparse drilling in complex geology.

To clarify the basis of the percentage matching values, the following explicit equation was used to quantify the agreement between CSAMT-derived k′ values and borehole-based k estimates: 4PercentageMatch=min⁡(k,k′)max⁡(k,k′)×100 Here, min (k,k′) is the smaller of the two permeability values, either the measured permeability (k) from borehole data or the estimated permeability (k′) from the CSAMT model, at a given depth. Conversely, max (k,k′) is the larger of the two values. This ratio offers a normalized agreement metric, where 100 % indicates a perfect match and lower values reflect greater divergence. Table 3 summarizes results for 18 representative data points (out of 116 total calibration points). Percentage matches range from 30 % to 100 %. Higher agreement is generally observed in moderate-resistivity formations, whereas lower matches occur primarily in highly resistive, low-permeability granite units (e.g., BH-3), where small absolute differences produce larger relative deviations. Despite local discrepancies, both predicted and measured values consistently classify the same aquifer potential zones.

Because the empirical model was derived from 116 paired measurements, predictive capability was evaluated using leave-one-point-out cross-validation (LOOCV). Each observation was excluded sequentially; the regression was recalibrated using the remaining 115 data points; and permeability was predicted for the excluded point. Prediction error was quantified using the root mean square error (RMSE): 5RMSE=1n∑i=1nki-ki′2 where ki denotes the measured permeability, ki′ represents the predicted value for the excluded observation, and n = 116 is the total number of paired resistivity–permeability data points used in the cross-validation procedure. This procedure yielded: 6RMSELOOCV=2.36mD Given the observed permeability range (0.01–19.9 mD), this error indicates stable predictive performance within the calibration domain. For the representative points listed in Table 3, LOOCV-predicted permeability values differ only slightly from those obtained using the full regression model, indicating that the fitted relationship is not strongly influenced by individual observations.

To further assess spatial transferability, a leave-one-well-out cross validation was conducted. In this approach, all data from one borehole were excluded, the regression was recalibrated using the remaining wells, and permeability was predicted for the omitted well. Using the same RMSE formulation (Eq. 5), this yielded: 7RMSEwell=2.78mD The modest increase in error relative to pointwise LOOCV reflects geological heterogeneity rather than model instability. This result demonstrates that the empirical resistivity–permeability relationship generalizes reasonably well across different boreholes and lithological domains.

Together, percentage agreement, leave-one-point-out validation, and leave-one-well-out validation demonstrate that the CSAMT-derived empirical model provides robust and transferable permeability estimates within the measured range. Although localized deviations occur, likely due to structural anisotropy and fracture-controlled flow, the regression is not dominated by single data points or individual wells, supporting its application for regional-scale groundwater assessment.

The integration of geophysics into groundwater studies provides an efficient and scalable substitute for borehole-based methods, especially in deep and geologically complex terrains. While boreholes provide direct k data, their use is limited by cost, logistics, and sparse coverage. Our study presents a robust framework for 2D and 3D k modeling beyond 1 km depth by integrating CSAMT with borehole data in a lithologically diverse setting. This approach addresses key challenges in areas with limited surface water and low-k granite near the surface, revealing deeper fractured zones with higher groundwater potential in granite, hornstone, and sandstone. These deep aquifer insights support China's national water security strategies and inform sustainable groundwater management under climate stress.

To minimize uncertainty and enhance accuracy, we implemented a rigorous workflow throughout data acquisition, processing, inversion, and modeling. For CSAMT, this included careful survey planning, optimized electrode configurations, and the application of advanced filtering and static shift corrections. Inversion was guided by multidimensional modeling constrained by borehole-derived a priori information, improving resolution and mitigating non-uniqueness. Permeability measurements were obtained under controlled laboratory conditions using high-quality, undisturbed core samples from six boreholes, reducing discrepancies between laboratory and field scales. These measures, together with integrated lithological data, enabled the development of a robust k model suitable for reliable groundwater assessment across the study area.

CSAMT, developed in the 1970s, remains uniquely valuable for deep subsurface exploration, particularly in resistive and fractured hard rock environments. Its ability to image at intermediate-to-deep depths (hundreds to over a thousand meters) with relatively high resolution and controlled signal strength enhances its ability to delineate lithological contacts and fluid-bearing formations where other resistivity methods (VES and ERT) may fall short. While electromagnetic methods such as MT and TDEM are also capable of probing deep subsurface structures, achieving comparable results in similarly complex hard rock settings presents notable challenges. MT, which relies on natural variations in electromagnetic fields, can reach even greater depths than CSAMT and has been successfully applied in regional-scale hydrogeological investigations, such as identifying deep groundwater circulation paths in mountain systems (Jiang et al., 2014) and tracing flow systems that recharge lowland aquifers (Gonzalez-Duque et al., 2024).

As summarized in Table 1, MT provides exceptional penetration (tens of kilometers) but has reduced resolution in the upper crust and is highly sensitive to cultural noise, limiting its suitability for detailed k-modeling at the site scale. TDEM, while rapid and effective for intermediate depths, suffers loss of sensitivity in highly resistive formations, making it less effective for fractured granite and hornstone settings. In contrast, CSAMT's controlled-source design and strong immunity to cultural noise provide a balance of penetration depth and resolution well-suited for site-specific groundwater studies in hard rock terrains.

Thus, the comparative analysis (Table 1) underscores why CSAMT is the most appropriate method for this study: it bridges the gap between large-scale regional techniques (MT, TDEM) and shallow, high-resolution methods (VES, ERT), enabling robust 2D and 3D hydrogeophysical modeling essential for evaluating deep aquifer potential.

We developed a robust empirical relationship between resistivity and k using 116 co-located data pairs, 62 from granite, 31 from sandstone, and 23 from hornstone, spanning 35–4765 Ωm and 0.01–19.9 mD, respectively. The strong correlation (R2 = 0.96) ensures reliable k prediction and minimizes lithological bias. The lithological classification derived from the resistivity–permeability relationship in this study is both geologically plausible and empirically supported by borehole data and field observations. Specifically, granite showed high resistivity (> 700 Ωm) and low k (0–5 mD), hornstone had intermediate resistivity (350–700 Ωm) and moderate k (5–10 mD), and sandstone was marked by low resistivity (< 350 Ωm) and higher k (10–20 mD). These ranges align with the distinct hydrogeological behaviors of each lithology under the site-specific structural and mineralogical conditions. The resistivity thresholds were selected through an integrated approach combining lithological logs from boreholes, established empirical resistivity values reported in the literature, and the geoelectrical contrasts identified in CSAMT profiles. For instance, the high resistivity of granite reflects its dense, low-porosity matrix and limited fluid content, whereas the lower resistivity of sandstone and hornstone corresponds to increased pore connectivity and higher saturation, often associated with structural features or thermal alteration. To ensure robust classification, the resistivity thresholds were calibrated using co-located borehole observations from multiple calibration sites and iteratively refined to maximize agreement between observed lithology and the modeled resistivity–permeability domains. While we acknowledge that resistivity can vary within a given lithology due to localized factors such as fluid saturation, mineral alteration, or fracture density, sensitivity analyses indicated that moderate adjustments to the threshold values had minimal impact on the overall lithological classification or the interpretation of k trends. This suggests that the chosen thresholds are well-suited to the structurally complex Jinji area. Nevertheless, we emphasize that these resistivity–permeability associations are localized and should be recalibrated to account for site-specific conditions before use elsewhere. Although site-specific, the approach demonstrates how minimal calibration data can support high-resolution 2D/3D k modeling in data-scarce settings. Future studies could benefit from probabilistic classification schemes or machine learning approaches to further refine lithological mapping in geologically heterogeneous terrains.

The fitted relationship between resistivity and k, as illustrated in Fig. 5, is shaped by several factors, including the geological setting, lithological heterogeneity, data distribution, and the accuracy of both measurements. The broad dynamic range in our dataset provides a strong basis for identifying trends across the three dominant lithologies: sandstone, granite, and hornstone. This broad range is especially beneficial for resolving low-k formations such as granite, where k remains uniformly low and shows minimal fluctuation. In these settings, even large shifts in resistivity translate to relatively small changes in k, resulting in a gently declining inverse relationship. In contrast, at lower resistivity values (e.g., < 1000 Ωm) where k exceeds 2 mD, small resistivity shifts result in larger changes in k, leading to a more scattered and nonlinear correlation. This pattern is geologically realistic and reflects the inherent variability of fractured and porous zones in complex lithologies.

Matching between measured and predicted permeability (k vs. k′) was also rigorously validated (Table 3). Among 18 selected points from boreholes, 10 showed a difference of less than 1 mD, with only two exceeding 4 mD. Despite minor deviations, all points were accurately classified by lithology. This confirms the empirical model's reliability and its utility for regional-scale k prediction, even in areas lacking direct measurements. The geophysical model effectively compensates for sparse drilling data, offering a scalable and cost-effective tool for hydrogeological evaluation in hard rock terrains.

A key limitation of this study is the restricted depth range of the calibration dataset. The empirical resistivity–permeability relationship (Eq. 3) was derived from 116 core measurements between 0 and 200 m depth. Application of this relationship to depths approaching 1300 m therefore represents extrapolation beyond the calibrated interval.

To explicitly address this uncertainty, a probabilistic permeability–depth framework was implemented (Fig. 13). Rather than extending Eq. (3) deterministically, prediction uncertainty was propagated from the regression and progressively inflated beyond the 200 m calibration limit. Within the calibrated interval, permeability estimates remain relatively well constrained. Below 200 m, however, the 95 % prediction intervals widen substantially, quantifying decreasing confidence with increasing depth.

Importantly, deep predictions remain conditioned by observed CSAMT resistivity trends and preserve the physically consistent monotonic decrease in permeability with increasing resistivity. Nevertheless, processes not captured by the shallow dataset, such as stress-dependent fracture closure, evolving fracture connectivity, and mechanical anisotropy, may modify permeability behavior at depth. While the probabilistic framework constrains extrapolation risk, it does not eliminate structural uncertainty. Deep borehole testing and stress-dependent hydraulic measurements are therefore required to validate permeability predictions below the calibration range.

Although pumping tests are widely regarded as the standard method for estimating aquifer permeability (k), they provide only bulk, large-scale averages of hydraulic conductivity over the tested interval. Such measurements are useful for assessing overall transmissivity but lack the spatial resolution required for detailed 2D or 3D geophysical modeling, where localized contrasts in hydraulic properties are critical. The objective of this study was to capture subsurface heterogeneity at scales compatible with CSAMT-derived resistivity. For this purpose, point-specific k measurements were necessary to ensure that calibration data reflected the same resolution and spatial variability represented in the geophysical models. Core samples, analyzed at discrete depths, offered this localized control and provided a closer match to the spatial scale of CSAMT blocks. Therefore, core-derived k values were used in lieu of pumping tests. While this approach inevitably shifts the focus from bulk aquifer transmissivity to matrix- and fracture-scale variability, it ensures that the calibration dataset is scale-compatible with resistivity measurements, thereby improving the reliability of the empirical k–ρ relationship and supporting more accurate heterogeneity mapping in crystalline terrains.

In addition to depth-related extrapolation, permeability estimation in this study is influenced by scale transition between centimeter-scale core measurements and tens-of-meter-scale CSAMT inversions. Core plugs (50 mm × 100 mm) primarily capture intrinsic matrix permeability and fractures intersecting the limited sample volume. In fractured crystalline systems, however, hydraulic flow is governed by connected fracture networks whose representative elementary volume (REV) may exceed the dimensions of a core specimen. Individual cores may therefore not reach the REV of the fractured rock mass, leading to systematic underestimation of bulk hydraulic conductivity.

By contrast, CSAMT inversions resolve an effective bulk resistivity over ∼ 50 × 50 m blocks, integrating matrix and fracture contributions across a much larger volume. The empirical k–ρ relationship thus links matrix-scale permeability measurements with block-scale electrical responses. The dispersion observed in Fig. 5 is therefore not merely statistical noise but a reflection of geological heterogeneity and scale-dependent flow processes.

For example, low k values from intact granite cores may correspond to CSAMT blocks intersecting fracture corridors that enhance effective permeability at the field scale. Conversely, cores intersecting localized fractures may yield elevated k relative to the surrounding bulk medium. Variability in cementation, fracture density, and stress-controlled aperture closure further contributes to scatter.

Bridging this scale gap requires intermediate-scale hydraulic constraints. Integration of packer testing, interval hydraulic testing, borehole geophysics, and pumping tests would help reconcile matrix-scale measurements with field-scale connectivity and better constrain the effective REV of the fractured system. Such multi-scale calibration would reduce uncertainty in empirical relationships and improve permeability modeling in structurally complex crystalline terrains.

The empirical resistivity–permeability (k–ρ) relationship developed in this study exhibits a sharp decline in k with increasing resistivity and a clear inflection near 1000 Ωm. This mirrors classic depth–permeability (k–z) trends (e.g., Manning and Ingebritsen, 1999; Saar and Manga, 2004; Ingebritsen and Manning, 2010), where k decreases exponentially at shallow depths and follows a power-law pattern deeper down. However, unlike those models that use depth alone, our resistivity-based approach captures additional controls such as lithology, porosity, fluid content, and fracturing, making it a more localized and physically representative proxy, especially in heterogeneous hard rock settings.

Depth was considered but not used as the primary variable due to strong lateral variations in resistivity and k caused by geological complexity. For instance, in the Jinji area, surface granite shows high resistivity and low k, consistent with standard crustal profiles. However, deeper hornstone and sandstone units exhibit lower resistivity and higher k, contrary to typical depth trends, likely due to localized faulting, thermal alteration, and contact metamorphism that enhance fracture connectivity. The resemblance between our k–ρ curve and established k–z models reinforces its physical validity. The observed transition near 1000 Ωm may reflect a shift from conductive, fractured zones to compact, resistive rock masses. While hybrid models incorporating depth may be useful in future work, our resistivity-based method provides a more reliable and site-specific approach for k estimation in structurally complex terrains.

The influence of factors beyond lithology, particularly groundwater salinity, on CSAMT-derived resistivity warrants careful consideration. Electrical resistivity is sensitive to porosity, fracture density, mineral alteration, fluid saturation, and fluid resistivity (ρf). In this study, the empirical k–ρ relationship was calibrated using core samples from 0–200 m across six boreholes under predominantly fresh groundwater conditions. Regional hydrochemical data from the Geological Survey of China (800–1000 m depth) consistently indicate low salinity, supporting the assumption of fresh groundwater within the investigated interval. However, no direct fluid data are available below ∼ 1 km, and the assumption of fresh conditions at greater depths represents an important model constraint.

To evaluate this uncertainty, a sensitivity analysis was performed. If fluid resistivity were reduced by 50 % due to increased salinity, formation resistivity would decrease proportionally, resulting in higher inferred permeability values when substituted into Eq. (3). Because permeability increases exponentially with decreasing resistivity in the fitted model, this effect is nonlinear and resistivity-dependent. Specifically, halving ρf increases inferred k by approximately a factor of 2 at 1000 Ωm, 7 at 2000 Ωm, and up to 18 at 3000 Ωm. These results indicate that salinity effects are modest in low-resistivity formations but may significantly influence permeability estimates in highly resistive deep crystalline units.

Accordingly, the permeability model should be interpreted as valid under the assumption of predominantly fresh groundwater conditions and should not be generalized to saline deep aquifers without recalibration. Future investigations should incorporate deep borehole fluid sampling, downhole conductivity logging, and hydrochemical analyses to directly constrain fluid resistivity and reduce salinity-related uncertainty in deep permeability predictions.

The 3D permeability (k) model was constructed by interpolating between 2D CSAMT inversion profiles calibrated with borehole-derived k values from six reference locations. Given the limitations in survey geometry and computational cost, full 3D inversion of the resistivity data was not feasible. Instead, we implemented a geostatistical framework using ordinary kriging, which integrated cross-sectional profiles and applied the resistivity–permeability relationship across the model volume. The interpolation was guided by variogram models tuned to reflect the spatial continuity of lithological units and constrained by borehole control points, thereby maintaining geological consistency. While this approach provides a volumetric representation of k that highlights the distribution of permeable zones, its reliability is scale- and data-density dependent. The model is most robust in the central areas where CSAMT lines intersect and are directly supported by borehole data. In contrast, reliability diminishes in regions between widely spaced profiles and toward the model edges and corners, where no direct constraints exist. Sensitivity analyses, based on alternative variogram structures and comparisons with inverse distance weighting, consistently revealed greater variability and uncertainty in these peripheral zones.

To address this, uncertainty contours were added to Figs. 10 and 11, delineating areas of higher and lower confidence. The black dots marking borehole and survey line positions serve as reference anchors, making it clear that interpolation quality decreases with increasing distance from these control points. As such, interpretations in boundary regions should be treated with caution, particularly where model predictions extend beyond the convex hull of available data. We emphasize that the current model provides a reliable first-order framework for k distribution in the study area, but future improvements should prioritize denser CSAMT line coverage and, where feasible, the use of full 3D inversion techniques. Such approaches would better capture lateral continuity, minimize edge effects, and enhance confidence in the extrapolated 3D structure.

A complete aquifer assessment requires evaluation of both permeability and storage parameters, including specific yield, specific storage, and storativity. This study primarily focuses on delineating spatial variations in permeability (k), referred to here as hydraulic flow potential, using CSAMT-derived resistivity calibrated with borehole data. While this approach provides robust insights into transmissivity patterns and fracture-controlled flow pathways, it does not directly quantify aquifer storage capacity.

Permeability and storage represent distinct hydrogeological properties. High k zones do not necessarily imply high storage if fracture porosity is limited, and conversely, formations with significant porosity may exhibit substantial storage despite moderate permeability. Due to the absence of deep pumping tests, drawdown analyses, and detailed porosity logs, storage parameters could not be independently constrained. As such, the present results characterize relative transmissivity and hydraulic connectivity rather than total extractable groundwater volume.

To avoid overgeneralization, the model outputs should therefore be interpreted as indicators of flow potential rather than comprehensive groundwater resource capacity. Future studies should integrate Nuclear Magnetic Resonance (NMR) logging, borehole geophysical porosity tools, interval hydraulic testing, and aquifer-scale pumping tests to better constrain storage properties alongside permeability. Such multi-parameter characterization would enable more rigorous evaluation of sustainable yield and groundwater resource potential in fractured hard rock systems.

Borehole placement in this study was guided by geological mapping, hydrological relevance, and preliminary CSAMT interpretation to ensure representative coverage of the principal lithologies and structural domains. The six boreholes were used both to calibrate the empirical resistivity–permeability relationship and to validate the CSAMT-derived permeability models. Cross-validation results demonstrate that calibration quality depends more on spatial distribution than on borehole number. Leave-one-out cross-validation (LOOCV) of the 116 paired measurements yielded an RMSE of 2.36 mD, indicating that the regression is not overly sensitive to individual data points. Leave-one-well-out cross-validation resulted in an RMSE of 2.78 mD, showing that the empirical relationship maintains reasonable predictive capability when applied to an entirely excluded borehole. The modest increase in error reflects geological heterogeneity rather than model instability.

These findings suggest that a limited but strategically distributed set of boreholes across key lithological and structural zones can provide stable calibration. Slightly higher prediction errors in highly resistive granite highlight the importance of including structurally complex units in calibration. Future work may further optimize efficiency by integrating preliminary CSAMT results into adaptive drilling strategies, targeting areas of higher uncertainty while minimizing drilling costs.

The variation in CSAMT profile lengths reflects site-specific logistical and geological constraints encountered during field deployment. Factors such as terrain accessibility, infrastructure (e.g., roads, buildings), and the need to capture key geological features (e.g., faults, lithological boundaries) influenced the extent of each profile. In some cases, shorter profiles were required due to rugged topography or land access limitations, while longer profiles were employed where feasible to ensure adequate coverage across broader structural domains. Despite the variation in length, all profiles were designed to achieve sufficient penetration depth and resolution for reliable resistivity–permeability modeling, as validated through borehole calibration.

The borehole data used for calibration were limited to 0–200 m depth, whereas the CSAMT-derived permeability model extends to approximately 1300 m. This vertical discrepancy reflects practical drilling limitations rather than conceptual inconsistency. The shallow calibration interval encompasses the principal lithologies (granite, hornstone, and sandstone) and captures a representative range of resistivity–permeability conditions required to establish the empirical relationship (Eq. 3).

Application of this relationship at greater depths constitutes extrapolation beyond the calibrated interval, and the associated uncertainty is explicitly treated through the probabilistic depth framework (Sect. 4.7) and salinity sensitivity analysis (Sect. 4.11). These analyses demonstrate that confidence decreases progressively with depth and that deep permeability estimates remain conditional on assumptions regarding fracture continuity and fluid resistivity.

Despite the absence of direct deep borehole validation, the extrapolated model exhibits spatial consistency with mapped lithological boundaries, structural trends, and regional hydrogeological interpretations reported by the Geological Survey of China. This structural coherence supports the plausibility of deeper projections, while acknowledging that they remain less constrained than the shallow interval.

Future deep drilling, in-situ hydraulic testing, and petrophysical logging will be essential to independently verify permeability estimates below 200 m and further reduce vertical extrapolation uncertainty.

Our results show strong agreement with regional geological and hydrogeological data from local and national surveys, confirming the reliability of the integrated CSAMT–borehole approach. This alignment supports the method's scientific validity and scalability for k estimation in structurally complex, data-scarce settings. While grounded in established geophysical principles, the strength of this study lies in its site-specific integration of deep k modeling, field validation, and empirical calibration. Overall, the findings highlight CSAMT's potential as a practical tool for deep groundwater exploration and sustainable resource management.