Density and magnetic susceptibility of major rock types within the Abitibi greenstone belt: a compilation with examples of its use in constraining inversion

Geophysical inversions give non-uniqueness solutions and unless constrained by appropriate initial values and geological constraints can give unrealistic results. One of the critical constraints can be the physical property values of different lithologies. We have compiled a density and magnetic susceptibility database consisting of thousands of measurements collated from different organisations and/or projects across the Abitibi greenstone belt. Statistical tools (histograms, quantile-quantile probability plots and boxplots) are applied to characterise systematically major and minor lithologies. We observed that the magnetic susceptibility frequently has a bimodal distribution, while density is typically unimodal. Our results are summarized in a table that includes the representative mean (or median) and a range of acceptable values. These values can be used to better understand the regional geology, but in this paper, we used the tabulated properties in a geophysical/petrophysical inversion of gravity data from the Chicobi area in the Abitibi subprovince to show the level of improvements that the petrophysical constraints can add to an unconstrained model. When our density database is used to seed the initial guess in a gravity inversion, an anomalous zone becomes apparent that was less evident on an unconstrained inversion.


Introduction
Characterisation of petrophysical properties (i.e.density and magnetic susceptibility) of different types of rocks is important for interpreting gravity and magnetic data, as it can be used to infer the regional geology.A knowledge of these properties also plays a key role in ensuring that potential-field (i.e.gravity and magnetic) data is modelled in a credible manner and/or that the interpretation is realistic.This is done by providing a significant link between the geophysical measurements and the different rock types (e.g.Clark 1997;Heincke et al. 2010;Kamm et al. 2015;Williams 2008).Density can be a good indicator of the silica or carbonate content of a rock (Dentith et al. 2020) while susceptibility can be an indicator of the iron content in some igneous rocks (Enkin, Hamilton, and Morris 2020).However, susceptibility is generally more poorly related to lithology, with Grant (1985) discussing how the magnetic susceptibility can vary depending on the iron, oxygen and silica content in the material forming the rock and on the temperature or metamorphic state.
Nonetheless, measured values of the physical properties can be critical in helping to constrain the values the world and these may or may not be applicable for different study areas.Given the general lack of a regional systematic characterisation that retains all information (e.g.number of measurements, standard deviations, mean and median values, maximum and minimum values, characterisation method, location), this study should be a step towards providing more information for a specific region.
In this paper, we describe a systematic petrophysical characterisation of key rock types within the Abitibi Greenstone Belt (AGB), including a coherent data compilation and collation, lithological/stratigraphic characterisation, and a statistical analysis of property values to define representative density and magnetic susceptibility values to assign to each lithology.These representative values are the mean, the standard deviation, the median, the absolute minimum, the absolute maximum and the skew.In addition to the summary of the statistical data, we also provide histogram and normal probability plots as a special case of the quantile-quantile probability plot for a normal (or lognormal) distribution (addressed as QQ plots in this report), so that the interpreter can determine the reliability and modality of the data.This might allow the user to pick other representative values when modelling data if there are peaks in the histogram above and below the mean or median.
This study of physical properties is intended to provide interpreters and modellers with knowledge that will allow them flexibility when modelling and interpreting data collected in the AGB.The methodology we describe could be used to compile databases and summary data in provinces where regional information is already available.When appropriate physical property values are not available, this database could be used in the unweathered parts of shield areas buried below regolith in other parts of the world, but the user should be aware that the values might not be completely representative.
In some cases, modelling and interpretation can be simplified by using a relationship between magnetic susceptibility and density.However, this relationship is complicated and depends on multiple factors including lithology, mineralogy, degree of alteration and grade of metamorphism.A good way of seeing the relationship between these two quantities is the Henkel plot, with metamorphic and basaltic rocks showing a positive correlation along two branches, the ferromagnetic branch being more magnetic and the paramagnetic branch less magnetic (Enkin 2018;Enkin, Hamilton, and Morris 2020).On both branches, density increases as the susceptibility increases.However, for other rock types, Enkin (2018) did not find such a correlation.Alteration can have a highly variable impact on magnetic susceptibility with oxidation and reduction often destroying magnetite, and significantly reducing the susceptibility with little impact on density (Enkin, Hamilton, and Morris 2020).In IOCG deposits, Williams and Chopping (2009) show that in some cases, alteration can decrease the density with little impact on magnetic susceptibility.Thus, to understand the complex relationship between density and magnetic susceptibility requires knowledge of the metamorphic grade, degree and style of alteration, and or the extent of oxidation or reduction.Our lithological database does not always include this information, and often just gives the protolith, so we cannot undertake a study to determine relationships between density and susceptibility.These types of studies are most useful when undertaken on rocks that are well characterized at a deposit or camp scale.

Methodology
Density is defined as the mass per unit volume of a substance (in units of kg m −3 or g cm −3 -1000 kg m −3 equals to 1 g cm −3 ) which can reflect lithological variations, contrasting alteration and weathering (Telford, Geldart, and Sheriff 1976).For example, sedimentary rocks generally have higher porosity resulting in typically lower densities than igneous or metamorphic rocks.Within igneous rocks, density differences are primarily due to the mineral assemblage present and the rock texture.In addition, an increase in the metamorphic grade generally increases density (Telford, Geldart, and Sheriff 1976).Finally, density varies with composition, as mafic minerals are typically denser than felsic minerals.Therefore, density is often well correlated with rock types.
Magnetisation is defined as the magnetic dipole moment per unit volume of material.The spin of unpaired electrons is the most important cause of these microscopic magnetic moments (Clark 1997).The total magnetisation of a rock is the vector sum of the induced and remanent magnetisation.The magnetic susceptibility (k) is proportional to the strength of magnetisation (M) that a material assumes in response to an applied magnetic field (H), divided by the strength of that applied magnetic field, (Clark 1997).In this formula, since M and H have the same dimensions, magnetic susceptibility is a dimensionless property.However, the value of k depends on the system of units and may be specified in CGS or SI with the following linear relationship: Remanent magnetisation can be observed, if present, when this induced field is removed and some "permanent" magnetisation remains (Telford, Geldart, and Sheriff 1976).The induced magnetic susceptibility of rocks is controlled by the proportion of ferromagnetic minerals (mostly magnetite and/or pyrrhotite), their distribution, grain size and orientation (Hansen, Racic, and Grauch 2005).It is important to note that a small change in the proportion of magnetised minerals within rock samples can result in a significant change in the recorded magnetic susceptibility and this proportion should be considered while measuring magnetic susceptibilities.For example, Church and McEnroe (2018) investigated the magnetic susceptibility values across different core samples and found that magnetic susceptibility variations at millimetre-or centimetre-scales are caused by either a complex mineral system or serpentinization/metamorphism and alteration or a possible magnetic remanence, or a combination of those factors.Typically, when the induced magnetic field is strengthened by the presence of paramagnetic minerals, k is positive.Whereas the magnetic field is somewhat weakened in the presence of diamagnetic minerals causing even slightly negative values of k.For example, quartz has a weak and negative magnetic susceptibility value of ∼ −0.0134 × 10 −3 SI (Hrouda and Kapička 1986).
Because the magnetic susceptibility of rocks is strongly depended on opaque iron minerals, and these minerals are accessory and do not change the rock type classification, the magnetic susceptibility is not always a good indicator of rock type, except in rocks that generally contain a lot of iron (mafic rocks, iron formations, etc.).However, these iron minerals are often created or destroyed by alteration or metamorphism associated with mineralising events, so magnetic susceptibility can be important in mineral exploration studies (e.g.Boroomand, Safari, and Bahroudi 2015;Cisowski and Fuller 1987).
In this study, all values are provided in the "g cm −3 " unit for density and the "× 10 −3 SI" unit for magnetic susceptibility.Therefore, if measurements compiled from other sources were measured using different units, they were converted to the stated units for coherency and consistency.

Petrophysical data compilation
In this study, a petrophysical database was compiled by collating and combining new density and magnetic susceptibility measurements at outcrops (Metal Earth 2017) with existing values provided by different organisations/geological surveys and projects across the Superior Craton (i.e.Chandler and Lively 2011;Footprint project 2018;Haus and Pauk 2010;Metal Earth 2017;Muir 2013;NRCAN 2017;OGS 2001;Rainsford 2017) and selecting petrophysical measurements associated with lithologies within the AGB.Table 1 outlines measurements collated and combined from different sources and the number of density and magnetic susceptibility values in the database across the Superior Craton and AGB.There are some existing petrophysical characterisations across the AGB mostly focusing on local scale characterisations.For instance, petrophysical properties of Sudbury were characterised by Hearst, Morris, and Thomas (1994) and McGrath and Broome (1994).In contrast, the advantage of the large-spatial-scale systematic petrophysical characterisation in this study is to compile a more comprehensive database taking into account measurements from different sources, as well as a regional characterisation to mitigate the impact of local weathering or metamorphism, and also to coherently and consistently characterise both density and magnetic susceptibility values.
The compiled database was divided into different lithologies based on the lithological hierarchy.This includes dividing the groups into major plutonic igneous rocks (felsic, intermediate, mafic and ultramafic), volcanic igneous rocks (felsic, intermediate, mafic and ultramafic), Proterozoic dykes (diabase), sedimentary (sedimentary and volcaniclastic rocks), metamorphic rocks (metamorphic and fault-associated rocks), and banded iron formation.In addition, minor rock types with a sufficient number of measurements within each hierarchy have been characterised independently and some examples are presented in this paper.For example, granite, granodiorite, tonalite, trondhjemite, felsic dykes and monzogranite rock types have a high number of density and/or magnetic susceptibility measurements within the felsic plutonic igneous rocks and were characterised as sub-types.In general, the number of samples to define reliably  the petrophysical properties of a rock type should be guided by the diversity of mineralogy and texture.For example, Tukey (1977) suggested 30 samples are required for a reliable statistical evaluation, and we have generally complied with this guideline.Figure 1 shows the spatial distribution of density and magnetic susceptibility values of the compiled database within the AGB; each sample location is indicated with a black dot, on a larger geological compilation from Montsion, Thurston, and Ayer (2018).Every compilation will have its limitations; ours is that there are fewer samples in the Quebec portion of the AGB (east of the blue borderline) and even the Ontario side is dominated by samples close to the border.The gravity samples are generally more widespread, while the magnetic samples are more localized, particularly in Quebec, where they are adjacent to the Metal Earth traverses.

Petrophysical characterisation
Tables 2 and 3 summarise density and magnetic susceptibility properties (i.e.number of samples, mean, standard deviation, median, minimum, maximum and skew) of major rock units across the AGB.In this characterisation, carbonatites and younger dykes (diabase), including the Matachewan dyke swarm (2450 Ma), Nipissing sills (2217-2210 Ma), Biscotasing (2167 Ma), Sudbury dyke swarm (1240 Ma) and Abitibi dyke swarms (1141 Ma) are characterised independently because these rocks are much younger compared to the Archean basement of the Abitibi, and were not metamorphosed during the major Archean metamorphism events (Osmani 1991).In addition, due to the abundance of granites across the AGB and their significant contribution to gravity lows, this type was independently characterised as a sub-type of felsic intrusive rocks.It should be noted that the density and magnetic susceptibility databases are independent and do not include exactly the same rock types.So, it is possible that some rock types have adequate density measurements for a reliable characterisation, while there are insufficient magnetic susceptibility measurements corresponding to that type and vice versa.
A detailed investigation of each rock type is performed using histograms and QQ plots of the physical properties for different rock types.The histogram is the number of samples in a bin of density or magnetic susceptibility values and shows the nature of the distribution to illustrate the number of samples in each physical property bin, which can be used to infer whether their distribution is unimodal, bimodal or multimodal.If there is a bimodal distribution (when there are two peaks evident), it can be quantified somewhat arbitrarily by calling the distribution strongly bimodal when the counts at the bottom of valley are less than 33% of the smallest peak; moderately bimodal when the counts in the valley are 33-66% of the smallest peak; and weakly bimodal when the counts in the valley are more than 66% of the smallest peak.If there are a relatively few samples in the smaller peak, it is difficult to confidently quantify the strength of the bimodality, so the bimodality in this case is said to be poorly defined.
In addition, QQ plots (the normal probability plot) show the distribution of values as a function of the quartile, with normal distributions plotting as straight lines, with the slope a function of the standard deviation.In contrast, a non-normal distribution returns non-linear QQ results.If the distribution is bimodal, there are two symmetric peaks evident on the histogram, with two straight lines on the QQ plot.Furthermore, QQ plots can show a right skew (if the curve appears to bend up and to the left of the normal line indicating a long tail to the right), left skew (if the curve bends down and to the right of the normal line indicating a long tail to the left), short tails (an S shaped-curve indicating shorter than normal tails), and long tails (a curve starting below the normal line, bends to follow it, and ending above it).For magnetic susceptibility measurements, the distribution is lognormal and appropriate QQ plots can be used to separate multimodal distributions (Lapointe, Morris, and Harding 1986;Latham et al. 1989).
The mean and/or the median can be used as the representative value for density and magnetic susceptibility.If the mean and median are the same or very close with a difference < 0.02 g cm −3 for density and < 0.5 × 10 −3 SI, we assume the representative value is the mean-median with a higher level of certainty.Otherwise, in this study, we typically use the mean as the representative value because this value takes into account all the different measurements.However, when there is a bimodal distribution and/or the mean value is less-representative based on an inspection of the histogram and QQ plots, we have assessed two scenarios of either (1) dividing the properties into two sub-types and determining properties for each subtype (more typical for magnetic susceptibilities due to the wider range and inherent heterogeneity associated with magnetic values (e.g.Enkin 2018)), or (2) used the median value as the representative property for the type.
In this study, histograms and QQ plots are exhibited on a linear horizontal scale when characterising density values.In contrast, due to a large range of magnetic susceptibility values, the magnetic susceptibilities are plotted on a logarithmic scale (Lapointe, Morris, and Harding 1986;Latham et al. 1989).In addition, some measurements are identified as outliers.These outlier values are not discarded from the database and histograms; they are just exempted when calculating representative values.Keeping the outliers on the histogram can give a modeller the option of using a larger or smaller value for some rock types when specifying models.Having a statistical plot such as those we present will not always be sufficient to allow modelling and lithological interpretation, as there may be other complexities such as the presence of significant remanence (e.g.Austin and Foss, 2014) or changes associated with alteration, metamorphism, weathering or strain (Dentith et al. 2020).

Results
In this section, we discuss the statistics of major lithological types and some of the sub-types in more detail, including in some cases a discussion of specific rock types within each subgroup.In the figures, histograms are shown on the left side and QQ plots on the right side.

Intrusive igneous rocks
Figure 2 returns a comparison of density properties and the density distribution (unimodal or bimodal) of the main intrusive igneous hierarchy.As can be noted as a general pattern, density increases from felsic intrusive rocks towards mafic and ultramafic lithologies.Felsic intrusive rocks (566 density measurements) return a relatively unimodal distribution with flat tails, excluding outliers, and the same mean and median density of 2.69 g cm −3 .Density values of the intermediate intrusive rocks (871 measurements) highlight a wide range of density values with a relatively unimodal distribution and a positive skew of 0.83 and the mean and median values of 2.74 and 2.71 g cm −3 , respectively.Further, the total number of 1354 density measurements classed as mafic intrusive rocks show a relatively unimodal normal distribution with the same mean and median value of 2.88 g cm −3 .
Finally, ultramafic intrusive rocks have 181 associated density measurements with a unimodal normal distribution and mean and median density values of 2.91 and 2.87 g cm −3 , respectively.Nevertheless, since this sub-group consists of a combination of different rock types, so is discussed in more detail in the Example minor rock types section below.Proterozoic-aged dykes typically consist of diabase rocks consisting of 328 density samples with a unimodal left-tailed distribution and the mean and median values of 2.97 and 2.99 g cm −3 , respectively.
Figure 3 investigates the magnetic susceptibility of the intrusive igneous rock hierarchy.Magnetic susceptibility characterisation of felsic intrusive rocks was conducted using 1073 measurements displaying a relatively lognormal distribution with a wide range of magnetic properties from non-magnetic to relatively high magnetic susceptibility values with the mean and median values of 2.58 and 0.39 × 10 −3 SI, respectively.A total number of 32 measurements have values greater than 16 × 10 −3 SI.The spatial location of these 32 samples suggests that they can be considered as outliers based on their correlation with other intrusions, metamorphism or the variable impacts of the original protolith.The new database, with the exemption of these 32 outliers, has a mean of 1.76 and median of 0.36 × 10 −3 SI.
The magnetic susceptibility database contains 392 measurements classed as intermediate intrusive rocks showing a mean and median of 9.14 and 1.07 × 10 −3   Therefore, it can be concluded that in this hierarchy, diorite is mostly non-magnetic while syenite has relatively high magnetic susceptibility values.
The magnetic susceptibility database of mafic intrusive rocks, consisting of 1744 measurements, infer a moderate bimodal non-normal distribution with a mean of 10.23 × 10 −3 SI and a median of 0.88 × 10 −3 SI.Of the two modes, the one with the largest population (1141 measurements) has low magnetic susceptibility values with the mean of 0.81 × 10 −3 SI and the latter population (524 measurements) exhibits a mean of 31.40 × 10 −3 SI.Therefore, the median value of 0.88 × 10 −3 SI is assigned to the sub-group with a wide range of allowed values, however, rocks within this hierarchy can define the representative range similar to the magnetic susceptibility of intermediate intrusive rocks.
Magnetic susceptibility characterisation of ultramafic intrusives (275 measurements) is very complex because they display a wide range of magnetic susceptibility values, varying from non-magnetic (minimum of 0.08 × 10 −3 SI) to anomalously high magnetic susceptibility (maximum of 763.7 × 10 −3 SI).Overall, ultramafic rocks exhibit an extended-tailed distribution and large mean and median values of 59.95 and 42.45 × 10 −3 SI, respectively.
Magnetic susceptibility measurements of young dykes clearly indicate two subpopulations, one is relatively non-magnetic (unit 1) and the other is highly magnetised (unit 2).Unit 1 consists of 168 measurements and returns mean and median magnetic susceptibility values of 0.83 and 0.76 × 10 −3 SI.Whereas, unit 2 (317 measurements) has a mean of 32.12 × 10 −3 SI and median of 26.78 ×10 −3 SI.
Figure 4 illustrates how the bimodal magnetic susceptibility distribution of the ultramafic intrusive package was due to different rock types.In order to obtain representative values, different lithologies within this hierarchy are studied independently.The lower tail in magnetic susceptibility of ultramafic intrusive rocks is from dunite which indicates a unimodal low magnetic susceptibility (41 measurements with the mean values of 0.47 × 10 −3 SI), while other major rock types within this hierarchy in this database return generally high magnetic properties including peridotite (129 measurements with the mean value of 36.60 × 10 −3 SI) and pyroxenite (26 measurement with the mean value of 63.18 × 10 −3 SI).
Other histograms and QQ plots similar to Figures 2 and 3 have been generated for other hierarchies and many of the minor rock types.For completeness, the authors refer you to Eshaghi, Smith, and Ayer (2019) which present and describe other histograms and QQ plots in detail.Here we discuss other major hierarchies and present some of the histograms and QQ plots of rock types that illustrate the heterogeneity of types and their significance in characterisation which should be noted during geophysical modelling.

Igneous extrusive rocks
Density characterisation of the major extrusive igneous hierarchy indicates that felsic extrusive rocks (a total of 958 measurements) has a unimodal distribution with a positive skew or a flat right tail and mean and median values of 2.74 and 2.73 g cm −3 , respectively.In comparison, the intermediate extrusive sub-group (280 density measurements) have a unimodal normal density distribution with the mean and median values of 2.78 and 2.76 g cm −3 , respectively.The mafic extrusive package consists of 1384 density measurements with a unimodal normal distribution, exempting outliers, with the same mean and median density value of 2.89 g cm −3 , respectively.
The ultramafic extrusive hierarchy (344 density measurements) mainly consists of komatiite, which expresses a wide range of densities with a weak bimodal distribution.Both of the two populations return relatively high-density values that allow us to estimate one property for this type.This population returns a mean density of 2.89 g cm −3 and a median value of 2.91 g cm −3 .The bimodal distribution of this type and the presence of outlying density values led to selecting the median density of 2.91 g cm −3 as the representative density of this type.
The magnetic susceptibility properties of volcanic extrusive rocks illustrate a unimodal distribution with an extended right tail for felsic extrusive rocks (810 magnetic susceptibility measurements) returning the mean and median values of 2.33 and 0.19 × 10 −3 SI, respectively.A total of 1351 magnetic susceptibility measurements classed as intermediate extrusive rocks show a unimodal distribution with an extended right tail and mean and median values of 1.743 and 0.35 × 10 −3 SI, respectively.
Magnetic susceptibility investigations of mafic extrusive rocks were performed using a total of 2747 measurements returning a wide range of magnetic susceptibility values (0-565.60 × 10 −3 SI) with mean and median values of 8.51 and 0.73 × 10 −3 SI, respectively.Based on the QQ plot, there is either a significant right skewed distribution or an extended right tailed distribution.However, the majority of magnetic susceptibility measurements (2226 out of the total 2747 measurements) display relatively low-magnetic values ( < 10 × 10 −3 SI) exhibiting a unimodal lognormal distribution with mean and median magnetic susceptibility values of 1.24 and 0.65 × 10 −3 SI, respectively.This character is indicative of overall heterogeneity in this sub-group.
Characterising magnetic susceptibility values of the ultramafic extrusive rocks was performed using a total of 473 measurements.The susceptibility values associated with this rock type have a weak bimodal distribution with two main subpopulations.Therefore, this hierarchy is divided into two units based on their magnetic susceptibility values.Unit 1 (104 measurements) has low magnetic susceptibility values with mean and median values of 0.37 and 0.39 × 10 −3 SI, respectively.In contrast, unit 2 (366 measurements) highlights high magnetic susceptibilities with a mean value of 32.33 × 10 −3 SI and a median value of 23.92 × 10 −3 SI.

Other major rock types
Other main hierarchies in this characterisation include sedimentary rocks, a volcanoclastic package, a metamorphic hierarchy and rocks characterised as the fault rocks.
The statistical characterization of the density of sedimentary rocks utilized a great number of density measurements (a total of 2432), which display a wide range of values from 2.30 g cm −3 to > 3.10 g cm −3 .This wide range of density variations associated with different rock types result in a non-simple unimodal normal distribution.In addition, the QQ plot of this package indicates a relatively asymmetrical distribution with flat tails.This hierarchy has mean and median density values of 2.75 and 2.76 g cm −3 , respectively.These values are not reliable and representative because of the inhomogeneity associated with different rock types and differing grades of metamorphism within the hierarchy.
There are 668 density measurements associated with volcanoclastic rocks in this database; they exhibit a weak bimodal distribution that is interpreted as an extended right-tailed distribution based on the QQ plot.This package has mean and median values of 2.86 and 2.84 g cm −3 , respectively, with two major populations evident.The first population occupies a density range between 2.66 and 2.80 g cm −3 , and the other one lies in a range of 2.95-3.10g cm −3 .The major rock types within this sub-group are pyroclastic and tuff.There are 34 density measurements of pyroclastics, which display a unimodal and relatively normal distribution with the same mean and median of 2.74 g cm −3 .There are 629 density measurements of tuff, which show a weak bimodal distribution with a right tail and the mean and median values of 2.87 and 2.85 g cm −3 , respectively.This rock type is weakly bimodal with two peaks between 2.71-2.74g cm −3 (82 measurements) and 3.03-3.06g cm −3 (84 measurements).This indicates that tuffs can be divided into two sub-groups characterised by either medium density (2.76 g cm −3 ) linked to intermediate tuffs or high density (3.03 g cm −3 ) values linked to mafic context tuffs.
Altered and metamorphic rocks in this database are associated with 1825 density measurements displaying a wide range of density values (2.24-3.58g cm −3 ) and highlighting a unimodal distribution, with either a positive skew or an extended right-tailed distribution based on the QQ plot, and the mean and median values of 2.78 and 2.75 g cm −3 , respectively.Also, in this database, density values classed as rock types typical along faults (i.e.cataclasite, mylonite and pseudotachylite) are characterised independently consisting of 49 density measurements displaying a unimodal normal distribution with the same mean and median value of 2.78 g cm −3 .
Histograms and QQ plots of the magnetic susceptibility of sedimentary rocks (1408 readings) exhibit a generally relatively unimodal lognormal distribution of dominantly non-magnetic material.The mean and median magnetic susceptibility values of this package are 1.45 and 0.30 × 10 −3 SI, respectively.In contrast, altered and metamorphic rocks (1111 measurements) show a generally unimodal distribution, excluding outliers.These measurements return mean and median magnetic susceptibility values of 3.45 and 0.36 × 10 −3 SI, respectively.While the graphs show a unimodal distribution, there is a positive skew and both left-and right-tailed distribution with a wide range of magnetic susceptibility values from non-magnetic to highly magnetic.However, the vast majority of measurements have low-magnetic values with few magnetic susceptibility measurements returning significantly large values (14 measurements with magnetic susceptibility values > 50 × 10 −3 SI).

Example minor rock types
Some of the minor rock types are also discussed to describe clearly the methodology and systematic characterisation leading to the final characterisation.Focusing on the well-sampled rock types within the felsic intrusive database, the granodiorite (Figure 5) contains 289 density measurements with a unimodal normal density distribution and the mean and median values being slightly different (2.70 and 2.69 g cm −3 , respectively).Also, 460 magnetic susceptibility measurements classed as granodiorite rocks indicate a weak bimodal   distribution with the mean and median magnetic susceptibility values of 2.82 and 0.73 × 10 −3 SI, respectively.This lithology can be divided into two subpopulations with the lower magnetic susceptibility values associated with population 1 centred on 0.28 × 10 −3 SI (245 measurements) and population 2 with the higher magnetic susceptibility values centred around of 5.79 × 10 −3 SI (212 measurements).
Focusing on density properties, within the ultramafic intrusive category, 121 peridotite samples return a unimodal normal density distribution with mean and median density values of 2.84 and 2.83 g cm −3 , respectively.In contrast, 40 density measurements of pyroxenite display a unimodal normal distribution with anomalously high mean and median density values of 3.13 and 3.14 g cm −3 , respectively (Figure 6).This detailed description illustrates that the observed bimodal distribution in density of the ultramafic intrusive package is caused by two sub-type rock types.
Finally, banded iron formation (BIF) can be investigated based on their magnetic properties contributing to magnetic measurements.There are 188 associated magnetic susceptibility measurements in the database (Figure 7).Typically, the values are large and based on the histogram and QQ plots exhibit a moderate bimodal distribution consisting of magnetic values with overall mean and median values of 158.01 and 75.66 × 10 −3 SI, respectively.The histogram shows two populations, the first with low-magnetic values which has a mean susceptibility of 1.47 × 10 −3 SI, and the second population returns a significantly higher mean value of 226.11 × 10 −3 SI.Therefore, it is difficult to provide one simple representative value for the entire hierarchy.
Two major types with sufficient number of measurements within this hierarchy are iron formation (IF)sulphide and IF-oxide.The IF-sulphide (73 measurements) displays slightly uniform distribution with a wider range of magnetic values from relatively nonmagnetic to high magnetic susceptibility values.In contrast, the IF-oxide contains 109 measurements that have an extended left-tailed distribution and typically high magnetic values, disregarding a small number of low-magnetic outliers.In summary, IF-sulphide presents highly heterogeneous magnetic values from relatively non-magnetic to large magnetic values and the lower mean and median magnetic susceptibilities of 52.61 and 2.12 × 10 −3 SI respectively, whereas, IF-oxide rocks are more homogeneously magnetised with high mean and median magnetic susceptibility values of 214.40 and 136.39 × 10 −3 SI, respectively.

Summary plots and tables
Summary density and magnetic susceptibility box-plots of typical petrophysical values for major lithologies are given in Figures 8 and 9, and the values or the range of values is explained and a comparison between different hierarchies or lithological groupings is provided.These figures use box-and-whisker diagrams, where the box spans the range from the 25 to the 75% quartile, the small square is the mean, the central horizontal line is the median and the whiskers show 1.5 × the interquartile range (IQR).IQR is the difference between upper and lower quartiles and is often used to find outliers in data which are typically defined as observations falling below quantile 1 − 1.5 IQR or above quantile 3 + 1.5 IQR.These box and whisker plots are used to display the range of the petrophysical properties for major hierarchies to provide an insight into density and magnetic susceptibility values.
The boxplot of density data for all major hierarchies (Figure 8) shows a general trend of increasing density from felsic igneous rocks toward ultramafic rocks.Granite exhibits the smallest median and the minimum range of density values, which emphasises the significance of this type on gravity lows in geophysical investigations.In contrast, Proterozoic dykes (diabase) have anomalously high-density values compared to other types.Based on the composition of mafic diabase dykes, it was initially thought that this type should have lower densities compared to ultramafic rocks; however, in fact diabase returns higher density values.This suggests the younger dykes, having experienced lower-grade metamorphism and alteration (subgreenschist facies) (Osmani 1991), and thus less hydration of their mafic minerals, has resulted in higher densities.Another instance is the characterised density properties of ultramafic intrusive dunite.While unaltered dunite is composed mostly of olivine with densities > 3.2 g cm −3 , nine density measurements of dolerite in this database return a mean of 2.70 g cm −3 which can show it has altered to serpentine/talc resulting in lower values.
The boxplot summary of the logarithm of magnetic susceptibility for all major hierarchies (Figure 9) highlights that felsic and intermediate igneous rocks, sedimentary rocks and metamorphic rocks typically return non-magnetic to low-magnetic values.In contrast, ultramafic igneous rocks, young dykes (diabase) and BIF exhibit large magnetic susceptibility values.These sub-groups are those that are mostly responsible for the anomalous magnetic responses evident on magnetic maps.This boxplot shows a large degree of magnetic susceptibility variations (orders of magnitude) with the highest magnetic heterogeneity belonging to BIF and ultramafic igneous rocks.In general, the larger the values, the greater the spread of values.

Application of the petrophysical compilation
Three-dimensional geophysical modelling was carried out to show the importance of using the representative values from the petrophysical compilation in performing constrained modelling.

Geology of the study area
The Chicobi transect lies in the Abitibi subprovince, Superior province, Quebec, Canada.The bedrock geology of the area is comprised of granites, sediments and volcanic rocks as shown in Figure 10.The volcanic and sedimentary rocks are folded and deformed by major shear zones (North Chicobi deformation zone [NCDZ] and Castagnier deformation zones [CDZ]).These basement rocks are covered by unconsolidated glacial sediments.A more detailed explanation of the geology of the study area is discussed by Zhou et al. (2021).

Geophysical datasets
A total intensity aeromagnetic grid (Figure 11(a)) with 50 m cell size, levelled to 120 m altitude obtained from the SIGEOM database was used for this study.Gravity data were collected along the seismic transect with an average spacing of 300 m (Maleki et al., 2021) and combined with publicly available Geological Survey of Canada data (http://gdrdap.agg.nrcan.gc.ca/) across the area of interest.A complete Bouguer anomaly grid (Figure 11(b)) was created after applying standard gravity processing (latitude, elevation, free-air, Bouguer and terrain corrections assuming a background density of 2.67 g/cm 3 ).Regional to residual separation was performed on the complete Bouguer anomaly grid by applying a first-order trend removal filter using Oasis Montaj software (https://www.seequent.com/productssolutions/geosoft-oasis-montaj/).A study in a nearby area by Della Justina (2022) showed that any error in the Bouguer correction was about 0.2 mGal and errors associated with erroneous densities being used in the terrain correction were less than 0.04 mGal.These errors are significantly less than the anomalies seen on Figure 11.Shuttle Radar Topographic Map grid (Figure 11(c)) with 30 m resolution was downloaded from the Geosoft public DAP server (http://dap.geosoft.com).High-resolution seismic data was acquired along the 12 km Metal-Earth Chicobi transect in a south-north direction, perpendicular to the geological strike (Figure 10).First-arrival travel-time tomographic inversion (Zhang and Toksöz 1998) was performed on the seismic data using the GeoThrust2D program (Geotomo 2022) to determine the V P structure of the near-surface material (Figure 11(d)).

Constraining basement elevation
To constrain the basement elevation (or overburden thickness), the depth-to-basement is estimated using the tomography velocity model (Figure 11(d)) generated from the seismic data.The points were picked assuming the top of the basement has a velocity of 4000 ms −1 with a depth-to-basement varying between 20 and 60 m.This depth-to-basement estimate is only reliable below the seismic line.To determine depth-to-basement estimates away from the seismic line, Euler deconvolution (Thompson 1982) depthto-source points were computed using the GOCAD mining suite on the residual total magnetic intensity grid with parameters (window size = 7 and structural index = 1).The Euler computations typically generate vast number of solutions many of which are artifacts.Typically clustering of solutions is a good indicator used to perform 3-D depth-to-basement and basementdensity gravity modelling (Pears, Fullagar, and Andrews 2001).A two-layer density model (cover and basement) was used for this study.The initial two-layer 3D density model was constructed within a volume of dimensions 18 km x 25 km x 3 km and a 300 m cell size.The thickness of the top cell varied between 20 and 100 m deep and the cell below went to 3 km depth.In the GOCAD mining suite, any geophysical model can be represented either by using block models or by layered surfaces.In the current study, all the models are displayed as surfaces (topography and basement) with a vertical exaggeration of 5.

Property modelling
In the first modelling process, the depth-to-basement was the only constraint applied and property values were unconstrained.The starting density model (Figure 13(a)) comprises a homogenous basement beneath a uniform overburden or cover.The overburden density contrast for this area is fixed at −0.17 g/cm 3 , a typical value for unconsolidated sediments.A simple basement density inversion was performed with an initial density-contrast value of 0 g/cm 3 for all the cells beneath the basement surface and VPmg was allowed to numerically change the property of each basement cell to fit the observed data.The final unconstrained density inversion of the basement is shown in Figure 13(b).The data misfit is shown in Supplementary Figure S1.The basalt and andesite (blue/green) and wacke (orange brown) north and south of the NCDZ respectively are inferred to be dense and the andesite south of the wacke and the CDZ is inferred to be less dense.

Constrained modelling
The starting model for constrained density modelling comprises an overburden with uniform density, as before.This overburden is overlying a heterogenous basement i.e. the basement surface is now discretised into six zones (rock types) extracted from the publically available basement geology maps (Figure 14(a)).The representative petrophysical properties, taken from Table 4 and summarized in Figure 14(b), are assigned to each type as a valuable initial model for the inversion.In addition, the range of density variation is also limited by the petrophysical property characterisation in this study.
The starting model for the constrained basement property inversion is shown in Figure 15(a).The inversion varies the basement density from the initial value, but cannot decrease it below the lower end of the range or increase it above the upper end of the range.The final basement surface after constrained inversion is shown in Figure 15(b) and the corresponding data misfit is shown in Supplementary Figure S2.The modelling result shows how the constrained inversion changes the basement densities from their initial mean values especially near major deformation zones thus identifying the anomalous zones that might be related to alteration.However, away from the seismic profile the model is not well constrained due to a sparsity of gravity stations as shown in Figure 11

Conclusion
Petrophysical properties of rocks across the Abitibi greenstone belt were systematically analysed from a database collated from historical databases and augmented with measurements taken by ME field crews.The resulting characterisation is based on a sufficiently large number of measurements from outcrops that have been classed as different rock types to provide typical values that can be used to constrain physical properties used in future geophysical models.There can be a large amount of spatial variabilities within geological types in many properties (e.g. chemical composition, mineralogy and porosity) and/or tectonic evolution factors (e.g.alteration, metamorphism, diagenesis, weathering, hydrothermal or magmatic fluid flow) which can affect physical properties.Therefore, this study tried to mitigate this inherently associated uncertainty in the characterisation by taking into account a range of components and variables influencing the density and magnetic susceptibility values.Unfortunately, the geological information provided, which was limited to the rock types, did not provide a lot of information that might be relevant (e.g. protolith, alteration, metamorphic grade, etc.).
A comparison between density and magnetic susceptibility values indicates that density values are more homogenous and the degree of variations in magnetic susceptibility is significantly greater.Histograms and QQ plots show that density distribution of rock types are more unimodal and normally distributed compared to magnetic susceptibility measurements, which commonly show a bimodal distribution and a high degree of variability.Recording of magnetic susceptibility values across a sample is typically heterogeneous, especially within magnetic rocks, due to contribution of nearby magnetite/pyrrhotite to the measurement.
Table 4 provides a summary of the systematically estimated representative density and magnetic susceptibility values and the representative ranges.These ranges are defined based on the representative value ± the standard deviation, which include ∼ 66% of measurements for major rock types across the AGB.These typical values can be assigned to lithologies during potential-field data inversions.
Although representative values have been selected in Table 4, in some cases a lithology may be comprised of rock that has an outlier value of the physical property, and the modeller needs to know what these outliers are, so they can be included in the modelling when required, so these outliers have been shown on the histograms and box plots.Hence, the recommended procedure for assigning physical properties values to lithologies is to start with a representative value in Table 4.If this is not suitable, some value within the range could be selected (perhaps the mean or medians in Tables 2 and 3).If these do not work, the modeller could look at the histograms and perhaps after experimentation one of the outliers might be selected as appropriate.
Our modelling example illustrates the value of a petrophysical database.The results from unconstrained inversion modelling do not show any clear additional geological information that is not in the data itself, but the modelling which used the mean values from the database as the initial values has a final model that shows where this model is different from the known geology and petrophysics and thus identifies anomalous zones.Thus, the above modelling example clearly demonstrates that the final constrained modelling results are more geologically relevant than the unconstrained modelling.Our example also shows how the petrophysical database could play an important role in achieving the exploration objective.

Figure 1 .
Figure 1.Final compiled petrophysical database within the Abitibi greenstone belt (AGB) superimposed on the Superior compilation geological map (Montsion, Thurston, and Ayer 2018), (a) density measurements; (b) magnetic susceptibility measurements.The Ontario-Quebec border is shown with the blue line and locations of the towns of Timmins, Rouyn-Noranda and Malartic are shown with the blue initials (T, RN and M).

Figure 2 .
Figure 2. Density measurements of intrusive igneous rocks in the AGB.The left column displays histograms (g cm −3 ) and the right column shows the quantile-quantile (QQ) plots.Note that the horizontal scale for ultramafic intrusive rocks is different from other rock types.

Figure 3 .
Figure 3. Magnetic susceptibility measurements of intrusive igneous rocks and major lithologies in the AGB shown on a log10 scale.The left column displays histograms of the values (× 10 −3 SI) and the right column shows the quantile-quantile (QQ) plots.

Figure 4 .
Figure 4. Magnetic susceptibility measurements of major lithological rock types within the ultramafic intrusive hierarchy in the AGB shown on a log10 scale.The left column displays histograms of the values (× 10 −3 SI) and the right column shows the quantilequantile (QQ) plots.

Figure 5 .
Figure 5. Petrophysical measurements of granodiorite in the AGB.The top row displays density (g cm −3 ) measurements (left column is the histogram and the right column is quantile-quantile (QQ) plot).The bottom row indicates magnetic susceptibility (× 10 −3 SI) values shown on a log10 scale (the left column is the histograms and the right column is the QQ plots).

Figure 6 .
Figure 6.Density measurements of peridotite and pyroxenite within the ultramafic intrusive rocks in the AGB.The left column displays histograms (g cm −3 ) and the right column shows the quantile-quantile (QQ) plots.

Figure 7 .
Figure 7. Magnetic susceptibility measurements of banded iron formation (BIF) rocks and major lithological types of this hierarchy in the AGB shown on a log10 scales.The left column displays histograms of the values (× 10 −3 SI) and the right column shows the quantile-quantile (QQ) plots.

Figure 8 .
Figure 8. Boxplot analysis of density measurements represented by major lithological groups.

Figure 9 .
Figure 9. Boxplot analysis of magnetic susceptibility measurements represented by major lithological groups.

Figure 10 .
Figure 10.Geological map of the study area, based on Système d'information géominière of Québec (SIGEOM) regional geology database (https://sigeom.mines.gouv.qc.ca/signet/classes/I1108_afchCarteIntr) and Zhou et al. (2021).The 12 km long profile line is shown in solid black.The study area is 16 km east west and 24 km north south.

Figure 11 .
Figure 11.Geophysical datasets used for constrained basement modelling.(a) Residual total magnetic intensity grid downloaded from https://sigeom.mines.gouv.qc.ca/.(b) Complete Bouguer anomaly gravity grid after regional removal (large black circles -GSC data, small red circles -ME data).(c) Shuttle Radar Topographic map (30 m).(d) Near-surface velocity model after traveltime tomographic inversion.The north and south end of the profile are labelled N and S. The maps in (a), (b) and (c) are 16 km (east west) by 24 km (north south).

Figure 12 .
Figure 12.GOCAD perspective view of two-layer basement model: (a) Combined depth-to-basement points extracted from traveltime tomography velocity model and Euler deconvolution depth-to-basement solutions from the magnetic grid.The colour of the displayed points represents depth.(b) Interpolated basement surface from extracted information in (a).

Figure 13 .
Figure 13.Two-layer basement model: (a) Starting model surface with homogenous basement (density contrast value of 0 g/cc).(b) Final inverted density model surface after basement property inversion.

Figure 14 .
Figure 14.Two-layer basement model: (a) Lithology assigned to basement from surface geology (b) Table showing the lithologies and their corresponding densities extracted from the Metal Earth petrophysics compilation.For the current study, mean density values are used for the initial model.
(b) and Supplementary Figures S1 and S2.The arrow mark in Figure 15(b) denotes the location where Zhou et al. (2021) identified a magnetotelluric conductivity anomaly.This anomalous zone is not as clearly identified or localized in the unconstrained property inversion (Figure 13(b)).

Table 1 .
The number of density and magnetic susceptibilities compiled across the Superior Craton and the Abitibi greenstone belt (AGB), categorized by source.
(Chandler and Lively 2011)SG_LU" is the density database delivered byRainsford (2017); "Footprints petrophysical data" is data collected by the Footprints project led by Laurentian University (Footprint Project 2018); "Minnesota Petrophysics" is the database compiled from the Minnesota Geological Survey(Chandler and Lively 2011).

Table 2 .
Summary statistics of density values (g cm −3 ) of major geological lithological groups across the AGB.

Table 3 .
Summary statistics of magnetic susceptibility values (×10 −3 SI) of major lithological groups across the AGB.BIF is Banded Iron Formations.