Carranza E. Geochemical anomaly and mineral prospectivity mapping in GIS

Подождите немного. Документ загружается.

110 Chapter 4

situated along the intrusive contact of the Aroroy Diorite with the Mandaon Formation

(see Fig. 3-9), suggesting that such anomalies are possibly associated with

hydrothermally altered rocks.

Synthesis of multi-element associations

It is appealing to integrate the PC3 and PC4 scores of the point stream sediment

geochemical data because there are some parts of the area where anomalies of PC3

scores and anomalies of PC4 scores are spatially coincident (Fig. 4-18 and 4-19). For

example, the southern parts of the area where two epithermal Au deposits occur and the

northern part of the area below one epithermal Au deposit occurrence. In addition, in the

northwestern parts of the area where many epithermal Au deposits occur, there is spatial

coincidence between high background PC3 scores and anomalous PC4 scores. A simple

multiplication can be applied to integrate the PC3 and PC4 scores, although this will

create false anomalies from PC3 and PC4 scores that are both negative. This problem

Fig. 4-18. Spatial distributions of background and anomalous populations of PC4 scores

representing an As-Ni association in stream sediments, Aroroy district (Philippines), based on

thresholds defined from the (A) continuous surface of PC4 scores (Fig. 4-17A) and (B) discrete

catchment basin surface of PC4 scores (Fig. 4-17C). L = low; H = high. Triangles represent

locations of epithermal Au deposit occurrences, whilst thin black lines represent lithologic

contacts (see Fig. 3-9).

Fractal Analysis of Geochemical Anomalies 111

can be overcome by first re-scaling the PC3 and PC4 scores linearly to the range [0,1]

and thereafter performing multiplication on the re-scaled variables. The product

‘integrated As-Ni-Cu’ scores can then be transformed into either a continuous or discrete

surface for the application of the concentration-area fractal method of modeling

anomalies.

The concentration-area models for the continuous and discrete surfaces of the

integrated As-Ni-Cu scores are very similar (Fig. 4-20). The three thresholds

recognisable from the concentration-area curves indicate that there are four populations

in the integrated As-Ni-Cu scores, which are interpreted, from lowest to highest, as (a)

low background, (b) high background, (c) low anomaly and (d) high anomaly.

The spatial distributions of low and high anomalies of the integrated As-Ni-Cu scores

show strong spatial associations with several of the epithermal Au deposit occurrences

(Fig. 4-21). Based on the discrete surface of the integrated As-Ni-Cu scores (Fig. 4-

21B), there seem to be two parallel north-northwest trending anomalies, one following

the trend of epithermal Au deposit occurrence and the other following the intrusive

Fig. 4-19. Spatial distributions of background and anomalous populations of PC3 scores

representing Cu-As association in stream sediments, Aroroy district (Philippines), based on

thresholds defined from the (A) continuous surface of PC3 scores (Fig. 4-17B) and (B) discrete

catchment basin surface of PC3 scores (Fig. 4-17D). L = low; H = high. Triangles represent

locations of epithermal Au deposit occurrences, whilst thin black lines represent lithologic

contacts (see Fig. 3-9).

112 Chapter 4

contact of the Aroroy Diorite with the Mandaon Formation (see Fig. 3-9). The latter

could be related to feeble hydrothermal alteration in the Mandaon Formation due to the

intrusion of the Aroroy Diorite. The continuous surface of the integrated As-Ni-Cu

scores suggests that the anomalies related to the epithermal Au deposit occurrences and

the anomalies associated to possible hydrothermally altered rocks along the contact

between Mandaon Formation and the Aroroy Diorite seem to overlap rather than run

parallel. This could be a result, however, of the smoothing effect during interpolation of

the point data of integrated As-Ni-Cu scores.

Combining the PC3 (Cu-As) and PC4 (As-Ni) scores as integrated As-Ni-Cu scores

results in downgrading of importance of anomalies (e.g., from anomalous PC3 or PC4

scores to high background integrated scores) in four localities indicated by Roman

numerals in Fig. 4-21. In localities I, II and III, which are underlain by the Aroroy

Diorite, anomalies of PC3 scores (Fig. 4-18), which are mostly due to Cu rather than As

(see Figs. 4-14 and 4-15), and anomalies of PC4 scores (Fig. 4-19), which are mostly

due to Ni rather than As (see Fig. 4-15) are downgraded in importance (i.e., they now

map as high background) after deriving and analysing the integrated As-Ni-Cu scores

(Fig. 4-19). These observations imply that the anomalies of PC3 and PC4 scores in

localities I, II and III are probably non-significant but due to variations in mineralogical

composition of the Aroroy Diorite (see Fig. 3-9). Thus, combining the PC3 (Cu-As) and

PC4 (As-Ni) scores into the integrated As-Ni-Cu scores has positive effects in these

cases. In locality I, which is underlain by the Sambulawan Formation and some alluvial

deposits (see Fig. 3-9), anomalies of PC4 scores (mainly due to As rather than Ni; see

Fig. 4-15) are downgraded in importance (i.e., they now map as high background) after

Fig. 4-20. Concentration-area models for the integrated As-Ni-Cu scores the stream sediment

geochemical data in the Aroroy district (Philippines), based on (A) transformation of the

integrated As-Ni-Cu scores of the point data as a continuous surface and (B) representation of the

integrated As-Ni-Cu scores of the point data as discrete geochemical surfaces. Solid lines are

obtained by least squares fitting through linear parts of the plots. Dots at breaks in slopes of the

lines represent threshold integrated scores (v

). Lines to the left of any threshold follow a power-

law relation represented by equation (4.6), whereas lines to the right of rightmost thresholds

follow a power-law relation represented by equation (4.7).

Fractal Analysis of Geochemical Anomalies 113

deriving and analysing the integrated As-Ni-Cu scores (Fig. 4-19). The anomalies of

PC4 scores in locality IV are probably significant as they occur downstream of

epithermal Au deposit occurrences, so combining the PC3 (Cu-As) and PC4 (As-Ni)

scores has a negative effect in this case. Combining the PC3 (Cu-As) and PC4 (As-Ni)

scores into integrated As-Ni-Cu scores has, nevertheless, an overall positive effect in this

case study and is therefore defensible.

CONCLUSIONS

In the analysis of exploration geochemical data to recognise significant anomalies, it

can be useful to consider that geochemical landscapes have spatial variability,

geometrical properties and scale-invariant characteristics. The concentration-area fractal

method, developed originally by Cheng et al. (1994), takes into account such attributes

of geochemical landscapes. The concentration-area method is not, however, the only

method for fractal analysis of geochemical anomalies. There are variants of the

Fig. 4-21. Spatial distributions of background and anomalous populations of integrated As-Ni-Cu

scores derived from the stream sediment geochemical data, Aroroy district (Philippines) based on

thresholds defined from the (A) continuous surface of integrated As-Ni-Cu scores (Fig. 4-20A)

and (B) discrete catchment basin surface of integrated As-Ni-Cu scores (Fig. 4-20B). L = low; H =

high. Triangles represent locations of epithermal Au deposit occurrences, whilst thin black lines

represent lithologic contacts (see Fig. 3-9). Roman numbers are locations referred to in the text

discussing the effect of combining the PC3 and PC4 scores into the integrated As-Ni-Cu scores.

114 Chapter 4

concentration-area method, e.g., a concentration-distance method (Li et al., 2003) and a

summation method (Shen and Cohen, 2005). The concentration-area method and its

variants are appropriate for geochemical data analysis in the spatial domain, in which the

scale-invariant characteristics of geochemical landscapes are related to the empirical

density distributions, spatial variability and geometrical patterns of geochemical data

sets.

Other methods for fractal analysis of geochemical anomalies involve converting

geochemical data into a function of ‘wave numbers’ in the frequency domain, in which

the scale-invariant characteristics of geochemical landscapes are represented by means

of a power spectrum. For details of fractal analysis of geochemical anomalies in the

frequency domain, readers are referred to authoritative explanations by Cheng et al.

(2000). Nevertheless, Cheng et al. (2000) aver that “because the spatial distribution of

power spectrum is determined not only by the wave numbers but also by the power-

spectrum function, it should be characterised by the concentration-area fractal method”.

This means that the concentration-area fractal method is a fundamental technique for

modeling of geochemical anomalies.

The case study on GIS-based application of the concentration-area fractal method

shows the multifractal nature of the geochemical landscape in the Aroroy district

(Philippines) based on stream sediment uni-element data. The results of the case study

illustrate that significant anomalies related to the epithermal Au deposit occurrences are

modeled better when the geochemical landscape is represented as discrete surfaces rather

than as continuous surfaces. Perhaps the application of inverse distance moving average

to derive the continuous geochemical surfaces from the point stream sediment uni-

element data is not optimal in this case, particularly because stream sediments do not

represent continuous geo-objects. The case study demonstrates, nonetheless, that either

continuous or discrete geochemical surfaces can be used in GIS-based concentration-

area multifractal modeling of significant anomalies in stream sediment uni-element data.

As shown in the case study, application of traditional methods of spatial interpolation

to derive continuous geochemical surfaces can undermine multifractal analysis of

geochemical anomalies. However, methods for multifractal interpolation (Cheng, 1999a)

and fractal filtering (Xu and Cheng, 2001) have been developed to take into account the

concentration-area relationship in deriving, from point geochemical data, ‘ready-to-use’

interpolated maps in which background and anomalies are already separated. These

methods have not been demonstrated here, not only because extensive discussion spatial

interpolation and filtering is beyond the scope of this volume but also because they

require specialised software, which is dedicated to such purposes and which is not

available in most commercial or shareware GIS software packages.

115

Chapter 5

CATCHMENT BASIN ANALYSIS OF STREAM SEDIMENT ANOMALIES

INTRODUCTION

Stream sediments are commonly used as the chief sampling medium in exploration

geochemical surveys. They represent, at any point along drainage systems, composite

materials derived from the weathering and erosion of one or more sources upstream. It

follows that uni-element concentrations in stream sediments are derived from multiple

(mostly background and rarely anomalous) sources. In most cases, a major proportion of

variation in stream sediment uni-element concentrations is due to lithologic units

underlying the areas upstream of sample points. Rose et al. (1970) have demonstrated

that certain chemical contents of stream sediments have (a) positive relationships with

areas of the lithologic units in a catchment basin and (b) negative relationships with the

total area of a catchment basin. Hawkes (1976) considered such relationships as due to

downstream of dilution of chemical contents of stream sediments and suggested an

idealised formula that relates the measured uni-element concentrations (Y

) in stream

sediment sample i and the area of its sample catchment basin (A

) to the uni-element

concentrations in and surface areas of source materials in the sample catchment basin:

)(

aiiaaii

AAYAYAY −

′

+= (5.1)

where Y

represents the uni-element concentrations due to anomalous sources occupying

a cumulative area A

′

represents the uni-element concentrations due to background

sources occupying a cumulative area equal to A

–A

. Hence, if a catchment basin

contains only background sources, then Y

is equal to

′

; whereas if a catchment basin

contains anomalous sources (e.g., mineral deposits), then Y

is greater than

′

. As stream

sediment geochemical exploration aims to identify catchment basins containing

anomalous sources, equation (5.1) can be re-arranged as:

aiiiiaa

AYYYAAY

′

−= )( (5.2)

and the term Y

can be considered an ‘anomaly rating’. The term )(

iii

YYA

′

− in

equation (5.2) is equivalent to the ‘productivity’ of a catchment basin (Polikarpochkin,

1971), which was demonstrated by Moon (1999) to be useful in identifying anomalous

catchment basins.

Geochemical Anomaly and Mineral Prospectivity Mapping in GIS

by E.J.M. Carranza

Handbook of Exploration and Environmental Geochemistry, Vol. 11 (M. Hale, Editor)

116 Chapter 5

In another study, Pan and Harris (1990) proposed a generalised equation to predict

uni-element concentration (Y

) at a source as a function of uni-element concentration (Y

)

in a stream sediment sample i and the distance (D

) of that sample from the source:

αθ

sin

DYY

(5.3)

where θ is a uni-element coefficient and α is the angle of topographic slope. The

generalised equation proposed by Pan and Harris (1990) worked well in their case study

with discrete anomalous sources of Au, Ag and Cu in soil. It can be noted, however, that

equation (5.3) does not take into account the area and uni-element background in a

sample catchment basin. Although background concentrations of Au can be relatively

insignificant compared to anomalous concentrations of Au, it is important to consider

background of other elements in order to recognise anomalies.

Analysis of stream sediment geochemical data alone can therefore be insufficient for

recognition of significant anomalies. Effective interpretation of stream sediment

geochemical data requires integration of every available piece of spatial information

pertinent to the zone of influence of every stream sediment sample location – its

catchment basin. The relation in equation (5.2) indicates that, in order to recognise

stream sediment anomalies, (a) background uni-element concentrations

′

must first be

estimated for each sample catchment basin, (b) background uni-element concentrations

′

must then be removed from measured uni-element concentrations Y

(i.e., Y

–

′

)

leaving geochemical residuals, which may include significant anomalies (i.e., derived

from mineral deposits) and (c) geochemical residuals must be corrected for downstream

dilution by taking into account area of sample catchment basin (i.e.,

)(

iii

YYA

′

−

) to

enhance anomalies. By considering areal proportions of lithologic units in every sample

catchment basin, it is possible to estimate local background uni-element concentrations

due to lithology in every sample catchment basin (Bonham-Carter and Goodfellow,

1984, 1986; Bonham-Carter et al., 1987; Carranza and Hale, 1997). Instead of areal

proportions of lithologic units in every sample catchment basin, Peh et al. (2006)

demonstrated that linear proportions of lithologic units along perennial streams in every

sample catchment are also useful in estimating local background uni-element

concentrations.

The objective of this chapter is to explain techniques, which can be implemented in a

GIS, for catchment basin analysis of uni-element anomalies in stream sediments in order

to (a) estimate local uni-element background concentrations due to lithology and (b)

derive and correct uni-element residuals for downstream dilution. Dilution-corrected uni-

element residuals are then used in the analysis of uni-element and multi-element

anomalies. These techniques are then demonstrated in a case study of the same stream

sediment geochemical data used to demonstrate the EDA and fractal analysis explained,

respectively, in Chapters 3 and 4.

Catchment Basin Analysis of Stream Sediment Anomalies 117

ESTIMATION OF LOCAL UNI-ELEMENT BACKGROUND DUE TO LITHOLOGY

Two techniques are explained here: (1) multiple regression analysis; and (2) analysis

of weighted mean uni-element concentrations. The former is demonstrated by Bonham-

Carter and Goodfellow (1984, 1986), Bonham-Carter et al. (1987) and Carranza and

Hale (1997), whilst the latter is demonstrated by Bonham-Carter et al. (1987).

Multiple regression analysis

In multiple regression analysis, measured stream sediment uni-element

concentrations (Y

) and areal proportions (X

) of j (=1,2,…,m) lithologic units in sample

catchment basin i (=1,2,…,n) are used, respectively, as dependent and independent

variables in order to estimate for every sample catchment basin local background uni-

element concentrations (

′

) due to lithology in sample catchment basin i, thus:

joi

XbbY

′

, (5.4)

where

X , b

and b

are the regression coefficients determined by the least-

squares method to minimise the quantity

′

−

)( . The multiple regression equation

implies that estimates of background uni-element concentrations are a result of additive

mixing of weathering products of lithologic units in sample catchment basins.

The coefficient b

can be interpreted as regional average uni-element content,

whereas the coefficient b

can be interpreted as average uni-element content of lithologic

unit j (=1,2,…,m) in any sample catchment basin i (=1,2,…,n). However, by inclusion of

, equation (5.4) is indeterminate because the regression matrix is singular, unless one

independent variable is discarded (Bonham-Carter et al., 1987). This problem can be

overcome by allowing round-off errors (e.g., using two decimals) in calculating areal

proportions of lithologic units so that

00.1

≅

. The multiple regression modeling

can also be forced through origin (i.e., setting b

=0) so that the singularity problem is

avoided and equation (5.4) is determinate (Bonham-Carter and Goodfellow, 1984, 1986).

In order to determine relative contributions of the independent variables and their

ability to account for total variation in Y

, the multiple regression analysis is performed

via forward and forced simultaneous inclusion of independent variables. That is to say,

the most significant independent variables are not searched and included in the final

regression equation according to a statistical criterion; rather, all independent variables

are included in the final regression model.

The ability of the independent variables to account for the variation of the dependent

variables can be characterised using R

(usually expressed as percentage), the ratio of

sum of squares explained by regression to the total sum of squares, which indicates

goodness-of-fit of the multiple regression model. Invariably, regression models have

poor fit to uni-element concentration data that are significantly positively skewed.

Logarithmic transformation of uni-element concentration data invariably results in

118 Chapter 5

multiple regression models with high R

, although the models become multiplicative

rather than additive. Logarithmic transformation of uni-element concentration data

results, however, in regression coefficients that are usually positive and easy to interpret.

Whether raw or log-transformed uni-element concentration data are used, statistical tests

of significance of the regression are inappropriate if the stream sediment sampling

density is high and/or if the stream sediment uni-element concentration data exhibit

some degree of spatial autocorrelation and thus are not independent (Bonham-Carter et

al., 1987).

For the stream sediment Cu and Zn data shown in Figs. 2-7A and 2-9A, respectively,

Table 5-I shows the regression coefficients for the lithologic units (see Fig. 1-1)

occurring in the sample catchment basins. The regression analysis was performed after

log

-transformation of the data to reduce asymmetry in their empirical density

distributions. The regression coefficients of the independent variables given in Table 5-I

are transformed back to normal values to illustrate that they represent average uni-

element concentrations in individual lithologic units. The average Cu concentrations (in

ppm) in each lithologic unit, except quartzite, are more or less uniform at about 50 ppm,

while the average Zn concentrations (in ppm) in each lithologic unit are different. The

values of R

indicate that the Cu and Zn concentrations in stream sediments in the area

are mostly entirely due to lithology, although about 4% of variability in Zn is not

accounted for by lithology. Consequently, the spatial distributions of local background

Cu and Zn concentrations in stream sediments per sample catchment basin, as estimated

according to equation (5.4), reflect mostly the patterns of the lithologic units (Fig. 5-1).

Analysis of weighted mean uni-element concentrations due to lithology

Local background uni-element concentrations due to lithology in every sample

catchment basin can also be estimated by first calculating a weighted mean uni-element

concentration M

in each of the j (=1,2,…,m) lithologic units in i (=1,2,…,n) sample

catchment basins, thus:

¦¦

ijij

XXYM

ˆˆ

, (5.5)

TABLE 5-I

Results of multiple regression analysis (forced simultaneous inclusion of independent variables

and forced through the origin) using log

-transformed stream sediment Cu and Zn data (n=102; see

Figs. 2-7A and 2-9A, respectively) as dependent variables and areal proportions of lithologic units

(see Fig. 1-1) in sample catchment basins as independent variables.

Anti-log

of regression coefficients of independent variables Dependent

variable

Basalt Limestone Phyllite Quartzite

Cu 49.2 50.6 48.7 29.8 99.58

Zn 25.2 84.9 41.9 11.1 96.21

Catchment Basin Analysis of Stream Sediment Anomalies 119

where Yi represents uni-element concentrations in stream sediment sample i (1,2,…,n)

and

is the area of each of the j (=1,2,…,m) lithologic units, but not their areal

proportions, in sample catchment basin i (=1,2,…,n) as in equation (5.4). Prior to

application of equation (5.5), raw uni-element concentration data showing asymmetric

empirical density distributions must be appropriately transformed to values whose

empirical density distributions are approximately symmetrical. The statistical

significance of the value of M

for each of the j (=1,2,…,m) lithologic units can be

inferred from its weighted standard deviation (SD

), which is estimated as:

()

¦¦

−=

ijjij

XXMYSD

ˆˆ

)(

. (5.6)

Then, the local background uni-element concentrations (

′

) due to j (=1,2,…,m)

lithologic units in each sample catchment basin i (=1,2,…,n) can be estimated as:

¦¦

′

ijji

XXMY

ˆˆ

. (5.7)

Bonham-Carter et al. (1987) have shown that M

in equation (5.5) and b

+¦b

equation (5.4) usually have good agreement; that means, there are usually small

differences between estimates of

′

by using either equation (5.4) or equation (5.7).

Only with lithologic units having small areas (about 1% of total area covered by sample

catchment basins) do large differences between the two methods of estimation occur.

Nevertheless, the method of estimating weighted uni-element concentrations in

lithologic units has an advantage over the multiple regression method because the former

can be implemented readily in a GIS whilst the latter is usually handled outside a GIS.

Fig. 5-1. Spatial distributions of local background element concentrations [(A) Cu, (B) Zn] in

stream sediments per sample catchment basin estimated via multiple regression analysis (see text;

Table 5-I). Polygons in thick grey or black outlines in the maps are lithologic units (see Fig. 1-1).