The aim of this study is to delineate and identify various mineralized zones
and barren host rocks based on surface and subsurface lithogeochemical data
from the Pulang porphyry copper deposit, southwestern China, utilizing the
number–size (N-S), concentration–volume (C-V) and power-spectrum–volume
(S-V) fractal models. The N-S model reveals three mineralized zones
characterized by Cu thresholds of 0.28 % and 1.45 %: <0.28 %
Cu represents weakly mineralized zones and barren host rocks,
0.28 %–1.45 % Cu represents moderately mineralized zones, and
> 1.45 % Cu represents highly mineralized zones. The results
obtained by the C-V model depict four geochemical zones defined by Cu
thresholds of 0.25 %, 1.48 % and 1.88 %, representing nonmineralized
wall rocks (Cu<0.25 %), weakly mineralized zones
(0.25 %–1.48 %), moderately mineralized zones (1.48 %–1.88 %) and
highly mineralized zones (Cu>1.88 %). The S-V model is used by
performing a 3-D fast Fourier transformation of assay data in the frequency
domain. The S-V model reveals three mineralized zones characterized by Cu
thresholds of 0.23 % and 1.33 %: <0.23 % Cu represents
leached zones and barren host rocks, 0.23 %–1.33 % Cu represents
hypogene zones, and >1.33 % Cu represents supergene enrichment
zones. All the multifractal models indicate that high-grade mineralization
occurs in the central and southern parts of the ore deposit. Their results
are compared with the alteration and mineralogical models resulting from the
3-D geological model using a log-ratio matrix. The results show that the S-V
model is best at identifying highly mineralized zones in the deposit.
However, the results of the C-V model for moderately and weakly mineralized
zones are also more accurate than those obtained from the N-S and S-V models.
Introduction
The definition and delineation of different mineralized zones and
non–mineralized wall rocks are the main goal in economic geology and
mineral exploration. The investigation of ore mineralogy and paragenetic
sequence provides useful data on ore-forming processes in deposits because
typical characteristics of various types of ore deposits are reflected by
their mineral assemblages (Craig and Vaughan, 1994; White and Hedenquist,
1995). Common methods generally use mineralography, petrography and
alteration mineral assemblage analysis to delineate various mineralized
zones in porphyry deposits (Beane, 1982; Schwartz, 1947; Sillitoe, 1997;
Berger et al., 2008). Lowell (1968) first proposed a conceptual model of the
lateral and vertical variations in mineralogy within alteration zones. Some
similar models were developed for potassic alteration, which is usually
situated in the center and deep parts of porphyry ore deposits, based on
this conceptual model (Sillitoe and Gappe, 1984; Cox and Singer, 1986;
Melfos et al., 2002). Fluid inclusion and stable isotope studies are other
methods used to outline different mineralization phases based on
thermometric and isotope element parameters and other geological parameters
(e.g., Boyce et al., 2007; Faure et al., 2002; Wilson et al., 2007).
Drill hole data and logging information, including mineralographical
information, host rock changes and alterations are helpful in delineating
mineralization zones. Different geological interpretations could be used to
detect zone boundaries, which may also lead to different results because the
elemental grade distribution may not be taken into consideration.
Non-Euclidean fractal geometry (Mandelbrot, 1983) is an important branch of
nonlinear mathematical sciences and has been applied in various research
fields of the geosciences since the 1980s. The relationships between
geology, geochemistry and mineralogical settings and spatial information can
be researched by methods based on fractal geometry (Afzal et al., 2011;
Carranza, 2008, 2009). Bolviken et al. (1992) and Cheng et al. (1994) have
shown that geochemical patterns of various elements have fractal dimensions.
The concentration–area (C-A) model was proposed by Cheng et al. (1994) to
recognize geochemical anomalies from background concentrations and calculate
elemental thresholds of different geochemical data. Furthermore, many other
fractal models have been proposed and applied in geochemical exploration
work, including the number–size (N-S) fractal model proposed by Mandelbrot
(1983) and Agterberg (1995), the power-spectrum–area (S-A) fractal model
proposed by Cheng (1999), the concentration–distance (C-D) fractal
model proposed by Li et al. (2003), the concentration–volume (C-V) fractal
model proposed by Afzal et al. (2011) and the power-spectrum–volume (S-V)
fractal model proposed by Afzal et al. (2012).
Methods of fractal analysis also illustrate the relationships between
geological, geochemical and mineralogical settings and spatial information
derived from the analysis of mineral deposit occurrence data (Carranza,
2008, 2010; Carranza et al., 2009; Goncalves et al., 2001). Various geochemical
processes can be described based on the differences in fractal dimensions
obtained from the analysis of relevant geochemical data. Afzal et al. (2011)
considered that the log–log plots obtained by fractal methods are useful
tools to delineate different geological populations of geochemical data, and
the thresholds could be determined as some breakpoints in those plots.
The application of fractal models to delineate various grades of mineralization
zones was dependent on the relationships between the metal grades and
volumes (Afzal et al., 2011; Agterberg et al., 1993; Cheng, 2007; Sim et
al., 1999; Turcotte, 1986). Afzal et al. (2011, 2012) proposed a
C-V and S-V fractal model to
delineate different porphyry-Cu mineralized zones and barren host rocks. In
this paper, N-S, C-V and S-V fractal models were applied to delineate
various mineralized zones and barren host rocks in the Pulang porphyry
copper deposit, Yunnan, southwestern China.
Fractal modelsNumber–size (N-S) fractal model
The N-S method proposed by Mandelbrot (1983) can be utilized
to describe the distribution of geochemical populations (Sadeghi et al.,
2012). In this method, geochemical data do not undergo any preprocessing
(Mao et al., 2004). This model shows a relationship between desirable
attributes (e.g., Cu concentration in this study) and their cumulative
number of samples (Sadeghi et al., 2012). A power-law frequency model has
been proposed to explain the N-S relationship according to the frequency
distribution of elemental concentrations and cumulative number of samples
with those attributes (e.g., Li et al., 1994; Sadeghi et al., 2012;
Sanderson et al., 1994; Shi and Wang, 1998; Turcotte, 1989, 1996; Zuo et al.,
2009).
The N-S model proposed by Mandelbrot (1983) can be expressed as follows:
N(≥ρ)=Fρ-D,
where ρ denotes the element concentration, N(≥ρ) denotes
the cumulative number of samples with concentrations greater than or equal
to ρ, F is a constant, and D is the scaling exponent or fractal
dimension of the distribution of element concentrations. According to
Mandelbrot (1983), log–log plots of N(≥ρ) versus ρ show
linear segments with different slopes -D corresponding to different
concentration intervals.
Concentration–volume (C-V) fractal model
Afzal et al. (2011) proposed a C-V fractal model
based on the same principle as the C-A model (Cheng et
al., 1994) to analyze the relationship between the concentration of ore
elements and accumulative volume with concentrations greater than or equal
to a given value (Afzal et al., 2011; Zuo and Wang, 2016;
Sadeghi et al., 2012; Soltani et al., 2014; Sun and Liu, 2014; Wang et al., 2011, 2012). This model can be expressed as follows:
V(ρ≤υ)∝ρ-a1;V(ρ≥υ)∝ρ-a2.V(ρ≥υ) and V(ρ≤υ) represent the
occupied volumes with concentrations above or equal to and less than or
equal to the contour value υ, υ indicates the threshold
value of a zone, and a1 and a2 are the characteristic indexes.
The thresholds obtained by this method indicate the boundaries between the
different grades of mineralization zones and barren host rocks of ore deposits.
The drill hole data of the elemental concentrations were interpolated by
using geostatistical estimation to compute V(ρ≥υ) and
V(ρ≤υ), which are the volume values enclosed by a
contour level ρ in a 3-D model.
Different geochemical patterns in the spatial domain could be seen as
layered signals of various frequencies. Cheng (1999) proposed the
S-A fractal model to recognize geochemical anomalies
from backgrounds utilizing the method of spectrum analysis in the frequency
domain according to this argument. This model is combined with a
C-A model (Cheng et al., 1994), offering a useful tool
to determine an optimum threshold value between various patterns based on
the scaling property.
Afzal et al. (2012) proposed the S-V fractal model
to delineate different grades of mineralization zones based on the same
principle as the S-A model proposed by Cheng (1999). The S-V model
was utilized in the frequency domain by applying a fast Fourier
transformation to the assay data. The straight lines obtained by log–log plotting indicate the relationships between the power spectra and relevant
volumes of ore elements. These relationships were utilized to recognize the
hypogene zones and supergene enrichment zones from the barren host rocks and
the leached zone of the deposit. The recognition of various mineralization
zones is based on the power-law relationships between the power spectra and
occupied volumes. The formula is as follows:
V(≥S)∝S-2/β,
where the power-law relationships between the power spectra (S=-∥F(Wx,Wy,Wz)∥) and occupied volumes with power
spectra greater than or equal to S can be indicated by this form; F
represents the fast Fourier transformation of the measurement μ(x,y,z); and Wx, Wy and Wz indicate wave numbers or angular frequencies in the x,
y and z directions in a 3-D model. The range of index β is 0<β≤2 or 1≤2/β with the special cases of β=2
and 2/β=1 corresponding to nonfractal and monofractal expressions,
and 1<2/β corresponding to multifractals (Cheng, 2006).
Geological 3-D models including lithology, alteration and 3-D
drill hole plot with the legend of each in the Pulang porphyry copper
deposit. Scale is in cubic meters (m3).
By using the method of geostatistical estimation, the drill hole data of
elemental concentration values were interpolated to construct a block model
of ore element distribution. The power spectrum values can be obtained by 3-D
fast Fourier transformation of the ore element grades. The logarithm of all
the power spectrum values and accumulative volume values were calculated.
Additionally, the log–log plot between power spectrum and volume was drawn
according to previously determined values. Then, the filters were
constructed on the basis of threshold values obtained by the log–log plot of
S-V. Finally, the power spectra were converted back to the space domain by
utilizing inverse fast Fourier transformation.
Photographs of alteration and mineralization in the Pulang
porphyry copper deposit, SW China: (a) quartz monzonite porphyry with
potassium-silicate alteration; (b) quartz diorite porphyrite with
quartz-sericite alteration; (c) quartz diorite porphyrite with propylitic
alteration; (d) hornfels. Qtz: quartz; Pl: plagioclase; Kfs: K-feldspar;
Bt: biotite; Ser: sericite; Chl: chlorite; Ep: epidote; Py: pyrite;
Ccp: chalcopyrite; Mo: molybdenite; Po: pyrrhotite.
Geological setting of the Pulang porphyry copper deposit
The Pulang porphyry copper deposit is situated in the southern end of the
Yidun continental arc, southwestern China (Fig. 1). The continental arc was
produced due to the westward subduction of the Garze–Litang oceanic crust (Deng
et al., 2014b, 2015; Wang et al., 2014). The Pulang ore deposit, one of the
largest porphyry copper deposits in China (Deng et al., 2012, 2014a; Mao et
al., 2012, 2014), is characterized by a typical porphyry-type alteration
zone. The geological characteristics of the deposit, including the
alteration types and their zonation, the geometry of the orebody, the
metallogenic time and the geodynamic settings, have been systematically
researched (Leng et al., 2012; Li et al., 2011, 2013). The deposit consists
of five ore-bearing porphyry bodies covering an area of approximately 9 km2, and the explored ore tonnage of Cu is estimated to be 6.50 Mt (Liu
et al., 2013).
The outcrop strata of the Pulang deposit are dominated by Upper Triassic
Tumugou Formation clastic rocks and andesite and Quaternary sediments (Fig. 1c). The Triassic porphyry intrusions primarily comprise quartz diorite
porphyry, quartz monzonite porphyry, quartz diorite porphyrite and
granodiorite porphyry. The Tumugou Formation strata were intruded by the
quartz diorite porphyry with an age of 219.6±3.5Ma (zircon U–Pb
dating) (Pang et al., 2009). Then, quartz monzonite porphyry with an age of
212.8±1.9Ma and granodiorite porphyry with an age of 206.3±0.7Ma (zircon U–Pb dating) (Liu et al., 2013) crosscut the quartz diorite
porphyry. The quartz monzonite porphyry is considered to be associated with
mineralization because its age is similar to the molybdenite Re–Os isochron
age of 213±3.8Ma from the orebody (Zeng et al., 2004). Moreover,
the Cu concentrations of the quartz monzonite porphyry are higher than those
of the other porphyries.
The porphyry-type alteration zones transition from early potassium-silicate
alteration through quartz sericite alteration to propylitization, upward and
outward from the core of the quartz monzonite porphyry (Fig. 4). The wall
rocks near the porphyries were mostly changed into hornfels. Systematic
drilling has demonstrated that the potassium-silicate and quartz-sericite
zones host the main orebodies, constituting the core of mineralized zones.
The propylitic zones and hornfels only develop weak mineralization. The
orebodies occur mainly in potassium silicate and quartz sericite and occur
as veins in the propylitic zones and hornfels. The major rock types in the
deposit are quartz monzonite porphyry, quartz diorite porphyrite, granite
diorite porphyry, quartz diorite porphyry and hornfels (Fig. 2). Metallic
minerals mainly include pyrite, chalcopyrite with a small amount of
molybdenite and pyrrhotite (Fig. 3).
Fractal modeling
Based on the geological data (which include the collar coordinates of each
drill hole, azimuth and dip (orientation) as well as lithology and mineralogy) recorded
from 130 drill holes in the Pulang deposit, 20 492 lithogeochemical samples
were collected at 2 m intervals. The laboratory of the Third Geological Team
of the Yunnan Bureau of Geology and Mineral Resources utilized the
iodine–fluorine and oscillo-polarographic method to analyze the
concentrations of Cu and associated paragenetic elements, and its analytical
uncertainty is less than 7 % (Yunnan Diqing Nonferrous Metal Co. Ltd.,
2009). Only Cu concentrations were studied in this study. The histogram and
Q-Q (quantile–quantile) plot of the log-transformed Cu data indicate that the distribution of Cu
data is log-normal (Fig. 5). The experimental semivariogram of the Cu data
of the Pulang deposit indicates a range and nugget effect of 320.0 m and
0.25, respectively (Fig. 6). The spherical model is fitted with regard to
the experimental semivariogram. The 3-D model of the Cu concentration
distribution of the Pulang deposit was produced with the ordinary kriging
method using GEOVIA Surpac software on the basis of the semivariogram and
anisotropic ellipsoid. Fundamentally, the accuracy of the interpolation
results mainly depends on whether the interpolation model accurately fits
the spatial distribution characteristics of the deposit. Ordinary kriging
was used because it is compatible with a stationary model; it only requires
a variogram, and it is the most commonly used form of kriging (Chilès
and Delfiner, 1999). Goovaerts (1997) showed that the values in unsampled
locations are estimated by the ordinary kriging method according to the
moving average of the interest variables, satisfying various distribution
forms of data. Ordinary kriging is a spatial estimation method in which the
error variance is minimized. This error variance is based on the
configuration of the data and its variogram (Yamamoto, 2005). The correct
variogram in kriging interpolation can guarantee the accuracy of the
interpolation results.
Cross section along exploration line 0 in the Pulang
porphyry copper deposit, SW China. Modified after Wang et al. (2012).
Histograms of (a) the Cu raw and (b) logarithmic
transformation data and (c) the Q-Q plot of the log-transformed Cu data in the
Pulang deposit.
The experimental semivariogram (omni-directional) of Cu data
in the Pulang deposit.
The accuracy of the spatial interpolation analysis is verified by comparing
the difference between the measured values and the predicted values to
select the best variogram model. To test the variogram model, the
cross-validation method was used to determine whether the parameters of the
variogram model were correct. The distribution of the residual is normal
(Fig. 7), and the mean error between the actual and estimated Cu grades is
equal to 0 (Table 1). This result indicates that this model is reasonable
and that the variogram parameters used for estimating the Cu grade are
unbiased.
The cross-validation results: (a) residual vs. Cu grade; (b) the residual distribution histogram.
The obtained block models were used as inputs to the fractal models. The
Pulang deposit was modeled by 20m×20m×5m voxels, and
they were decided by the grid drilling dimensions and geometrical properties
of the deposit (David, 1970). The Pulang deposit is modeled with
150 973 voxels in total. The terms “highly”, “moderately” and “weakly” have been
used to classify mineralized zones based on fractal modeling, in accordance
with the classification of the ore grades in the deposit.
Number–size (N-S) fractal modeling
The N-S model was applied to the Cu data (Fig. 8). The selection of
breakpoints as threshold values is an objective decision because geochemical
populations are defined by different line segments in the N-S log–log plot.
The straight fitted lines were obtained based on least-square regression
(Agterberg et al., 1996; Spalla et al., 2010). In other words, the intensity
of element enrichment is depicted by each slope of the line segments in the
N-S log–log plots (Afzal et al., 2010; Bai et al., 2010).
N-S log–log plot for Cu concentrations in the Pulang
deposit.
Based on the classification of the 3-D model of Cu data and the thresholds
obtained from the N-S fractal model (Table 2), highly mineralized zones are
situated in the southern and central parts of the Pulang deposit and
coincide with the potassium-silicate alterations. However, small and highly
mineralized zones are located in the central parts of the Pulang deposit
(Fig. 9). Moderately mineralized zones occur along a northwest–southeast
trend and correlate with the phyllic zones. Weakly mineralized zones and
barren host rocks are situated in the marginal parts of the area.
Threshold concentrations obtained by using a N-S model based
on the copper percentage (Cu %) in the Pulang deposit.
Mineralized zonesThresholdsRange(Cu %)(Cu %)Barren host rock and weakly mineralized<0.28Moderately mineralized0.280.28–1.45Highly mineralized1.45>1.45
Zones in the Pulang deposit based on thresholds defined from
the N-S fractal model of Cu data: (a) highly mineralized zones; (b) moderately mineralized zones; (c) weakly mineralized zones and barren host
rocks. Scale is in cubic meters (m3).
Concentration–volume (C-V) fractal modeling
The occupied volumes corresponding to the Cu grades were computed to obtain
the C-V model according to the 3-D model of the Pulang
deposit. Through the obtained C-V log–log plot, the threshold values of the
Cu grades were determined (Fig. 10). These results indicate the power-law
relationship between Cu grade and volume. According to these results (Table 3), the low-concentration zones exist in many parts of the deposit and occur
along a northwest–southeast trend. Moderately and highly mineralized zones
are situated in several parts of the central deposit and to the south of the
deposit (Fig. 11).
Threshold concentrations obtained by using a C-V model based
on copper percentage (Cu %) in the Pulang deposit.
C-V log–log plot for Cu concentrations in the Pulang
deposit.
Zones in the Pulang deposit based on thresholds defined
from the C-V fractal model of Cu data: (a) highly mineralized zones; (b) moderately mineralized zones; (c) weakly mineralized zones; (d) barren host
rock. Scale is in cubic meters (m3).
Power spectrum-volume (S-V) fractal modeling
Based on the geological data (which include the collar coordinates of each
drill hole, azimuth and dip (orientation) as well as lithology and mineralogy) recorded
from 130 drill holes in the deposit, a 3-D model and block model of the
distribution of Cu in the Pulang deposit were constructed with ordinary
kriging using GEOVIA Surpac software.
The power spectrum (S) was calculated for the 3-D elemental distribution
using 3-D fast Fourier transformation in MATLAB (R2016a). The logarithmic
values of the power spectra and relevant volumes were plotted against each
other (Fig. 12). The straight lines fitted in the log–log plot indicate
different relationships between the power spectra and occupied volumes. The
thresholds of logS=7.81 and logS=8.70 were determined by the log–log S-V plot. The 3-D filters were designed to separate different mineralization
zones on the basis of these threshold values. Inverse fast Fourier
transformation was used to convert the decomposed components back into the
space domain by using MATLAB (R2016a). According to the results, the Cu
concentrations of the hypogene zones range from 0.23 % to 1.33 % (Table 4), and values of >1.33 % Cu correspond to the supergene
enrichment zones, whereas values of <0.23 % Cu correspond to the
leached zone and barren host rocks (Fig. 13).
S-V log–log plot for Cu concentrations in the Pulang
deposit.
Zones in the Pulang deposit based on thresholds defined
from the S-V fractal model of Cu data: (a) the supergene enrichment zones,
(b) the hypogene zones, (c) the leached zone and barren host rock. Scale is
in cubic meters (m3).
Ranges of the power spectrum (PS) for different mineralization
zones in the Pulang deposit.
Mineralized zonesPSRangeRangethresholdof PS(Cu %)Leached zone and barren host rock<7.81<0.23Hypogene zones7.817.81–8.700.23–1.33Supergene enrichment zones8.70>8.70>1.33Comparison of the fractal models and geological model of the
deposit
Alteration models have a key role in zone delineation and in presenting
geological models, as described by Lowell and Guilbert (1970). The potassic
and phyllic alterations control major mineralization within supergene
enrichment and hypogene zones according to these models. Models of Cu
mineralization zones derived via fractal models can be compared with
geological data to validate the results of analysis in different porphyry Cu
deposits. The results of the fractal modeling of the Pulang deposit were
compared with the 3-D geological model of the deposit constructed by using
GEOVIA Surpac and drill hole data (Fig. 2). Moreover, the results obtained
from these fractal models were controlled by mineralogical investigations.
Matrix for comparing performance of fractal modeling
results with the geological model. A, B, C and D represent the number of voxels in
overlaps between classes in the binary geological model and the binary
results of fractal models (Carranza, 2011).
Geological model Inside zoneOutside zoneFractal modelInside zoneTrue positive (A)False positive (B)Outside zoneFalse negative (C)True negative (D)Type I error=C/(A+C)Type II error=B/(B+D)Overall accuracy=(A+D)/(A+B+C+D)
Carranza (2011) has illustrated an analysis for the calculation of spatial
correlations between two binary datasets, especially mathematical and
geological models. An intersection operation between the mineralization
zones obtained from fractal models and the different alteration zones in the
geological model was performed to derive the amount of voxels corresponding
to each of the classes of overlap zones (Table 5). Using the obtained
numbers of voxels, the Type I error (T1E), Type II error (T2E) and overall
accuracy (OA) of the fractal model were estimated with respect to different
alteration zones and the geological data (Carranza, 2011). The OAs of the
fractal models of the mineralized zones were compared as follows.
A comparison between highly mineralized zones based on the fractal models
and potassic alteration zones resulting from the 3-D geological model shows
that there is a similarity among these fractal models (Fig. 14). The overall
accuracies for the C-V, N-S and S-V models are 0.50, 0.51 and 0.52,
respectively (Table 6), which indicate that the S-V model gives better
results for identifying highly mineralized zones in the deposit. The number
of overlapped voxels (A) in the S-V model is higher than those in the N-S
and C-V models. The correlation (from OA results) between highly mineralized
zones obtained from S-V modeling and potassic alteration zones is better
than that of the N-S and C-V model because of a strong proportional
relationship between the extension and positions of voxels in the S-V model
and the potassic alteration zones in the 3-D geological model.
Overall accuracy (OA), Type I and Type II errors (T1E and
T2E, respectively) with respect to potassic alteration zone, resulting from
the geological model and threshold values of Cu obtained through C-V, N-S and
S-V fractal modeling.
Potassic alteration of geological model Inside zonesOutside zonesC-V fractal model of highly mineralized zonesInside zonesA 2850B 1360Outside zonesC 77 927D 76 913T1E 0.96T2E 0.02OA0.50N-S fractal model of highly mineralized zonesInside zonesA 3092B 1570Outside zonesC 75 025D 75 473T1E 0.96T2E 0.02OA0.51S-V fractal model of supergene enrichment zonesInside zonesA 4431B 2318Outside zonesC 72 985D 75 726T1E 0.94T2E 0.03OA0.52
Overall accuracy (OA), Type I and Type II errors (T1E and
T2E, respectively) with respect to phyllic alteration zone, resulting from
the geological model and threshold values of Cu obtained through C-V, N-S and
S-V fractal modeling.
Phyllic alteration of geological model Inside zonesOutside zonesC-V fractal model of moderately and weakly mineralized zonesInside zonesA 36 518B 48 027Outside zonesC 25 461D 69 155T1E 0.41T2E 0.40OA0.59N-S fractal model of moderately mineralized zonesInside zonesA 35 555B 46 943Outside zonesC 23 955D 48 223T1E 0.40T2E 0.49OA0.54S-V fractal model of the hypogene zonesInside zonesA 40 080B 44 943Outside zonesC 26 899D 54 239T1E 0.40T2E 0.45OA0.56
Results of XRF analysis of samples collected from different
mineralized zones in the Pulang porphyry copper deposit.
Sample no.Mineralized zones obtained by fractal modelsCu (%)PL-B74Weakly mineralized zones0.41PL-B62Moderately mineralized zones1.32PL-B82Highly mineralized zones1.80
Highly mineralized zones in the Pulang deposit: (a) potassium-silicate zone resulting from the 3-D geological model from drill hole
geological data, (b) N-S modeling of Cu data, (c) C-V modeling of Cu
data and (d) S-V modeling of Cu data. Scale is in cubic meters (m3).
Moderately mineralized zones in the Pulang deposit: (a) quartz–sericite zones resulting from the 3-D geological model from drill hole
geological data, (b) N-S modeling of Cu data, (c) C-V modeling of Cu
data and (d) S-V modeling of Cu data. Scale is in cubic meters (m3).
Chalcopyrite content in several samples based on
mineralographical study: (a) the PL-B82 sample was collected from the drill hole
situated in the high-grade mineralization zones, (b) the PL-B62 sample was
collected from the drill hole situated in the moderate-grade mineralization
zones, (c) and (d) the PL-B74 sample was collected from the drill hole located
at the weakly mineralized zones.
A comparison between phyllic alteration zones resulting from the 3-D
geological model and moderately and weakly mineralized zones from the
fractal modeling shows that the overall accuracies of the C-V, N-S and S-V
fractal models with respect to phyllic alteration zones of the geological
model are 0.59, 0.54 and 0.56, respectively. The overall accuracy of
moderately and weakly mineralized zones obtained from C-V modeling is higher
than that of mineralized zones obtained from N-S and S-V modeling (Table 7).
On the other hand, moderately mineralized zones defined by C-V modeling
overlap with phyllic zones defined by the 3-D geological model (Fig. 15). However, the
results of the C-V model are more accurate than those of the N-S and S-V
models with respect to the phyllic zones defined by the 3-D geological model.
It could be considered that there are spatial correlations between different
modeled Cu zones and geological features such as alterations and mineralogy.
Several samples were collected from different drill holes in different grades of mineralization zones of the Pulang deposit to validate the results of the
fractal models. These samples were analyzed by microscopic identification
and XRF (X-ray fluorescence spectrometry). The PL-B82 sample was collected
from the drill hole situated in a high-grade mineralization zone and includes
a high chalcopyrite content and some molybdenite (Fig. 16a). The PL-B62
sample was collected from the drill hole situated in a moderate-grade
mineralization zone and includes a low chalcopyrite content and some
pyrrhotite in the polished section (Fig. 16b). The PL-B74 sample was
collected from the drill hole located in a weakly mineralized zone with lower
chalcopyrite content and some pyrrhotite (Fig. 16c and d). The
results obtained from the mineralogy, microscopic identification and
drill hole scanning by XRF of these samples indicate that the Cu
concentrations are 1.80 %, 1.32 % and 0.41 % in the PL-B82, PL-B62 and
PL-B74 samples, respectively (Table 8).
Conclusions
In many cases, drill hole logging is dealing with the lack of proper
diagnosis of geological phenomena, which can undermine the delineation of
mineralized zones because it depends on the subjective interpretation of
individual loggers, and no two loggers provide the same interpretations.
However, conventional geological modeling based on drill hole data is
fundamentally important for understanding the orebody spatial structure.
Grades of ore elements are not determined by conventional methods of
geological ore modeling, while the variation in ore grades in a mineral
deposit is an obvious and salient feature. Given the problems mentioned
above, using a series of newly established methods based on mathematical
analyses such as fractal modeling seems to be inevitable.
In this paper, the number–size (N-S), concentration–volume (C-V) and power
spectrum-volume (S-V) fractal models were used to delineate and recognize
various Cu mineralized zones of the Pulang porphyry copper deposit in the
southern end of the Yidun continental arc, southwestern China. All these
fractal models reveal that high-grade Cu mineralized zones are situated in
the central and southern parts of the deposit. The Cu threshold values of
highly mineralized zones are 1.45 % and 1.88 % based on the N-S and C-V
fractal models. The Cu threshold of supergene enrichment zones is 1.33 %
based on the S-V fractal model. The models of moderately mineralized zones
contain 0.28 %–1.45 % Cu according to the N-S model and 1.48 %–1.88 % Cu
according to the C-V model. The hypogene zones contain 0.23 %–1.33 % Cu
according to the S-V model. The N-S model reveals weakly mineralized zones
and barren host rocks containing <0.28 % Cu. In contrast, the C-V
model reveals that the barren host rocks contain <0.25 % and that
the weakly mineralized zones contain 0.25 %–1.48 % Cu. The S-V model reveals
that the barren host rock and leached zone contain <0.23 % Cu.
The comparison between highly mineralized zones based on the fractal models
and potassic zones resulting from the 3-D geological model illustrates that
the S-V fractal model is better than the N-S and C-V model because the
number of overlapped voxels (A) in the S-V model is higher than those in the
N-S and C-V model. The overall accuracies for the C-V, N-S and S-V models
are 0.50, 0.51 and 0.52, respectively (Table 6), which indicates that the
S-V model gives the best results for identifying highly mineralized zones in
the deposit. On the other hand, the correlation (from OA results) between
the highly mineralized zones obtained from S-V modeling and the potassic
alteration zones is better than those of the N-S and C-V models because of a
strong proportional relationship between the extension and positions of the
voxels in the S-V model and potassic alteration zones in the 3-D geological
model.
A comparison between phyllic alteration zones obtained from the 3-D
geological model and moderate-grade mineralization zones obtained from the
fractal models indicates that the OA values of the C-V, N-S and S-V fractal
methods in reference to the phyllic alteration zones of the geological model
are 0.59, 0.54 and 0.56, respectively. The overall accuracy of the
moderately and weakly mineralized zones obtained from C-V modeling is higher
than the mineralized zones obtained from N-S and S-V modeling (Table 7).
According to the correlation between the results driven by fractal modeling
and geological logging from drill holes in the Pulang porphyry copper
deposit, high-grade mineralization zones generated by fractal models,
especially the S-V model, have a better correlation with potassic alteration
zones resulting from the 3-D geological model than from the N-S and C-V
models. The highly and moderately mineralized zones obtained from the
fractal models are both situated in the southern and central parts of the
Pulang deposit and coincide with potassic and phyllic alteration zones.
There is a better relationship between the moderately and weakly mineralized
zones derived by the C-V model and the phyllic alteration zones from the 3-D
geological model than those derived by the N-S and S-V models.
Data availability
The underlying data is confidential information and therefore cannot be made publicly accessible.
Author contributions
XW is the major contributor to this paper, including writing this paper, data processing and so on. QX provided many critical reviews and constructive suggestions. TL, SL, YL, LK and ZC participated in the field investigation. LW provided parts of the raw data.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
This research was supported by the National Key R&D Program of China
(2016YFC0600508). The authors thank Tao Dong, Haijun Yu, Qiwu Shen, Zhipeng Li, Baosheng Shi and Jinhong Yang for supporting in field investigation and
providing parts of the raw data.
Financial support
This research has been supported by the National Key R&D Program of China: The three-dimensional prediction model of deep minerals and virtual reality (grant no. 2016YFC0600508).
Review statement
This paper was edited by Behzad Ghanbarian and reviewed by two anonymous referees.
References
Afzal, P., Khakzad, A., Moarefvand, P., Rashidnejad Omran, N., Esfandiari,
B., and Fadakar Alghalandis, Y.: Geochemical anomaly separation by multifractal
modeling in Kahang (GorGor) porphyry system, Central Iran, J. Geochem.
Explor., 104, 34–46, 2010.Afzal, P., Fadakar Alghalandis, Y., Khakzad, A., Moarefvand, P., and
Rashidnejad Omran, N.: Delineation of mineralization zones in porphyry Cu
deposits by fractal concentration–volume modeling, J. Geochem. Explor.,
108, 220–232, 10.1016/j.gexplo.2011.03.005, 2011.Afzal, P., Fadakar Alghalandis, A., Moarefvand, P., Rashidnejad Omran, N.,
and Asadi Haroni, H.: Application of power–spectrum–volume fractal method
for detecting hypogene, supergene enrichment, leached and barren zones in
Kahang Cu porphyry deposit, Central Iran, J. Geochem. Explor., 112,
131–138, 10.1016/j.gexplo.2011.08.002, 2012.Agterberg, F. P.: Multifractal modeling of the sizes and grades of giant and
supergiant deposits, Int. Geol. Rev., 37, 1–8,
10.1080/00206819509465388, 1995.
Agterberg, F. P., Cheng, Q., and Wright, D. F.: Fractal modeling of mineral
deposits, in: Proceedings of the 24th APCOM Symposium, Montreal, Canada,
43–53, 1993.
Agterberg, F. P., Cheng, Q., Brown, A., and Good, D.: Multifractal modeling of
fractures in the Lac du Bonnet batholith, Manitoba, Comput. Geosci., 22,
497–507, 1996.
Bai, J., Porwal, A., Hart, C., Ford, A., and Yu, L.: Mapping geochemical
singularity using multifractal analysis: application to anomaly definition
on stream sediments data from Funin Sheet, Yunnan, China, J. Geochem.
Explor., 104, 1–11, 2010.
Beane, R. E.: Hydrothermal alteration in silicate rocks, in: Advances in
Geology of the Porphyry Copper Deposits, Southwestern North America, edited by: Titley,
S. R., The University of Arizona Press, Tucson, 117–137, 1982.
Berger, B. R., Ayuso, R. A., Wynn, J. C., and Seal, R. R.: Preliminary Model
of Porphyry Copper Deposits, USGS, Open-File Report, 1321 pp., 2008.
Bolviken, B., Stokke, P. R., Feder, J., and Jossang, T.: The fractal nature
of geochemical landscapes, J. Geochem. Explor., 43, 91–109, 1992.
Boyce, A. J., Fulgnati, P., Sbrana, A., and Fallick, A. E.: Fluids in early
stage hydrothermal alteration of high-sulfidation epithermal systems: a view
from the volcano active hydrothermal system (Aeolian Island, Italy), J. Volcanol. Geoth. Res., 166, 76–90, 2007.
Carranza, E. J. M.: Geochemical Anomaly and Mineral Prospectivity Mapping in
GIS, Handbook of Exploration and Environmental Geochemistry, 11,
Elsevier, Amsterdam, 351 pp., 2008.Carranza, E. J. M.: Controls on mineral deposit occurrence inferred from
analysis of their spatial pattern and spatial association with geological
features, Ore Geol. Rev., 35, 383–400,
10.1016/j.oregeorev.2009.01.001, 2009.
Carranza, E. J. M.: From predictive mapping of mineral prospectivity to
quantitative estimation of number of undiscovered prospects, Resour. Geol., 61, 30–51, 2010.Carranza, E. J. M.: Analysis and mapping of geochemical anomalies using
logratio-transformed stream sediment data with censored values, J. Geochem.
Explor., 110, 167–185, 10.1016/j.gexplo.2011.05.007, 2011.Carranza, E. J. M., Owusu, E. A., and Hale, M.: Mapping of prospectivity and
estimation of number of undiscovered prospects for lode gold, southwestern
Ashanti Belt, Ghana, Miner. Deposita, 44, 915–938,
10.1007/s00126-009-0250-6, 2009.Cheng, Q.: Spatial and scaling modelling for geochemical anomaly separation,
J. Geochem. Explor., 65, 175–194,
10.1016/S0375-6742(99)00028-X, 1999.
Cheng, Q.: Multifractal modelling and spectrum analysis: methods and
applications to gamma ray spectrometer data from southwestern Nova Scotia,
Canada, Sci. China Ser. D, 49, 283–294, 2006.Cheng, Q.: Mapping singularities with stream sediment geochemical data for
prediction of undiscovered mineral deposits in Gejiu, Yunnan Province,
China, Ore Geol. Rev., 32, 314–324,
10.1016/j.oregeorev.2006.10.002, 2007.Cheng, Q., Agterberg, F. P., and Ballantyne, S. B.: The separation of
geochemical anomalies from background by fractal methods, J. Geochem.
Explor., 51, 109–130, 10.1016/0375-6742(94)90013-2, 1994.
Chilès, J. P. and Delfiner, P.: Geostatistics: Modeling Spatial
Uncertainty, Wiley, New York, 695 pp., 1999.
Cox, D. and Singer, D.: Mineral deposits models, US Geological Survey
Bulletin, 1693 pp., 1986.
Craig, G. R. and Vaughan, D.: Ore Microscopy and Ore Petrography, John
Wiley and Sons, Inc., New York, 434 pp., 1994.
David, M.: Geostatistical Ore Reserve Estimation, Elsevier, Amsterdam, 283
pp., 1970.
Deng, J., Wang, C. M., and Li, G. J.: Style and process of the superimposed
mineralization in the Sanjiang Tethys, Acta Petrol. Sin., 28,
1349–1361, 2012 (in Chinese with English abstract).Deng, J., Wang, Q. F., Li, G. J., and Santosh, M.: Cenozoic tectono-magmatic
and metallogenic processes in the Sanjiang region, southwestern China, Earth
Sci. Rev., 138, 268–299, 10.1016/j.earscirev.2014.05.015,
2014a.Deng, J., Wang, Q. F., Li, G. J., Li, C. S., and Wang, C. M.: Tethys tectonic
evolution and its bearing on the distribution of important mineral deposits
in the Sanjiang region, SW China, Gondwana Res., 26, 419–437,
10.1016/j.gr.2013.08.002, 2014b.Deng, J., Wang, Q. F., Li, G. J., Hou, Z. Q., Jiang, C. Z., and Danyushevsky,
L.: Geology and genesis of the giant Beiya porphyry–skarn gold deposit,
northwestern Yangtze Block, China, Ore Geol. Rev., 70, 457–485,
10.1016/j.oregeorev.2015.02.015, 2015.Faure, K., Matsuhisa, Y., Metsugi, H., Mizota, C., and Hayashi, S.: The
Hishikari Au–Ag epithermal deposit, Japan: oxygen and hydrogen isotope
evidence in determining the source of paleo hydrothermal fluids, Econ.
Geol., 97, 481–498, 10.2113/gsecongeo.97.3.481, 2002.Goncalves, M. A., Mateus, A., and Oliveira, V.: Geochemical anomaly
separation by multifractal modeling, J. Geochem. Explor., 72, 91–114,
10.1016/S0375-6742(01)00156-X, 2001.
Goovaerts, P.: Geostatistics for Natural Resources Evaluation, Oxford
University Press, New York, 496 pp., 1997.
Leng, C. B., Zhang, X. C., Hu, R. Z., Wang, S. X., Zhong, H., Wang, W. Q., and
Bi, X. W.: Zircon U–Pb and molybdenite Re–Os geochronology and
Sr–Nd–Pb–Hf isotopic constraintson the genesis of the Xuejiping porphyry
copper deposit in Zhongdian, Northwest Yunnan, China, J. Asian Earth
Sci., 60, 31–48, 2012.
Li, C., Xu, Y., and Jiang, X.: The fractal model of mineral deposits, Geol.
Zhejiang, 10, 25–32, 1994 (in Chinese with English Abstract).Li, C., Ma, T., and Shi, J.: Application of a fractal method relating
concentrations and distances for separation of geochemical anomalies from
background, J. Geochem. Explor., 77, 167–175,
10.1016/S0375-6742(02)00276-5, 2003.Li, W. C., Zeng, P. S., Hou, Z. Q., and White, N. C.: The Pulang porphyry copper
deposit and associated felsic intrusions in Yunnan Province, Southwest
China, Econ. Geol., 106, 79–92,
10.2113/econgeo.106.1.79, 2011.
Li, W. C., Yu, H. J., and Yin, G. H.: Porphyry metallogenic system of Geza arc in the Sanjiang region, southwestern China, Acta Petrol. Sin., 29, 1129–1144, 2013 (in Chinese with English abstract).
Liu, X. L., Li, W. C., Yin, G. H., and Zhang, N.: The geochronology, mineralogy
and geochemistry study of the Pulang porphyry copper deposits in Geza arc of
Yunnan Province, Acta Petrol. Sin., 29, 3049–3064, 2013 (in Chinese with
English abstract).Lowell, J. D.: Geology of the Kalamazoo orebody, San Manuel district,
Arizona, Econ. Geol., 63, 645–654,
10.2113/gsecongeo.63.6.645, 1968.Lowell, J. D. and Guilbert, J. M.: Lateral and vertical
alteration-mineralization zoning in porphyry ore deposits, Econ. Geol.,
65, 373–408, 10.2113/gsecongeo.65.4.373, 1970.
Mandelbrot, B. B.: The Fractal Geometry of Nature, W. H. Freeman, San
Fransisco, 468 pp., 1983.
Mao, J. W., Zhou, Z. H., Feng, C. Y., Wang, Y. T., Zhang, C. Q., Peng, H. J., and
Yu, M.: A preliminary study of the Triassic large-scale mineralization in
China and its geodynamic setting, Geol. China, 39, 1437–1471, 2012 (in
Chinese with English abstract).Mao, J. W., Pirajno, F., Lehmann, B., Luo, M. C., and Berzina, A.:
Distribution of porphyry deposits in the Eurasian continent and their
corresponding tectonic settings, J. Asian Earth Sci., 79, 576–584, 10.1016/j.jseaes.2013.09.002, 2014.
Mao, Z., Peng, S., Lai, J., Shao, Y., and Yang, B.: Fractal study of geochemical
prospecting data in south area of Fenghuanshan copper deposit, Tongling
Anhui, J. Earth Sci. Environ., 26, 11–14, 2004.Melfos, V., Vavelidis, M., Christodes, G., and Seidel, E.: Origin and
evolution of the Tertiary Maronia porphyry copper–molybdenum deposit,
Thrace, Greece, Miner. Deposita, 37, 648–668,
10.1007/s00126-002-0277-4, 2002.
Pang, Z. S., Du, Y. S., Wang, G. W., Guo, X., Cao, Y., and Li, Q.: Single-grain
zircon U–Pb isotopic ages, geochemistry and its implication of Pulang
complex in Yunnan Province, China, Acta Petrol. Sin., 25, 159–165, 2009
(in Chinese with English abstract).Sadeghi, B., Moarefvand, P., Afzal, P., Yasrebi, A. B., and Saein, L. D.:
Application of fractal models to outline mineralized zones in the Zaghia
iron ore deposit, Central Iran, J. Geochem. Explor., 122, 9–19,
10.1016/j.gexplo.2012.04.011, 2012.
Sanderson, D. J., Roberts, S., and Gumiel, P.: A fractal relationship between
vein thickness and gold grade in drill core from La Codosera, Spain. Econ.
Geol., 89, 168–173, 1994.Schwartz, G. M.: Hydrothermal alteration in the “porphyry copper” deposits,
Econ. Geol., 42, 319–352, 10.2113/gsecongeo.42.4.319,
1947.
Shi, J. and Wang, C.: Fractal analysis of gold deposits in China: implication
for giant deposit exploration, Earth Sci. J. China Univ. Geosci., 23,
616–618, 1998 (in Chinese with English abstract).Sillitoe, R. H.: Characteristics and controls of the largest porphyry
copper–gold and epithermal gold deposits in the circum-pacific region,
Aust. J. Earth Sci., 44, 373–388,
10.1080/08120099708728318, 1997.
Sillitoe, R. H. and Gappe, I. M.: Philippine porphyry copper deposits:
geologic setting and characteristics, Common Coordination Joint Resource
(CCOP), 14, 1–89, 1984.
Sim, B. L., Agterberg, F. P., and Beaudry, C.: Determining the cutoff between
background and relative base metal contamination levels using multifractal
methods, Comput. Geosci., 25, 1023–1041, 1999.Soltani, F., Afzal, P., and Asghari, O.: Delineation of alteration zones
based on Sequential Gaussian Simulation and concentration–volume fractal
modeling in the hypogene zone of Sungun copper deposit, NW Iran, J. Geochem.
Explor., 140, 64–76, 10.1016/j.gexplo.2014.02.007, 2014.
Spalla, M. I., Morotta, A. M., and Gosso, G.: Advances in interpretation of
geological processes: refinement of multi-scale data and integration in
numerical modelling, Geolog. Soc., London, 240 pp., 2010.Sun, T. and Liu, L.: Delineating the complexity of Cu-Mo mineralization in a
porphyry intrusion by computational and fractal modeling: A case study of
the Chehugou deposit in the Chifeng district, Inner Mongolia, China, J.
Geochem. Explor., 144, 128–143,
10.1016/j.gexplo.2014.02.015, 2014.
Turcotte, D. L.: A fractal approach to the relationship between ore grade and
tonnage, Econ. Geol., 18, 1525–1532, 1986.
Turcotte, D. L.: Fractals in geology and geophysics, Pure Appl. Geophys.,
131, 171–196, 1989.Turcotte, D. L.: Fractals and Chaos in Geophysics, second edn., 81–99, Cambridge
University Press, Cambridge UK, 1996.
Wang, G. W., Carranza, E. J. M., Zuo, R., Hao, Y. L., Du, Y. S.,
Pang, Z. S., and Sun, Y.: Mapping of district-scale potential targets using
fractal models, J. Geochem. Explor., 122, 34–46,
10.1016/j.gexplo.2012.06.013, 2012.Wang, Q. F., Deng, J., Liu, H., Wang, Y., Sun, X., and Wan, L.: Fractal
models for estimating local reserves with different mineralization qualities
and spatial variations, J. Geochem. Explor., 108, 196–208,
10.1016/j.gexplo.2011.02.008, 2011.Wang, Q. F., Deng, J., Li, C. S., Li, G. J., Yu, L., and Qiao, L.: The boundary
between the Simao and Yangtze blocks and their locations in Gondwana and
Rodinia: constraints from detrital and inherited zircons, Gondwana Res.,
26, 438–448, 10.1016/j.gr.2013.10.002, 2014.
White, N. C. and Hedenquist, J. W.: Epithermal gold deposits: styles,
characteristics and exploration, SEG Newsletter, 23, 1–14, 1995.Wilson, A. J., Cooke, D. R., Harper, B. J., and Deyell, C. L.: Sulfur
isotopic zonation in the Cadia district, southeastern Australia: exploration
significance and implications for the genesis of alkalic porphyry
gold–copper deposits, Miner. Deposita, 42, 465–487,
10.1007/s00126-006-0071-9, 2007.
Yamamoto, J. K.: Comparing Ordinary Kriging Interpolation Variance and Indicator Kriging Conditional Variance for Assessing Uncertainties at Unsampled Locations, in: Application of Computers and Operations Research in the Mineral Industry, edited by: Dessureault, S., Ganguli, R., Kecojevic, V., and Girard-Dwyer, J., Balkema, 2005.
Yunnan Diqing Nonferrous Metal Co. Ltd.: Exploration Report of Pulang Copper
Deposit, Diqing, Yunnan, China, Yunnan Diqing Nonferrous Metal Co. Ltd.,
Diqing Tibetan Autonomous Prefecture, 2009 (in Chinese).
Zeng, P. S., Hou, Z. Q., Li, L. H., Qu, W. J., Wang, H. P., Li, W. C., Meng, Y. F.,
and Yang, Z. S.: Age of the Pulang porphyry copper deposit in NW Yunnan and
its geological significance, Geological Bulletin of China, 23,
1127–1131, 2004 (in Chinese with English abstract).Zuo, R. and Wang, J.: Fractal/multifractal modeling of geochemical data: A
review, J. Geochem. Explor., 164, 33–41,
10.1016/j.gexplo.2015.04.010, 2016.Zuo, R., Cheng, Q., and Xia, Q.: Application of fractal models to
characterization of vertical distribution of geochemical element
concentration, J. Geochem. Explor., 102, 37–43,
10.1016/j.gexplo.2008.11.020, 2009.