# Variability of geological interpretations of a mineral deposit: Quantitative study and implications

Paul Marchal, Guillaume Caumon, Pauline Collon, Patrick Ledru, Kelsey Mckee, Pat Taylor, Julien Mercadier

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Paul Marchal, Guillaume Caumon, Pauline Collon, Patrick Ledru, Kelsey Mckee, et al. Variability of geological interpretations of a mineral deposit: Quantitative study and implications. Ore Geology Reviews, 2025, 187, pp.107010. 10.1016/j.oregeorev.2025.107010. hal-05484447

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# Variability of geological interpretations of a mineral deposit: Quantitative study and implications

Paul Marchal<sup>a,●,*</sup>, Guillaume Caumon<sup>a,b</sup>, Pauline Collon<sup>a</sup>, Patrick Ledru<sup>a</sup>, Kelsey McKee<sup>c</sup>, Pat Taylor<sup>c</sup>, Julien Mercadier<sup>a</sup>

## ARTICLE INFO

**Keywords:**

Interpretation

Mining

Uncertainties

Mineral exploration

Hydrothermal alteration

Unconformity-related uranium deposit

## ABSTRACT

Assessing uncertainties is an essential step throughout the mineral resource development cycle, from exploration campaigns to development planning and remediation. These uncertainties reflect the scarcity of subsurface data, which need to be complemented by geological knowledge.

This paper aims to assess the impact of conceptual variations on the geometry of uranium deposits. For this purpose, a case study was carried out on the interpretation of drilling data in a 2D section, in the context of an unconformity-related uranium deposit in the Athabasca Basin. Based on a reference section from this area, a blank cross-section with synthetic drillcores was produced and given to 32 interpreters. These 32 interpreters are from various backgrounds and are divided between experts in uranium geology (8) and non-experts (24). A set of fifty mathematical criteria is defined and correspond to five categories: mineralized zones, associated altered zones, structural network, geometric relationship between structures and mineralization, and annotations. Individual and group analyses of the defined criteria are performed.

Results show that uranium experts and non-experts are difficult to discriminate by the metrics used in this study, but experts tend to filter out the most speculative conceptual models. A generalized parsimony of interpretations is observed for all survey respondents. What also emerges is that fault network connectivity is key to conceptual model discrimination in hydrothermal deposits.

## 0. Introduction

Uncertainty is pervasive in the exploration and the evaluation of ore deposits. Therefore, uncertainty assessment is important throughout the resource development lifecycle: from exploration campaigns (McManus et al., 2021; Mern and Caers, 2023), to remediation (Longoni et al., 2016), via planning of operating strategies (Langanay et al., 2021).

In a geological data interpretation context, Bond (2015) and Li et al. (2008) identify two major types of uncertainties: aleatory uncertainties, and epistemic or conceptual uncertainties. On the one hand, aleatory uncertainties correspond to measurement errors, linked to the measurement itself, to the used equipment or to the choice of sample locations. Conceptual or epistemic uncertainties, on the other hand, correspond to variability in the interpretation of a dataset between interpreters and/or through time. This type of uncertainty has a significant impact on the evaluation of resources and the understanding and quantification of geological processes (Bond et al., 2007; Madsen et al., 2022). This understanding generally implies a conceptual

model, defined by Chamberlin (1890) as the framework of geological knowledge and concepts that guides geologists in their interpretations of geological data. However, multiple conceptual models for a given dataset can often be considered (Chamberlin, 1890).

First and foremost, variations exist between the individuals who interpret the data: each interpretation decision is influenced by personal experience, area of expertise and by the choice of a specific interpretation methodology. Second, the same geologist is not exempt from intra-individual variability over time – what Polson and Curtis (2010) call “dynamic uncertainties”. Indeed, the interpreter’s methodology and experience can evolve over time, and the scarcity of data can also increase the anchoring bias when making choices (Pochepsova et al., 2009). Chamberlin (1890) further highlights the difficulty for a geologist to work with several interpretative hypotheses at the same time. Teamwork helps to limit this effect by bringing in different interpretations and comparing them. Confronting opinions allows geologists to discuss a problem and propose alternative interpretative solutions.

<footnote><sup>a</sup>GeoRessources, Université de Lorraine, CNRS, Paris, F-54000, Lorraine, France</footnote>

<footnote><sup>b</sup>Institut Universitaire de France, France</footnote>

<footnote><sup>c</sup>Orano Paris, Chatillon, 92320, Ile de France, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: paul.marchal@univ-lorraine.fr (P. Marchal).</footnote>
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Examples of historical interpretations of the geometry of the Cigar Lake deposit modified from Jefferson et al. (2007), Hoeve and Kyser (1986), Martz et al. (2019), Cuney and Kyser (2009).</figcaption></figure>

The limit is that the group's majority opinion may prevail, without being the most reliable (Sniezek and J.A, 1992). Consensus-building, by averaging all opinions, may lead to under-statement of uncertainties.

Assessment of conceptual uncertainties is a popular topic in many areas of geology. In geothermal projects, for example, Witter and Trainor-Guitton (2019) consider that conceptual uncertainties have a greater impact on risk evaluation than data uncertainties, in terms of generated energy evaluation. In hydrogeology, Nilsson et al. (2007) propose a range of techniques for assessing and identifying uncertainties linked to data interpretation. They define the hydrogeological conceptual model as a simplification of the interpretation problem in the form of mathematical variables combined with a model of the area's geological structures. There are also a number of studies (Rankey and Mitchell, 2003; Bond et al., 2007; Curtis, 2012) on the assessment of uncertainties in the oil industry, particularly about the interpretation of seismic and production data. Lark et al. (2014) look at conceptual uncertainties in a geotechnical framework, concerning the location of a formation. Geologists of varying experience were asked to interpret subsets of drillholes. They demonstrate that the interpretation error is spatially correlated and also correlated with the degree of experience of the geologists. The interpretation aspect of uncertainty assessment in mining projects is underrepresented in the literature, especially concerning the geological interpretation of drillhole datasets.

Notably, the geostatistical simulation aims at capturing and assessing the impact of spatial uncertainty in mining projects. For instance, Li et al. (2008) and Dimitrakopoulos and Lamghari (2022) seek to optimize the production components of a mining complex, from extraction to waste, including processing and storage. They mainly take into account uncertainties linked to data (statistical representativeness, and changes in analysis methods over time) (Li et al., 2008) or uncertainties over ore volumes and penalties produced, and production costs and sale prices (Dimitrakopoulos and Lamghari, 2022). Blannin et al. (2023) proposes a geostatistical-based tailing modeling workflow for mine waste reclamation, with the aim of recovering metals and limiting the impact of pollution. In this case too, the considered uncertainties are linked to the ranges of data values. On the upstream side of mineralization characterization, Mery et al. (2017) and Emery and Ortiz (2008) propose to characterize the uncertainties surrounding the proportions of facies associated with mineralization. The idea is to handle the relationships between a set of interdependent petrophysical variables using a set of plurigaussian models, in order to model facies (Mery et al., 2017) and in the approach proposed by Emery and Ortiz (2008), the aim is to improve consideration of uncertainties in the position of interfaces between facies by improving the conditioning of plurigaussian methods. McManus et al. (2021) stress the prevalence of uncertainties in mine production losses. However, few studies focus on the quantification of conceptual uncertainties for exploration and resource evaluation.

To address this gap, this paper addresses the uncertainties on the interpretation of drillhole data i.e. on how geologists correlate well information, as well as the characterization of the diversity of concepts associated to a particular deposit type. For a single deposit type, different conceptual assumptions coexist in the literature and influence geologists' interpretations (Fig. 1). We focus here on deposits linked to hydrothermal fluid circulation (Leach et al., 2010; DeMatties and T.A, 2017; Jefferson et al., 2007). These deposits are sources of many metals of interest (Cu, Au, U, Fe), and form through complex fluid circulation and reactions. Fluid flows are mainly driven by chemo-thermo-hydraulic conditions and by permeability heterogeneity in the rocks, which lead to diverse geometries of mineral deposits (Bruce et al., 2020; Chauvet, 2019). This heterogeneity is linked to multi-scale geological features: faults, fractures, foliations, or layering. In this study, we aim at identifying how geologists link the geometry of hydrothermal deposits with these geological control factors. The focus is not only on mineralization, but also on alteration facies associated with mineralization in the form of halos. These facies may potentially be of mining interest, both from a geotechnical perspective (mine or drillhole stability) and from a geometallurgical point of view (Langanay et al., 2021). This article focuses on a subtype of hydrothermal deposits: unconformity-related uranium (U.R.U.) deposits. Comparative studies of historical models (Fig. 1) of a single deposit (Cigar Lake) show that the interpreted geometries of Cigar Lake vary depending on the roles given to the tectonic structures, the sedimentary environment and the unconformity (Jefferson et al., 2007; Cuney and Kyser, 2009; Cramer, 1995). Here, we seek to identify the "typical geometries" associated with these U.R.U. deposits and especially the significance of each of these features on the geometry of alteration and mineralization facies differs widely between these historical interpretations. These include different spreading patterns at unconformity, different facies sequences, different deformations around faults, and fine-scale variations in the sedimentary basin. A better assessment of these conceptual differences would enable us to better understand their impact on volume estimates, and to compare scenarios for the development of deposits.

In practice, most numerical deposit modeling methods rely on drillhole data, possibly complemented by geological sections with local projections. Experts then perform wireframing using more or less automated methods (Sides, 1997; Lemon and Jones, 2003; Kaufmann and Martin, 2008; Wood and Kessler, 2021). In principle, implicit approaches bypass such projections, but using sections often remains necessary to constrain the results (Arienti et al., 2024). Indeed, implicit and explicit interpolation methods numerically define what the structures between the data look like, which is not always in line with the geologist's a priori idea. Taking anisotropy into account, for example, remains delicate in implicit modeling (Pizzella et al., 2022; Irakarama and Thierry-Coudon, M. Zakari, M. and Caumon, G.; Arienti et al., 2025). The purpose of this work is therefore to provide a baseline of what two-dimensional geological interpretations and images look like
<figure><img src="image_5.png" /><figcaption>**Fig. 2.** (a). Conceptual model of types of U.R.U. deposits according to fluid flow direction inspired by Jefferson et al. (2007), (b). Outcrops at the Rabbit Lake mine, from Thomas (2022), mineralization and alteration halos of unconformity-related uranium (U.R.U.) deposits of the Athabasca Basin, Canada.</figcaption></figure>

for the specific U.R.U. deposits, using the simplest tool for expressing geological concepts in a tool-independent way: pen and paper. Identifying a uniform conceptual model for the geometry of mineralization and of the alteration halos and for their relationship with other geological features would indeed also help to design accurate modeling methodologies.

Therefore, we propose a case study based on the interpretation of a cross-section with interpreted drillholes, by a group of expert and non-expert uranium geologists (Section 1). We first define a set of metrics and methodologies for comparing interpretations of drilling data related to mineral deposits (Section 2). These metrics are then used in Section 4 to compare a panel of interpretations of geologists from different fields and different levels of expertise in uranium geology.

# 1. Experimental design

## 1.1. Geological context

This study considers a type of mineral deposit linked to hydrothermal pulse events (Jefferson et al., 2007; Walsh et al., 2018; Yang et al., 2004). This choice is motivated by the specific architecture of this type of hydrothermal deposits in which the process of metal concentration is linked to fluid circulation. Fluids act as either oxidizing or reducing reactants, depending on their composition, enabling metals to be solubilized or precipitated in relation to the redox conditions of the surrounding rocks. These fluid flows depend on several factors: the presence of fluid sources, pressure gradients, and heterogeneity in rock hydraulic conductivity. This heterogeneity includes bedding geometries, facies in sedimentary contexts (Koltermann and Gorelick, 1996), foliations in metamorphic contexts, which are overprinted by tectonic structures, such as faults and fractures (Han et al., 2019; Wigley et al., 2013). The interpreter can give varying importance to these geological factors when delineating the geometry of the deposits.

As an example, we consider an U.R.U. deposit (Fig. 2 b). These deposits are characterized by the mineralization location at the contact between a sedimentary basin and a metamorphosed basement. Depending on the circulation patterns of the hydrothermal brine, deposits form in the basement (ingress type) or in the basin (egress type) (Fig. 2 a) with varying extensions and mineralogical signatures (Jefferson et al., 2007). In both cases, concentric envelopes of alteration minerals surround the mineralization. These envelopes or halos are used as exploration guides to detect mineralized zones, which motivated us choosing this type of ore deposit. Indeed, the interpreter has to think about interpreting the geometry of several interconnected, geometrically complex objects in terms of formation processes: major faults, unconformity, mineralization and alteration facies.

The chosen synthetic dataset was generated from an existing conceptual model of the Cigar Lake deposit (Cuney and Kyser, 2009), which is a typical and well-known example of an egress model, with concentric envelopes of alteration facies. It is of interest for its exceptional uranium concentration (20%) and it has been mined by Cameco since 2015 (IAEA, 2018).

## 1.2. Design of the cross section

The objective was to take an example of a deposit that is sufficiently documented and whose geometry is representative of an egress type of U.R.U. deposits. The reference Cigar Lake section defined by Cuney and Kyser (2009) is based on an interpretation by Cameco (Fig. 3 b).

It is drawn N-S, transversally to the major mineralized axis (Fig. 3(b)) (Martz et al., 2019; Cuney and Kyser, 2009). It does not correspond to an existing location but synthesizes the conceptual interpretation of the deposit. In such areas, most drillholes are drilled along the main graphitic faults, to define its longitudinal extension. Few drillholes explore the orthogonal extension of the mineralization. To mimic as close as possible the real data, which are not publicly available, we have designed seven virtual drillholes regularly spaced, generally subvertical, with slight deviations at greater depths. Four facies, with a subconcentric organization around the mineralization, are considered in the synthetic data. These include the uranium mineralization itself (in green), and three types of alteration: massive clays (in pink), kaolinite alteration (in blue) and pyritic alteration (in yellow). The intersection of the facies with the drillholes is not oriented, meaning that the marks correspond only to the location of the facies, but do not provide any information on the dip of the layers.

As for the structures, the faults crossing the virtual drillholes have been digitized so as to be oriented (in red). This is also the case for the regional unconformity (in purple). Care was taken not to intersect all the structures found on the reference section. Of the four regional faults shown, only three are intersected by drillholes, including one intersected by two different drillholes, making a total number of four fault observations and seven unconformity observations.

## 1.3. Collection of interpretations

The gathered data consist of a total of 38 drawings: 37 interpretation samples of the 2D section, made by 32 participants, plus the reference section. Fourteen of them were produced during a workshop organized by two communities of geologists working either on uranium deposits or hydrothermalism. Four models were interpreted by middle to high-school students (these French system 3rd grade students had
<figure><img src="image_6.png" /><figcaption>**Fig. 3.** (a) Conceptual 3D model of alteration envelopes in the Cigar Lake area and approximate placement of the Cuney conceptual section, modified from Martz et al. (2019). (b–c) Design of the experimental cross-section from one of the reference models of Cigar Lake unconformity-type deposit (Cuney and Kyser, 2009), modified from Cameco.</figcaption></figure>

introductory geoscience classes and were doing a one-week discovery internship in the GeoRessources laboratory). Among the obtained 37 cross-sections, eight correspond to multiple interpretations made by the same geologists at different times. The origin of the models is detailed in Table 1. It is worth noting that the participants are of diverse origins in terms of country, age and education.

Survey participants were asked to indicate if they are working in the field of uranium (Fig. 4 a) and what they consider to be their main area of expertise (Fig. 4 b). The 32 participants were divided into 7 categories: structural geology (7), hydrothermal systems (5), geophysics (3), geochemistry (4), numerical geology (software development, ML and geostatistics) (4), mining (6) and high-school students (4). Interpreters are divided also between university graduate students (masters and PhD) and professionals (Fig. 4 b). Although these numbers are relatively small, they provide representativeness from a variety of fields, with different conceptual knowledge. In the following sections, we refer to “uranium experts” as interpreters who have indicated during the survey that they work in the uranium field (9 people in all). Non-experts are the other interpreters, excluding high-school students, who are considered independently in this comparison.

It is important to note that the information and caption given to study participants were systematically the same:

* This is a 2D vertical section with synthetic drillcores.

* This is an unconformity uranium deposit in Athabasca.

* Fault and unconformity markers in drillholes are oriented.

* Alteration zones are not oriented.

* The unconformity marks the sharp transition from a verticalized metamorphic basement to a tabular sedimentary basin.

People were asked to correlate facies geometry and structures between drillholes.

## 2. Data processing and analysis metrics

### 2.1. *Data preparation of the interpreted sections*

For comparison purposes, the drawn cross-sections are prepared and standardized before calculating the metrics. The standardization is carried out in several stages (Fig. 5). The first step, after scanning
<figure><img src="image_7.png" /><figcaption>Fig. 4. Area of competence entered by participants in the survey.</figcaption></figure>

the images, consists in cleaning up the cross-sections, removing the common background (input data: drillhole traces, markers and zones). In a second step, the image contrast is adjusted to better highlight the hand-drawn lines. The third step consists in importing the images into a vector drawing software (Inkscape) for semi-automatic vectorization. Solid colors corresponding to the 4 facies (pyritic alteration: yellow, kaolinite alteration: blue, massive clays: pink, and uranium mineralization: green) are applied homogeneously to all sections. The faults and the unconformity are digitized in the same way, with uniform thickness and colors (red and purple). When vectorizing, objects sketched as dashes are drawn as a single line. The use of a vector format enables images to be separated into several polygons and lines, and to apply different treatments to these components.

Some features are studied directly in vector format (svg files) and others are studied on rasterized images (PNG files), using python libraries, such as scikit-learn (Pedregosa et al., 2011), scikit-image (Vandert Walt et al., 2014), vgpathtools (Port, 2021), numpy (Harris et al., 2020) and scipy (Virtanen et al., 2020). Annotations are not vectorized and are directly studied on the input images. Most of the discrete or binary criteria are obtained by visual analysis. The features and properties systematically analyzed for each image are detailed in the following section.

## 2.2. Analysis criteria & workflow

Comparing geological models is a common problem, particularly when it comes to assessing the differences between complex objects such as mineralization or fault networks. Several authors have proposed solutions based on quantitative metrics: connectivity and geometry measures to assess the complexity of a structural model in 3D models (Pellerin et al., 2015), semi-automatic tools to map fractures and geological contacts from images (Thiele et al., 2016), and global and local uncertainty indicators to analyze variability between 2D raster models (Pirot et al., 2022). These approaches help to ensure that generated models and interpretations can be compared objectively. However, few approaches are tailored for comparing interpretations of mineral deposit models, which is why we propose a series of metrics dedicated to U.R.U. deposits to characterize facies, faults, unconformity and their interactions.

1. **Criteria on the whole image** (Fig. 6 a) Image rasterizations are used to calculate global adjacency matrices of the four facies (pyritic alt., kaolinite alt., massive clays, uranium min.) and faults. Although no instructions were given to the interpreters regarding the use of annotations, a variety of annotations can be identified on the drawn sections (Fig. 6 e - f). These are either a way for the interpreters to add more information, or to indicate their doubts. To capture these, we define five Boolean criteria: presence of dashes, presence of question marks, presence of fault displacement arrows, presence of fluid displacement arrows, presence of other annotations. Finally, we also consider four Boolean criteria reflecting the parsimony of interpretations: the presence of objects or features between the drillholes (faults, isolated alteration halos, higher order geometric features).

2. **Facies criteria** (Fig. 6 b) The area $A_i$ of each facies $i$ is computed on a raster of the vectorial image and rescaled to obtain values in square meters. The perimeter $P_i$ and convex envelope $E_i$ are also calculated. The total length of the perimeters can be seen as a clue for the existence of second-order features. A smooth model is likely to have a smaller perimeter sum than a model with digitations or a more tortuous model. From these values, a coefficient $\alpha$ is calculated. It corresponds to the sum of the convex envelopes of the 4 facies $E_{tot}$ divided by the sum of the perimeters $P_{tot}$. This metric indicates whether facies are highly deformed with regards to structures. If the ratio between convex envelope and perimeter is close to 1, this means that facies are not very deformed. On the contrary, values close to 0 indicate a divergence between the two, and therefore more sharply distorted contours. Alteration front limits in models with low $\alpha$ values are more concentrated around fault zones.

3. **Mineralization criteria** (Fig. 6 c) To characterize how geologists interpret the shape of mineralization from drilling data, we consider the number of connected components in the mineralization, and their Riley circularity $\rho$ (Allen Riley, 1941). We also define a discrete shape classification for the mineralization set to either “veins”, “blobs” or “tabular”. Finally, we use a binary property corresponding to kinematics to characterize whether the mineralization is displaced by faults (YES) or not (NO).

4. **Fault network criteria** (Fig. 6 d) Fault network analysis is a fundamental factor in establishing the characteristics of hydrothermal deposit models. Indeed, in the case of such deposits,
<figure><img src="image_8.png" /><figcaption>Fig. 5. Data preparation steps and information extracted (text in gray rectangles).</figcaption></figure>

faults either act as vectors or as barriers to fluid circulation. The study of the fault network topology is based on the metrics proposed by Sanderson and Nixon (2015) and Manzocchi (2002), focusing on the types of fault terminations and connections. The slope and length are calculated for each fault identified on each vectorized cross-section. From that, several representative statistics are computed: the number of fault lines $N_L = \frac{1}{2} * (N_I + N_Y)$ (Sanderson and Nixon, 2015), the number of branches $N_B = \frac{1}{2}(N_I + 3 * N_Y + 4 * N_X)$ (Sanderson and Nixon, 2015), the ratio $\frac{N_L}{N_B}$, the length distribution, mean $\bar{L}_f$ and standard deviation $\sigma_L$. The number of connections of type X, or Y, or independent fault extremities I are counted for each section. For the slope, distributions are bimodal as there are only two orientation families in the data (conjugate faults of around 60°), so we consider the means of two main modes: $\mu_1$ and $\mu_2$ and the concentration parameter for the same two modes: $\kappa_1$ and $\kappa_2$.

5. **Links between structures and mineralization** The relationship between mineralization and geological structures is also explored. To this end, the distribution of the surface orientation of mineralized zones (Fig. 7 a–b) is compared with the distribution of the orientation of controlling structures. The idea is to identify the portions of mineralization oriented in the direction of the structures and to count their number in relation to the total number of portions. To obtain representative samplings, the vectorial shapes are resampled with regular steps. For each oriented structure S of mean slope $\theta_S$, a density $\Psi(S)$ is computed. It represents the density of the mineralization boundary oriented in the same way as the structure S within a tolerance $\epsilon$, (Fig. 7 c):

$$ \Psi(S) = \frac{\sum_{k=1}^{n} \mathbb{1}_{(m_k - \theta_S) < \epsilon}}{n * 2\pi} \quad (1) $$

This proportion is calculated three times (Fig. 7 d): once for all faults: $\Psi(Faults)$, once for all unconformity pieces $\Psi(Unc)$, and once for all structures combined $\Psi(Struct)$. The first two values are used to determine whether interpreters attach more importance to the fault network or to the unconformity in the geometry of the mineralization. The third indicates the degree of structural knowledge incorporated by geologists into the geometry, ranging from a strong correlation with the overall structures (high value) to a total absence of correlation (low value).

### 3. Spatial summary statistics

If all the interpreted drawings are looked at in terms of local frequency estimates, or E-Type, (Journel, 1986) (Fig. 8), a generalized tendency to propose solutions of a minimum of complexity (parsimony) is observed. This may be due to the smoothing effect of the E-Type, but the general observations of mean and variance for facies, faults and unconformity confirm this observation. Mean and variance are calculated independently for each facies (sum of indicators 1: facies present, 0: facies absent), as well as for the unconformity and fault network.

Alteration facies means (Fig. 8 a - d), show areas of highest values around the data points, decreasing progressively as distance from the data increases. This is particularly noticeable in the pyritic halo between the first two drillholes (left), where the distance between data points is greater than between the other drillholes, and also beyond the last drillhole on the right. Divergent oval shapes can be seen around the data points (emphasized on the figure by dotted isovalues). The absence of observed data in the drillholes does not prevent interpreters from drawing facies. Drawings can be seen intersecting drillholes in blank (facies less) zones. These observations apply to all four facies. These oval areas around the data are found when looking at the variance, corresponding to areas of low variance. For all four facies, the highest variance is found at the facies boundaries, i.e. at the interfaces.

The unconformity position (Fig. 8 f) varies little between the models, except in the central zone, where the unconformity may be folded or displaced by the faults. Regarding the fault network (Fig. 8 e), it is clear that very few interpretations go beyond the proposed data. The many scattered faults emphasized by the dotted 0.01 isovalue actually only correspond to a single drawing (model 15), and if this model is ignored, only three main faults stand out, derived from drilling data. The following section describes the characteristics of the fault networks drawn by the interpreters.

### 4. Do experts and non-experts differ fundamentally in their data interpretation?

#### 4.1. Statistical comparison of experts in uranium deposits and non-experts

This section first investigates if there are any significant differences between the groups of interpreters. Two main groups are of interest: those with experience of uranium deposits (A with 8 interpreters and
<figure><img src="image_9.png" /><figcaption>(a) Full image</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>(b) Alteration and Mineralization</figcaption></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

component C₂: Area A₂,
Perimeter P₂

<figure><img src="image_13.png" /></figure>

component C₁: Area A₁, perimeter P₁

<figure><img src="image_14.png" /><figcaption>(c) Mineralization only</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>(d) Fault network & Unconformity</figcaption></figure>

<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /><figcaption>(e) Glyphs conveying parsimony</figcaption></figure>

In the example :

<figure><img src="image_18.png" /><figcaption>(f) Glyphs conveying uncertainties and/or additional informations</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>**Fig. 6.** Breakdown of the parameters studied on each section, subdivided by geological objects of interest for the whole of all image (a); all facies (b); mineralization facies (c); fault networks (d), and annotations ((e) and (f)).</figcaption></figure>

13 drawings) and those without (B with 20 interpreters and 20 drawings). Here, the high-school students' interpretations (4 drawings) are not considered to avoid biasing the results, since the idea here is to compare the interpretation work of expert and non-expert geologists in uranium deposits. But they will be considered in the other sections as distinct groups. It is worth noting that we are comparing populations of interpreters with varying backgrounds in geology. This may have an impact on the characterization of variability between the two groups: experts and non-experts. Indeed, variance is reduced by the training of

geologists, who all learn a more similar set of interpretive techniques than a non-geologist control group (Stoch et al., 2022).

A Shapiro-Wilk test (Shapiro and Wilk, 1965) is first performed on groups A and B jointly, to test normality for all variables. The proportions of fault branch types $N_X$, $N_Y$, $N_I$ are here transformed into centered log-ratio (CLR<sub>X</sub>, CLR<sub>Y</sub>, CLR<sub>I</sub>) to be taken into account (Aitchison, 1994). In the Shapiro-Wilk test, Hypothesis $H_0$ is that the variable follows a normal distribution. Fig. 9 (a) shows that this hypothesis is rejected for 18 out of 28 variables at a 0.05 significance
<figure><img src="image_20.png" /><figcaption>**Fig. 7.** Definition of Ψ(*C*), the density of points on the mineralization surface oriented like object *C* with tolerance *σ*. Three Ψ values are defined: relative to all faults, relative to the entire unconformity and relative to all control structures (faults + unconformities).</figcaption></figure>

level. This suggests that variables behave in a strongly non Gaussian way.

A Mann–Whitney–Wilcoxon test is also performed (Wilcoxon, 1945) to check whether two populations have the same distribution. For each variable *x* of interest and two groups *A* (uranium experts) and *B* (non-experts), the equality of the group distribution is tested by assessing the difference between *P*(*x*<sub>*A*</sub> > *x*<sub>*B*</sub>) and *P*(*x*<sub>*B*</sub> > *x*<sub>*A*</sub>). The groups are considered to have the same behavior when this difference is zero (null hypothesis). This test uses only the global rank of each sample, hence applies to non Gaussian variables and small sample sizes, only under the assumption of independent samples. Here, the majority of variables have the same behavior between the two groups (in green on Fig. 9 b), except two of them (in red on Fig. 9 b): fault size standard deviation *σ*<sub>*L*</sub>, and the concentration of the modes *κ*<sub>1</sub>. As visible on Fig. 9 b, the *p*-value for several other variables would lead to different conclusions for a slightly higher significance level. Therefore, the remainder of this section considers more specific tests for the median and the spread of the distribution between the two groups.

A Mood test (Brown et al., 1951), or median test, is then performed. This is a non-parametric test that verifies the equality of the medians of two populations (null hypothesis) (Fig. 9 c). It compares the number of elements in the two groups below the median of the entire set. At a 0.05 significance level, the *H*<sub>0</sub> hypothesis is validated for all variables (in green on Fig. 9 c)so the medians for both groups are the same for all variables, except Kaolinite surface (*A*<sub>k</sub>). However, some other variables are very close to the threshold: *μ*<sub>1</sub>, *κ*<sub>2</sub>, and *CLR*<sub>*X*</sub>, *CLR*<sub>*Y*</sub>. Because of this non Gaussian behavior and the small group sizes, a Bonett statistical test is carried out (Bonett, 2005) to compare the two groups’ variances (Fig. 9 d). At a 0.05 significance level, the variance differences between experts and non-experts of all variables are not significant (in green on Fig. 9 c).

The results show that, overall, uranium experts and non-experts are difficult to distinguish. As mentioned above, this may be due to the training of the geologists. All geologists learn similar principles of interpretation, which may explain why experts and non-experts do not form two clearly distinct groups.

## 4.2. Fault network analysis

Fault length distribution is shown for each model in Fig. 10 (a), in comparison with the reference model (in red). Drawings are separated in four groups: experts in uranium (green), non-experts (gray), and high-school models (pink). Half of the models (18/37) have a mean length value greater than or equal to that of the initial model. The interpreted fault length tends to be negatively biased as compared to the reference. The values cover a range of 565 m of magnitude (from 70 m in Model 16 to 800 m in Model 12).

The number of faults is underestimated in the drawings, in comparison to that of the reference model (Fig. 10 b). Out of 37 interpretations, 26 interpretations underestimate the number of faults (3 faults versus 4 in the reference). This trend is consistent with the parsimony principle taught in scientific formations (Section 3), as one of the faults in the reference model is not intersected by the provided drillholes.

Concerning dips (Fig. 11 a), two mean modes $\mu_1$ and $\mu_2$ are computed. For mode $\mu_1$, mean angle values do not diverge significantly from the value (65°) of the reference section. However, the $\kappa_1$ concentration parameter around this mode is for many models more concentrated than for the reference model (between 2.5 and 10). The values of mode $\mu_2$, values are slightly higher than the reference value (112°) for all models, up to 20° higher. Furthermore, $\kappa_2$ values remain very low (below 2), corresponding to a relatively large dip variability. An explanation is that $\mu_1$ corresponds to a single fault observation in the drillholes, whereas $\mu_2$ corresponds to the three other observations: the
<figure><img src="image_21.png" /><figcaption>**Fig. 8.** E-type of mean and variance between all drawings for each characteristics (the four facies (a) (b) (c) (d), fault network (e) and unconformity (f)). Dotted lines are 0.001 isovalues.</figcaption></figure>

interaction between the three similarly oriented observations can con-
strain more the angles due to how interpreters connect the observations
together. The single fault observation leads to more uncertainty.

Both for dips and lengths, there is no specific difference between
expert and non-expert groups. A notable observation is that high-school
students seem to underestimate fault lengths, which highlights the role
of geoscience education on the knowledge of faulted structures. A study
of the total length of faults per drawing (Fig. 10 c in orange) confirms

this assertion to some extent, although it seems to be more related to
the number of faults. Models with higher total fault lengths than others
are those with the most faults (Models 15, 13, 2, 11 and 5).

Considering fault connectivity, only 6 out of 37 interpretations in-
clude X-shaped intersections. This is also visible on the ternary diagram
(Fig. 11 b), which further highlights that most interpreters tend to draw
isolated faults.
<figure><img src="image_22.png" /><figcaption>Fig. 9. (a) Wilcoxon test: test if uranium experts and non-experts are similar; (b) Shapiro–Wilk test: verifying if variables follow normal law; (c) Bonett’s test: verification of the significance of the difference between two reference groups: uranium experts and non-experts.</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>Fig. 10. (a) Distribution of fault sizes (m) by models; (b) and number of faults by models; (c) total fault length (m).</figcaption></figure>
<figure><img src="image_24.png" /><figcaption>Fig. 11. (a) Rose diagram of observed fault dips (average dip of reference in red) and (b) Ternary plot of fault connection types (X, Y and free node I).</figcaption></figure>

### 4.3. Facies analysis: Halo complexity, second-order variations and surfaces

Facies analysis mainly involves calculating the areas, perimeters and convex envelope lengths of the four facies. Regarding the surface area evaluations for the different facies (Fig. 12), the expert group is generally closer to the reference solution for the four facies of interest. However, there is no consistency in the dispersion of estimated surfaces: for the two outer alteration facies (pyrite and kaolinite), uranium experts are less dispersed than non-experts, while the opposite is observed for clays and uranium. Differences between groups are less obvious in terms of the length of alteration fronts (perimeters) (Fig. 13). This time, the experts are not particularly close to the reference.

In terms of sum of the perimeters $P_{tot}$ (Fig. 14 a), no particular difference is observed between experts (in green) and non-experts (in gray), as also highlighted by the p-value (Fig. 9 b to d). However, the number of models with fine-scale variations is very low, only 7 drawings (3 from the expert group and 4 from the non-expert group). A steep drop is apparent between the second point (Model n° 12) and the third point (Model n° 21) on Fig. 14(a), and from the tenth model (Model n° 16) onwards, the models become very smooth. Only a few interpreters propose models with features with details finer than the drillhole spacing, and the majority of interpreters tend to propose smooth models. As for faults, this is in line with the geological training that encourages parsimony, i.e. to propose consistent solutions without extrapolation.

The ratio $\alpha$ between the sum of perimeters $P_{tot}$ and the sum of convex envelopes $E_{tot}$ also shows this parsimony (Fig. 14 b). Values of $\alpha$ are relatively high, ranging from 0.90 to 0.55. Half of the models have higher values of this coefficient than the reference model and are therefore less tortuous. Experts and non-experts are evenly distributed along this criterion.

The study of circularity $\circ$ (Fig. 14 c) gives us two main pieces of information. The majority of the interpretations have lower circularity values than the reference model and are therefore less globular than the latter. This may correspond to tabular forms along the unconformity or veins along faults. This criterion alone does not allow us to differentiate these forms, but we can see on Fig. 14 (c) that none of the models are globular, with blob mineralization. Only two models have high higher circularity values than the reference model and they are clearly not isotropic (Models 20 and 10). The majority of interpreters draw tabular mineralization ($c < 0.2$ for 25 out of 37 drawings). Here again, no group difference can be identified.

<caption>Table 1</caption>

Number of faulted patterns on 38 samples (37 drawings + reference), number of patterns with abnormal adjacencies between facies and reason for abnormal adjacencies. Py. : Pyritic alteration; Ka. : Kaolinite alt.; Cl. : Massive Clay alt.; Ur. : Uranium mineralization.

<table><thead><tr><th>Facies</th><th>Py.</th><th>Ka.</th><th>Cl.</th><th>Ur.</th></tr></thead><tbody><tr><td>Number of models with facies offset by faults</td><td>13/38</td><td>11/38</td><td>11/38</td><td>10/38</td></tr><tr><td>Unconformable contact</td><td>Py. & Cl.</td><td>Py. & Ur.</td><td>Ka. & Ur.</td><td></td></tr><tr><td>Number of models with unconformable contact</td><td>21/38</td><td>1/38</td><td>1/38</td><td></td></tr><tr><td>Contact due to fault</td><td>4/21</td><td>-</td><td>-</td><td></td></tr><tr><td>A facies is locally missing from the sequence</td><td>17/21</td><td>-</td><td>-</td><td></td></tr><tr><td>A facies is perched in an unusual zone</td><td>-</td><td>1/1 (ref)</td><td>1/1 (ref)</td><td></td></tr></tbody></table>

Lastly, the number of connected components drawn in the mineralization is investigated (Fig. 14 d). The reference model includes a main mineralization and a perched mineralization not intersected by the synthetic data. Only 10 models also have two components, and 16 models have one component. The expert group seems to propose multicomponent scenarios more often: 8/13 or 61% for experts, and 11/20 or 55% for non-experts. However, a Fisher-Irwin-Yates statistical test (for small samples) shows that this difference in proportion is not significant between the two groups, with a p-value of 1 >> 0.05.

All these observations point to a general parsimony trend, which seems slightly more pronounced among non-experts. Driven by their experience acquired on this type of deposit, experts are more likely to design complex geometries, i.e., with more components, more deformed shapes and second-order variations, but always in accordance with the presented data. However, the difference between the two groups is not obvious, because it is not statistically representative, and parsimony appears as the main characteristic for both expert and non-expert geologists.

### 4.4. The adjacency of facies: when do facies form in relation to faults?

Another way of comparing models is to examine facies contiguity patterns, anomalous adjacencies, and the tectonic scenario indicated
<figure><img src="image_25.png" /><figcaption>**Fig. 12.** Distribution of surfaces by facies and by interest groups (U-experts vs. U-non-experts). Black line is the kernel density estimate (Scott's rule: kernel width $σ * n^{-1/5}$ with $σ$ the standard deviation and $n$ the number of data). Blue line with value is the reference.</figcaption></figure>

by the fault/facies relationship (Table 1). In the experiment, no information to help interpreters consider mineralized and altered facies as ante- or post-tectonic was provided about the chronology of events. Adjacencies may indicate normal contacts (corresponding to increasing alteration intensity) or abnormal ones (reflecting more complex processes such as polyphased alteration, displacement of rocks by faults after hydrothermalism, or depositional gaps). Unconformable adjacencies are subdivided into three subcategories: fault block displacement, depositional conditions, i.e. facies are directly adjacent without block displacement, or contact due to chemical remobilization.

There are three abnormal contacts: pyritic alteration and massive clays, pyritic alteration and uranium mineralization, kaolinite alteration and uranium mineralization. All other contacts are normal according to the facies sequence. About 21/38 samples display abnormal Py/Clay contact, of which 17/21 are via a kaolinite depositional gap that brings Py and Clay into contact, and 4/21 via facies displacement by faults. This suggests that interpreters are keen to consider variations in depositional conditions/chemical reactions (with depositional gaps and lateral thickness variations), but less so to consider faults as a factor in abnormal contacts. Only 1 drawing brings Py/U and K/U into contact. This adjacency is only found in the reference model. It involves the remobilization of uranium, bringing it into contact with the outer envelopes. The reference model is therefore the only one to highlight polyphased alteration. From 10 to 13 samples on 38 show facies blocks offset by faults. This means that around 1/3 of interpreters consider that faults have moved again after alteration.

### 4.5. What knowledge is used to determine the geometry of mineralization and its relationship with structures?

A first observation on the proportion of orientations consistent with structures $Ψ_{struct}$ (Fig. 15) shows that the expert models are scattered across all values. However, the models of Uranium experts (in green) tend to be located in the zone of high correlation to structures, while the models of high-school students (in pink) tend to be in the zone of low correlation. The group of experts (in green) and the group of non-experts (in gray) are mixed. Moreover, if we look at the position of the models in a two-dimensional space $Ψ_{unc}$ vs. $Ψ_{flt}$ (Fig. 16), the drawings can be positioned in relation to five reference solutions (in orange). These reference mineralization models are (1) oriented only along faults, (2) mineralization purely along the unconformity, (3) oriented along both faults and the unconformity, (4) oriented obliquely to both faults and unconformity and (5) oriented in an isotropic way. All models are located to the right of the round (central) model, which means that all interpretations incorporate at least some orientation similarity with the structures (faults and unconformity).

Models are close to the model correlated to both (3), so mineralization patterns follow both faults and unconformity. However, models are especially found in the lower zone, i.e., correlated mainly to the unconformity. This means that interpreters tend to correlate the geometry of mineralization more closely to the unconformity than to the faults. This is consistent with the circularity analysis, which shows that most interpretations are tabular.
<figure><img src="image_26.png" /><figcaption>Fig. 13. Distribution of perimeter lengths by facies and by interest groups (U-experts vs. U-non-experts). Black line is the kernel density estimate (Scott's rule: kernel width $σ * n^{-1/5}$ with $σ$ the standard deviation and $n$ the number of data). Blue line with value is the reference.</figcaption></figure>

## 4.6. About Glyphs and extrapolation

The majority of drawings include annotations (Fig. 17 a): only 11 of the 37 interpretations do not. Over the remaining 27 interpretations, 20 have more than one annotation. Based on the totality of annotations observed, two subfamilies of annotations are considered. The first corresponds to the way in which the interpreter transcribes doubts, i.e., what the geologist thinks is uncertain. In this category, we find correlations in the form of dashes, question marks, arrows to indicate fluid flow directions or fault displacements. The other category corresponds to parsimony. Some geologists simply correlate and interpolate observed features, while others add or extrapolate interpretations beyond the areas defined by the data.

Dashes are the most frequent glyphs added to the drawings (on 19 models), followed by faults added outside the data (10 models). Other annotations include second-order variations (7), tectonic movement arrows (7), text (6), question marks (5), stratigraphic layers (4), fluid arrows (2), and alteration halos (2). If we compare the presence of annotations among uranium experts and non-experts (Fig. 17 b), we can observe different proportions of markings.

Non-experts are more adept at using dashes, reflecting doubt about their interpretation. Experience can be a source of certainty for experts, justifying the lesser use of hyphens.

# 5. Are there any proximities between models?

## 5.1. Multidimensional scaling

The criteria described above are analyzed with Multi-Dimensional Scaling (MDS) (Cox, 2001), which is a dimension reduction method.

Its purpose is to define the positioning of interpretations in a reduced space by defining a distance that represents the similarity between each model, so that patterns can be identified in that space. Further explanations of MDS configuration are given in the appendices (Appendix A).

A first observation may be to look at the influence of each variable on the MDS. Linear regression is performed for each dimension of the MDS (Fig. 18), modeling it as a linear combination of the original variables. The absolute sum of the regression coefficients obtained provides the overall importance of each variable. The relative importance of each variable, i.e., its ability to discriminate between drawings in MDS, is shown in the log scale on the Fig. A.23 (b). Note that the 6 variables with the greatest influence on drawing dispersion in MDS are the three branch type ratios $CLR_X$, $CLR_Y$, $CLR_I$ and the three $Ψ$ parameters that study the relationship between deposit geometry and control structures. Then the influence of the parameters on MDS collapses.

Regarding the metric MDS, several observations can be made. Certain categories of models, in terms of interpreter type, are clustered, while other categories are more dispersed (Fig. 18). For example, models made by high-school students tend to be clustered. There are several main outliers, all from non-experts: Model 15, because the faults have been digitized as fracture complexes, artificially increasing the number of faults; Model 24 for the length of its perimeters; Model 20, a veined model; Model 18, which is missing the pyritic alteration; Model 41 which has a greater kaolinite surface and Model 42 due to its network topology (see Fig. B.25). If outliers are taken into account, the area covered by the non-experts is larger than that of the experts;
<figure><img src="image_27.png" /><figcaption>**Fig. 14.** Classification of interpretations according to four criteria:(a) P<sub>tot</sub> perimeter sum, proxy for second-order digitization; (b) ratio α = C<sub>tot</sub>/P<sub>tot</sub> proxy for halo deformation; (c) Riley circularity o; (d) Number of disconnected components N<sub>c</sub>.</figcaption></figure>

<figure><img src="image_28.png" /><figcaption>**Fig. 15.** Ψ<sub>struct</sub>, density of mineralization points oriented like the structure as a whole. Proxy of geological knowledge used to select the shape of mineralization.</figcaption></figure>

if outliers are not taken into account, it is almost twice as small. The core of non-experts (gray zone) is more compact than that of experts (green zone). The greater variability of non-experts may be due solely to outlier scenarios, which are not necessarily the most consistent with

the data studied. Perhaps the experts filter the proposed scenarios according to their knowledge. This can be constructive if supported by evidence, but it can also be a bias, reducing the range of possibilities that can be explored.
<figure><img src="image_29.png" /><figcaption>**Fig. 16.** $\Psi_{\text{flt}}$ versus $\Psi_{\text{unc}}$: model positioning according to whether they are more correlated with the fault network or the unconformity, both or neither. Orange shapes depict the synthetic end member models corresponding to brown circles.</figcaption></figure>

<figure><img src="image_30.png" /><figcaption>**Fig. 17.** Presence or absence of annotations and added objects on interpretations.</figcaption></figure>

In order to check for particular trends and coherent groups of models, the distance obtained in MDS can serve as the basis for clustering by Hierarchical Ascending Classification (Fig. 18 b). With this method, all samples are initially in their own class, and classes are iteratively merged. Ward's method (Murtagh and Legendre, 2014), used here, is a merging method based on the minimization of cluster variance. Outliers are made all the more visible by the use of a Hierarchical Ascending Classification (Fig. 18 b). Models are divided into five clusters. They are well mixed between experts, non-experts and high-school students. The outliers observed are consistent with visual assessment: they include Model 15, which is surely the least parsimonious model with numerous faults and halos outside the data, Model 20 with vein mineralization, Model 18 pyritic alteration halo, Model 41 with a higher Kaolinite surface and Model 42 with a Y-shaped structural network (Fig. B.24).

It is worth examining the average characteristics of the five clusters obtained by hierarchical clustering. These characteristics are presented in Fig. 19. Each row represents a cluster and each column represents the E-Type (Journel, 1986) of a characteristic (unconformity, mineralization, fault network). The E-type study shows us that the most distinctive aspect between model clusters is the structural network: Cluster 1 shows Y-shaped faults connecting in the basin, Cluster 2

a similar Y-shaped fault network but more vertical and more shifted unconformity, Cluster 3 straight Y-shaped faults connecting in the basement, Cluster 4 numerous isolated short faults, Cluster 5 even more short isolated faults. Mineralization, and in particular the number of related components changes between clusters: Clusters 1, 2, and 3 have three disconnected components, while clusters 4 and 5 have two disconnected components. Cluster 5 is the only cluster with continuous mineralization body around the unconformity and the one with the straightest unconformity. Differences in unconformity are less marked although we can distinguish faulted unconformities (clusters 2 and 3) from non-faulted unconformities (clusters 4 and 5). Although there are no differences between expert and non-expert groups, differences between interpreters are observed and they can be grouped in consistent families.

## 5.2. Raw image analysis and clustering using histogram of oriented gradient method

A second approach is to compare the raw images directly, to check whether the observed clustering trends match those obtained using the metrics defined in this study. Many approaches allow raster images to
<figure><img src="image_31.png" /><figcaption>Fig. 18. (a) Multidimensional scaling results on the continuous variables and temporal evolution of some users; (b) Hierarchical ascending classification.</figcaption></figure>

be compared by using pixel information, such as calculating the differences between them (Liwei et al., 2005), applying machine learning algorithms to extract specific features (Chang et al., 2017), or studying gradients (Dalal and Triggs, 2005). Since this study focuses on the relationship between the orientation of structures and mineralization, gradient analysis seems particularly suitable, as it enables contours to be detected and their orientation to be examined.

The histogram of oriented gradients (HOG) method (Dalal and Triggs, 2005) is used to determine the contour orientation of an image, after it has been grayscaled (Fig. 20 a) and the gradient of brightness calculated. Gradient orientation histograms are then calculated, normalized and grouped by pixel packets. The result is a vector representation of contour orientations (Fig. 20 b). Clustering strategies can then be applied to the vector representations to classify the drawings. Here, t-SNE (t-distributed stochastic neighbor embedding) (Van der Maaten and Hinton, 2008) is used, and in a similar way to MDS, enables drawings to be placed by proximity in terms of HOG (Fig. 20 c).

As in the analysis of comparison criteria by MDS, there is a homogeneous distribution of expert and non-expert models. The outliers are also the same, and the high-school models are very close to the reference model, which was also visible in the MDS space (Fig. 18).

## 6. Temporal variability

To assess the impact of temporal variability, members of the expert group in the field of uranium repeated the interpretation of the cross-section several times. The interpreted models are shown in Fig. 21. These models are also placed in the MDS (Fig. 18) with arrows to show the temporal evolution of models in MDS space for these three experts. Visually and in the MDS plot, the interpreter A (in red outlines in Fig. 18 a) and B (in orange outlines in Fig. 18 a) produced quite similar models through time. The overall shape of the fault network changes little. In one case we have independent straight faults, in the other case Y-shaped flower-like structures, but the general idea remains the same. This is also the case for the shape of the facies. Interpreter C (in blue outlines in Fig. 18 a) is a little different. The geometries change a lot, even if the role of the structural network with regard to mineralization remains the same (faults seem to control the geometry of mineralization). So it seems that for the persons tested here, there is consistency of interpretation over time. They remain faithful to the geological ideas

used for the first interpretation. Nonetheless, the temporal variations in metric space are significant as compared to the variations between different experts. This is consistent with the importance of occasional noise as mentioned by Kahneman et al. (2011). This also illustrates that the lack of observations entails significant geometric uncertainties in geological section interpretation, even when the conceptual model is the same.

The greater variations for interpreter C can be explained by the greater time interval between the first and last interpretations: 2 months and a half for interpreter A, 5 months for interpreter B, and 8 months for interpreter C. They may also be influenced by anchoring bias (e.g., the expert being influenced by something he/she has seen just before the interpretation exercise.)

## 7. Discussion

### 7.1. Experimental setup

To validate the findings reported here, it would be valuable to extend this study to a larger number of drawings. Indeed, with 40 drawings, statistical representativeness can be improved. In addition, the choice of the cross-section used is questionable. It may also be useful to consider other elements of comparison, such as the level of expertise in structural geology or alteration processes, as well as the amount of experience, particularly in interpretation of drillcore data, or on similar deposits.

It is based on synthetic drillcores: This may introduce a bias in term of parsimony. One possible improvement would be to create an interpretation exercise based on real drillcores, to get closer to the real working conditions of data interpretation in a professional setting.

Another difference concerns the two-dimensional nature of the exercise, while most practitioners work in three dimensions to integrate data directly. To focus on geological concepts and avoid comparing software or software skills, we relied on pen and paper interpretations, but the extension of our study would be interesting to extend to three dimensions. For instance, it would allow for integrating the effect of branching faults on the hydrothermal alterations. However, comparing human interpretation work in 3D could be of interest, but this is a difficult exercise, as it requires more time from participants, and would involve mixing together tools and concepts used by modelers (Schaaf
<figure><img src="image_32.png" /><figcaption>Fig. 19. E-Type of the four cluster characteristics obtained after Hierarchical Ascending Clustering.</figcaption></figure>
<figure><img src="image_33.png" /><figcaption>Fig. 20. (a) Grayscale image; (b) histogram of oriented gradient descriptor of (a); (c) 2D positioning of models using t-SNE according to their HOG values.</figcaption></figure>

and Bond, 2019). Moreover, despite the central role of 3D deposit modeling, gaps remain in the geological knowledge required to constrain 3D interpretation. Possible avenues include dedicated methods as proposed for instance by Marchal et al. (2024). Alternatively, recent machine learning approaches are being developed to build geological models (Garayt et al., 2025; Hillier et al., 2023; Gao and Wellmann, 2025) and to integrate conceptual knowledge carried by hand-drawn 2D sections. Geologically constrained geophysical inversions as proposed for instance by Liang et al. (2023) and Giraud et al. (2024) also appear as a possible ways forward to bridge the gap between geological models and geophysical data.

Secondly, given the design of the interpretation exercise, with contiguous facies color bands to be interpreted, all geologists have considered non-intersecting contiguous zones. From a geological point of view, alteration halos are fronts that correspond to varying concentrations of chemical elements. Front limits are arbitrarily set to correspond to threshold values, but the presence of an alteration facies is a continuum, not a defined zone. This means that several mineral phases can coexist at the same location above the centimeter scale. The

end of the pyritic alteration zone towards the kaolinite alteration zone may be seen as a clear contact, or as a gradient where the quantity of pyritic alteration decreases until it is no longer the main mineral phase.

The choice of interpretive terminology may also be seen as a source of bias. It was designed to be as neutral as possible, but this can be a source of parsimony. A less neutral statement might be considered, for example, focused in a competitive way on the exploration of mineral resources.

The $\Psi$ criterion was chosen to distinguish the models, as it provides a good separation between the synthetic reference models and also synthetic extreme cases (Section 4.5). However, other criteria were tested, but did not discriminate as well between extreme cases: the Wasserstein distance or earth mover distance (EMD) (Rubner et al., 1998), Kulback-Leibler divergence (Kullback and Leibler, 1951), and Jensen Shannon distance (Nielsen, 2020).

## 7.2. Group differences

Data interpretation varies between individuals (Bond, 2015) according to their background, as confirmed here by the comparative
<figure><img src="image_34.png" /><figcaption>**Fig. 21.** Examples of models made by the same users (per line) but at different times.</figcaption></figure>

study of the interpretations of expert and non-expert geologists in uranium deposits. However, variations are visible between all individuals, and there are no truly distinctive characteristics between experts and non-experts.

Non-experts have a slight tendency to produce larger variability than experts, especially when looking at all variables in the MDS space. Although experts propose more complex mineralization shapes, more faults on average or second-order geometries, they appear in the MDS space as a more compact region than non-experts, and are therefore less variable. This observation depends on the consideration of statistical outliers, all produced by non-experts, which can be considered at two levels of pertinence. Either non-experts are considered as not biased by previously known cases, and therefore propose more extreme but still relevant scenarios. Alternatively, it can be considered that experts use their knowledge of the context to screen out these more extreme and less relevant cases. This difference in relevance is subjective and depends on the importance attached to the interpreters' degree of expertise. Moreover, there is a limit to the above observations: despite a divergence of interpretation, the exploration of the domain of possibilities remains limited, as we observe a generalized parsimony. Having many users interpret the model is not enough to generate scenarios that properly explore the range of scenarios. Another point is the fragmentation that would be detrimental for tonnage/grade and mining efficiency. Choosing a conceptual model at the start of a decision chain can have an impact on resource estimation. This suggests the importance of group collaboration and the multiplication of interpretation work. However, this variability of interpretations requires the use of stochastic approaches (Dimitrakopoulos and Lamghari, 2022).

### 7.3. Influence of structures

Interpretation variation is a source of uncertainty about the characteristics of geological objects of interest, in particular their connectivity, volume estimation and their geometries (Bond, 2015). Here, further confirmation of these aspects is provided by this study, which highlights the impact of interpretation variation on the estimation of altered and mineralized surfaces, the number of components of the mineralization, and the resulting deposit shapes. This result is particularly relevant in cases where altered facies need to be avoided for geotechnical or chemical reasons during mine design and planning, as incorrect assessment of adjacencies can lead to higher mining costs. The generation of probable alternative adjacency scenarios should, therefore, be one of the steps in the deposit modeling process, when compatible with the geological conceptual model, e.g. during a succession of different alteration phases over time with different brine circulation pathways. The importance of characterizing fault intersections is also highlighted here. Fault intersections are seldom encountered in wells and are therefore poorly represented in geologists' interpretations. Nevertheless, their impact on the circulation of hydrothermal fluids, and hence on the genesis of deposits, is crucial (Yang et al., 2004; Walsh et al., 2018). The tendency to interpret isolated faults can affect prospectivity.

The findings presented in this study can provide guidance for exploration. A good characterization of the structural network is essential when assessing fluid circulation zones, as they play a key role in the deposit settings. Furthermore, it appears that less parsimonious deposit geometry models need to be generated, either by multiplying the interpretation work carried out by various geologists, or by using stochastic modeling processes to produce realistic deposit shapes that take account of the interaction between structures and facies geometry. This quantitative methodology is suitable for other settings, in
particular for comparing geometrical interpretations of fluid circulation phenomena, linked to fluid-rock interactions, along known geological features.

Overall, variations in drawings show fundamental differences in conceptual models, concerning the timing and influence of faults upon the mineralization setting. While some drawings illustrate post-mineralization faults, others show ante-mineralization faults.

## 8. Conclusion

The present analysis confirms that the interpretation of a geoscience dataset can lead to multiple (Bond et al., 2007; Jackson et al., 2003), divergent and sometimes contradictory interpretations (Polson and Curtis, 2010). The present study addresses this problem using a drillhole dataset related to a hydrothermal deposit, applying a new methodological framework to compare different populations of geologists, whether or not they are specialists in one type of deposit. A series of quantitative metrics is proposed to investigate interpretation variation around hydrothermal deposits. Some are adapted from previous studies (Sanderson and Nixon, 2015; Manzocchi, 2002; Pirot et al., 2022; Pellerin et al., 2015) and others are novel. In particular, the link between controlling structures (faults and regional unconformities) and mineralization geometry is studied by looking at the orientation of the structures and the mineralized surface.

In this study, it is hard to distinguish experts in uranium deposits from non-experts in quantitative terms. Non-experts have a slight tendency to diverge more than experts: taking their interpretative work into account allows us to explore the range of possible scenarios more widely, whether their interpretations are geologically relevant or not. The lack of familiarity of non-experts with the topic allows them to generate interpretations with greater variance. It raises the question of the relevance of outliers in terms of geological concepts. Are non-experts less biased or are experts filtering out non-relevant cases from their experience ?

Although interpretations differ in many aspects, they all tend to be parsimonious. This is consistent with the way people are trained. There is a tendency to push the interpretation of data by proposing solutions that require the minimum of extrapolation. This is the principle of Occam's razor, also known as the principle of parsimony, which suggests that all reasoning should be based on solutions that minimize the number of elements. However, this methodology has its limits for exploration and exploitation, since it only offers a limited exploration of the space of possibilities and hence may give a false sense of security. Results highlight complex (non-Gaussian behavior) and show that some rare individuals have a tendency to propose interpretations distinct from the rest of the group. This type of behavior is essential to appropriately capture uncertainty and avoid overconfidence. However, it is challenging in practice, because in general only one person does the interpretation. Getting lots of users to interpret is not enough to generate scenarios that adequately explore the space of possibilities. This implies the use of probabilistic modeling methods. The modeling methods used must, therefore, be closer to the concepts of interpretations used by geologists. However, interpretative exercise instructions may influence the approach taken to the problem. Here, depending on the question, the interpreter can either go for strict interpolation or extrapolation. In our case, people were asked to "correlate" and not to "extrapolate" or "evaluate uncertainties", which may have indirectly led to more complex features away from the drillholes. The same interpretation exercise could be carried out with various prompts to study this effect.

This study also confirms the impact of conceptual uncertainty on volume estimation and connectivity. The role of fault network connectivity is particularly noteworthy: model clusters are characterized primarily by their fault network type. This is one of the dominant categories of metrics in Multi-Dimensional Scaling. The other metric

family is the $Ψ$ variable defined in this study to determine the relationship between control structures and mineralization form. The way people link deposit geometry and structures is key to distinguish one interpretation from another. These variables also reveal the importance of unconformity in the tabular geometry of deposits.

## CRediT authorship contribution statement

**Paul Marchal:** Conceptualization, Methodology, Software, Formal analysis and investigation, Writing – original draft preparation, Writing – review & editing. **Guillaume Caumon:** Methodology, Supervision, Writing – review & editing, Funding acquisition, Project administration. **Pauline Collon:** Methodology, Supervision, Writing – review & editing, Funding acquisition, Project administration. **Patrick Ledru:** Writing – review & editing, Funding acquisition, Project administration. **Kelsey McKee:** Writing – review & editing, Funding acquisition, Project administration. **Pat Taylor:** Writing – review & editing, Funding acquisition, Project administration. **Julien Mercadier:** Writing – review & editing, Funding acquisition, Project administration.

## Funding

The research leading to these results received funding from French Agence Nationale de la Recherche (ANR) under Grant Agreement ANR-21-CHIN-0006 (project Geomin3D). Partial financial support was received from Orano and the RING-GOCAD Consortium managed by ASGA.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgments

This work was performed in the frame of the RING project at Université de Lorraine (https://www.ring-team.org/). We would like to thank them for their support: the industrial and academic sponsors of the RING-GOCAD Consortium managed by ASGA. The authors would also like to thank Orano for providing the data used in this study and partial funding for the PhD scholarship of Paul Marchal. The authors acknowledge the support of the French Agence Nationale de la Recherche (ANR), under grant ANR-21-CHIN-0006 (project Geomin3D). Special thanks also to all the study contributors for taking the time to get out their crayons to interpret the section.

## Appendix A. MDS parametrization

From a set of $N_S$ drawings, each with a measurement of $N_V$ continuous variables, the matrix $X$ of available data can be defined as

$$X = \begin{bmatrix} x_{11} & \cdots & x_{1,N_V} \\ \vdots & \ddots & \vdots \\ x_{N_S,1} & \cdots & x_{N_S,N_V} \end{bmatrix}$$

This matrix dimensions correspond to $N_S = 38$ samples with $N_S = 33$ continuous variables measured per pattern. Prior to the computation of the distance matrix $D$, data are first centered and reduced to avoid bias due to differences in scale, forming a new matrix $Z$. The coefficients $z_{ij}$ of this matrix are given by $z_{ij} = \frac{x_{ij} - \mu_i}{\sigma_i}$. Indeed, variables have very different scales (proportions, surface areas, perimeters, etc.) and this may impact the MDS by artificially giving more weight to some variables.

Then, from the normalized data $Z$, a $N_S \times N_S$ distance matrix $D$ is calculated, which contains the distances/similarities between each model. This distance is calculated relative to the continuous available
<figure><img src="image_35.png" /><figcaption>Fig. A.22. (a) PCA on variables; (b) Matrix of correlation.</figcaption></figure>

<figure><img src="image_36.png" /><figcaption>Fig. A.23. (a) scree plot, stress optimization parameter of the Multidimensional Scaling versus the number of dimensions of reduced space. (b) Ranking of variables importance in MDS.</figcaption></figure>
<figure><img src="image_37.png" /><figcaption>**Fig. B.24.** Drawings digitalization: non-experts, high-school students.</figcaption></figure>

variables, using the Euclidean norm: the coefficients $d_{ik}$ of $\mathbf{D}$ are given by $d_{ik} = \sqrt{\sum_{j=1}^{N_S} (z_{ij} - z_{kj})^2}$. Euclidean distance is standard for continuous, uncorrelated data indeed the Principal Component Analysis (Fig. A.22 a) and the correlation matrix (Fig. A.22 b) between variables indicate that there are no strong correlations between the variables.

The aim of MDS is then to place model samples in a metric space of reduced dimensions ($N_S \times m$) with $m \ll n$ so as to preserve the inter-model distances as much as possible. The matrix $\mathbf{\Delta}$ is the distance matrix in reduced dimension $m$ space. The idea is to find a value of $m$ that is

as low as possible, but which minimize the distortions. To achieve this, a stress function $S = \sqrt{\sum_{i<j} (d_{ij} - \delta_{ij})^2}$ is optimized.

The selection of the optimal dimension $m$ is made by plotting the evolution of stress as a function of the number of dimensions, called the scree plot (Fig. A.23a). In this case, two dimensions appears as a good compromise to obtain distance values close to those in the initial space.

Note that to avoid parameter redundancy, a choice had to be made between keeping the sum of the perimeters $P_{\text{tot}}$ or the individual perimeters ($P_p, P_k, P_c, P_u$) (and similarly for convex envelopes). MDS
<figure><img src="image_38.png" /><figcaption>Fig. B.25. Drawings digitalization: experts in Uranium and reference model.</figcaption></figure>

performed equally well in both cases, giving almost identical results, the main difference being the positioning of the high-school students models. The choice was to retain only the sums of perimeters and convex envelopes, with a view to considering the set of perimeters as a proxy for the presence of second-order variations.

## Appendix B. Digitalized cross-sections used for this study

See Figs. B.24 and B.25.

## Data availability

Data will be made available on request.

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