## Abstract

**ABSTRACT** This paper revisits catchment basin modelling of stream sediment geochemical anomalies with regard to two aspects: (1) standardization of uni-element residuals derived from analysis of a number of subsets of stream sediment geochemical data in order to obtain a single set of uni-element residuals for classification of anomalies; and (2) objective classification of anomalies in dilution-corrected uni-element residuals and in derivative scores representing multi-element associations. These two aspects of catchment basin modelling of stream sediment geochemical anomalies were examined in the Aroroy epithermal-Au district (Philippines). For the first aspect, the results of the case study show that, for the standardization of dilution-corrected uni-element residuals per data subset in order to derive a single set of dilution-corrected uni-element residuals for classification of anomalies, the application of robust statistics in exploratory data analysis is preferable to the application of classical statistics in confirmatory data analysis. For the second aspect, the results of the case study show that anomalies in standardized dilution-corrected uni-element residuals and in derivative scores representing multi-element associations can be identified objectively by application of the concentration-area fractal analysis. The results of the case study further show that the area of individual sample catchment basins is useful in GIS-based screening of significant anomalies by integrating derivative geochemical variables with fault/fracture density, which was estimated as the ratio of number of pixels representing faults/fractures in a sample catchment basin to number of pixels in the same sample catchment basin.

- local background
- geochemical residuals
- downstream dilution
- exploratory data analysis
- concentration-area fractal analysis
- spatial data integration
- GIS
- Aroroy (Philippines)

## INTRODUCTION

Stream sediments are composite materials derived from the weathering and erosion of one or more sources upstream. It follows that uni-element contents of stream sediments are derived from multiple (usually background and rarely anomalous) sources. In most cases, a major proportion of variation in stream sediment uni-element contents is due to lithological units underlying the areas upstream of stream sediment sample sites. Rose *et al*. (1970) have demonstrated that concentrations of certain elements in stream sediments are (a) positively correlated with areas of lithological units in catchment basins and (b) negatively correlated with areas of catchment basins. Hawkes (1976) considered such relationships as due to downstream dilution of chemical contents of stream sediments and proposed an idealized formula relating measured uni-element contents (*Y _{i}*) of stream sediment sample

*i*and the area of its catchment basin (

*A*) to uni-element contents and areas of source materials in the catchment basin of stream sediment sample

_{i}*i*, thus:

*Y*represents uni-element contents of anomalous sources occupying a cumulative area

_{a}*A*in the catchment basin of stream sediment sample

_{a}*i*,

*Y*

_{i}

^{′}represents uni-element contents of background sources occupying a cumulative area equal to

*A*in the catchment basin of stream sediment sample

_{i}– A_{a}*i*. Hence, if a sample catchment basin contains only background sources, then

*Y*=

_{i}*Y*

_{i}^{′}; whereas, if it contains anomalous sources (e.g. mineral deposits), then

*Y*>

_{i}*Y*

_{i}^{′}. Because stream sediment geochemical exploration aims to identify sample catchment basins containing anomalous sources, Equation (1) can be re-arranged as

*Y*can be considered an ‘anomaly’ rating for every sample catchment basin.

_{a}A_{a}*A*(

_{i}*Y*)in Equation (2) is equivalent to the ‘productivity’ of a catchment basin (Polikarpochkin 1971; Moon 1999). Supposing that mineral deposits of a unit area of 1 km

_{i}– Y_{i}^{′}^{2}(i.e.

*A*= 1 km

_{a}^{2}) contribute to stream sediments in sample catchment basin

*i*, then Equation (2) can be modified as

*Y*can be considered a ‘mineralization’ rating for every sample catchment basin (Bonham-Carter & Goodfellow 1984, 1986).

_{a}Equation (2) or (3) tells us that analysis of stream sediment geochemical data alone can therefore be insufficient for recognition of significant anomalies. On the one hand, Equations (2) tells us that, in order to recognize anomalous sample catchment basins, local background uni-element contents *Y*_{i}^{′} per sample catchment basin *i* must be estimated first and then removed from the corresponding measured uni-element contents *Y _{i}* (i.e.

*Y*

_{i}–

*Y*

_{i}

^{′}) in order to leave uni-element residuals, which may include significant anomalies (i.e. due to mineral deposits). On the other hand, Equation (3) tells us that, in order to enhance anomalies, uni-element residuals must be corrected for downstream dilution by taking into account the area of each sample catchment basin (i.e.

*A*

_{i}(

*Y*

_{i}–

*Y*

_{i}

^{′})).

In order to estimate local background uni-element contents (*Y*_{i}^{′}) due to lithology in each sample catchment basin *i*, multiple regression analysis can be performed by using measured stream sediment uni-element contents (*Y _{i}*) as dependent variables and areal proportions (

*X*) of

_{ij}*j*(=1,2,…,

*m*) lithological units in

*i*(=1,2,…,

*n*) sample catchment basins (Bonham-Carter & Goodfellow 1984, 1986; Bonham-Carter

*et al*. 1987), thus:

*b*and

_{o}*b*are the regression coefficients determined by the least-squares method to minimize the quantity

_{j}*b*can be regarded as average uni-element content of stream sediments in the region/district under examination, whereas the coefficient

_{o}*b*can be regarded as average uni-element content of each of the

_{j}*j*(=1,2,…,

*m*) lithological units in each sample catchment basin. However, Equation (4) is indeterminate because the regression matrix is singular, unless one independent variable is discarded (Bonham-Carter

*et al*. 1987). According to Bonham-Carter & Goodfellow (1984, 1986), the matrix singularity problem can be avoided, so that Equation (4) is determinate, by either (a) allowing round-off errors (e.g. using two decimals) in estimates of areal proportions of lithological units so that

*b*=0).

_{o}As alternative to the multiple regression technique, a weighted mean uni-element content *M _{j}* of each of the

*j*(=1,2,…,

*m*) lithological units in each of the

*i*(=1,2,…,

*n*) sample catchment basins can be calculated first (Bonham-Carter

*et al*. 1987), thus:

*Y*represents uni-element contents of stream sediment sample

_{i}*i*(1,2,…,

*n*) and

*j*(=1,2,…,

*m*) lithological units, but not their areal proportions, in each of the

*i*(=1,2,…,

*n*) sample catchment basins. Then, local background uni-element contents (

*Y*

_{i}

^{′}) associated with each of the

*j*(=1,2,…,

*m*) lithological units in each of the

*i*(=1,2,…,

*n*) sample catchment basins are estimated as

It has been shown that *M _{j}* in Equation (5) and

*b*+Σ

_{o}*b*in Equation (4) usually have good agreement (Bonham-Carter

_{j}*et al*. 1987), meaning that there are usually small differences between estimates of

*Y*

_{i}

^{′}by using either Equation (4) or (6). However, the multiple regression technique is less robust than the technique based on weighted mean uni-element content in lithological units particularly if some lithological units occupy less than 10% of the total area covered by the sample catchment basins (Bonham-Carter

*et al*. 1987).

In this paper, it is further demonstrated that the technique based on weighted mean uni-element content in lithological units is more satisfactory than the multiple regression technique for estimation of local background uni-element contents (*Y*_{i}^{′}) due to lithological units in each sample catchment basin. Nevertheless, the main objective of this paper is to address two other aspects of catchment basin modelling of stream sediment geochemical anomalies. Firstly, estimation of local background uni-element contents per stream sediment sample catchment basin via either the multiple regression technique or the analysis of weighted mean uni-element contents of lithological units can be undermined by the presence of multiple populations in the geochemical data. If a geochemical data set is subdivided, however, into a number of data subsets according to a certain criterion (e.g. rock type at/near each sample site) and if local background uni-element contents due to lithology are estimated for every sample in each data subset, then there is a corresponding number of subsets of uni-element residuals. It is important that uni-element residuals per data subset are standardized prior to the application of downstream dilution correction (i.e. Equation (3)), so that dilution-corrected uni-element residuals in individual data subsets are comparable and, thus, uni-element anomalies can be analysed in a single data set of standardized dilution-corrected uni-element residuals. For this purpose, Carranza & Hale (1997) standardized dilution-corrected uni-element residuals in individual data subsets into *Z*-scores based on classical statistics in confirmatory data analysis (CDA). However, it is demonstrated in this paper that data standardization based on robust statistics in exploratory data analysis (EDA) is more satisfactory than data standardization based on classical statistics in CDA. Secondly, in previous works of catchment basin modelling of stream sediment anomalies (Bonham-Carter & Goodfellow 1984; 1986; Bonham-Carter *et al*. 1987; Carranza & Hale 1997; Moon 1999; Carranza 2004), anomalous sample catchment basins were identified based on arbitrary threshold percentiles of dilution-corrected uni-element residuals. In contrast, it is demonstrated in this paper that anomalous sample catchment can be identified objectively from standardized dilution-corrected uni-element residuals and from derivative scores representing multi-element associations by application of concentration-area (C-A) fractal analysis (Cheng *et al*. 1994). The applications of EDA-based statistics and the C-A fractal analysis in GIS-based catchment basin modelling of stream sediment geochemical anomalies are demonstrated in the Aroroy district (Philippines).

## THE CASE STUDY AREA

### Lithology and mineralization

The Aroroy district, which is located in the northwestern portion of Masbate Island in the Philippine archipelago (Fig. 1), is one of the epithermal-Au districts in the archipelago (Mitchell & Balce 1990; Mitchell & Leach 1991). The oldest exposed rocks in the district (Fig. 1a) are mainly andesitic-dacitic agglomerates belonging to the Eocene–Oligocene Mandaon Formation, which lies unconformably on unexposed basement of schists and metabasic rocks of pre-Cenozoic age (Baybayan & Matos 1986; JICA-MMAJ 1986). The Miocene Aroroy Diorite, which varies in composition from quartz diorite to hornblende diorite, intrudes into the basement rocks and the Mandaon Formation. Feldspathic wackes belonging to the Early Miocene Sambulawan Formation unconformably overlie the Mandaon Formation and the Aroroy Diorite. Andesitic lithic tuffs belonging to the Late Miocene to Early Pliocene Lanang Formation lie disconformably on the Mandaon and Sambulawan Formations. The Pliocene Nabongsoran Andesite Porphyry, which consists of porphyritic stocks, plugs and dikes, intrude into the series of dacitic-andesitic volcanic-sedimentary rocks (i.e. the Mandaon, Sambulawan and Lanang Formations) and the Aroroy Diorite.

Gold, in at least 13 mineral deposits in the district (Fig. 1), is associated with sulphide (pyrite, chalcopyrite and arsenopyritic) minerals in wide-sheeted and manganese-bearing quartz/silicified veins in mostly NW-trending faults/fractures that cut the volcanic-sedimentary rocks. The 10 gold deposits in the central parts of the district are known as the ‘Atlas’ deposits because the open pit operations of Atlas Consolidated Mining and Development Corporation in the early 1980s then comprised the Philippines' largest gold mine. The two gold deposits in the southern part of the district were mined prior to World War II and are now defunct. The gold deposit in the northern part of the district was investigated in some detail by the Indo-Pacific exploration company in the late 1980s. The characteristics of the gold deposits and associated hydrothermal alterations in the district are typical of low-sulphidation epithermal systems (Mitchell & Leach 1991).

### Geochemical data

In the study area, there are stream sediment geochemical data for 135 samples representing a total catchment area of *c*. 101 km^{2} (i.e. an average sampling density of one sample per 1.3 km^{2}) (Fig. 1b). These data are a subset of multi-element geochemical data for more than 2 200 stream sediment samples representing catchment basins measuring a total of *c*. 3 000 km^{2} in Masbate Island (JICA-MMAJ 1986). The quality of the individual uni-element geochemical data sets (based on results of replicate analyses; JICA-MMAJ 1986) has been re-examined by Carranza (2004) using robust analysis of variance (Ramsey *et al*. 1992) and those uni-element data sets with procedural variances exceeding or approaching 20% of the total (i.e. geochemical + procedural) variance were not used in this case study. Thus, out of 10 elements determined in the stream sediment samples (JICA-MMAJ 1986), only six elements (Cu, Zn, Ni, Co, Mn, As) are studied here. The raw uni-element data sets have positively skewed empirical frequency distributions ( Table 1), which are reduced effectively by converting the data into natural logarithms. The log_{e}-transforms of the individual uni-element data were therefore used in the succeeding analyses in order to alleviate effects of asymmetry of data distributions on statistical analysis, but not because of judgment of a possible log-normal data distribution (Miesch 1977; Joseph & Bhaumik 1997).

## ESTIMATION OF LOCAL BACKGROUND UNI-ELEMENT CONTENTS

The multiple regression analysis and the analysis of weighted mean uni-element contents of lithological units were performed on two subsets (A and B) of log_{e}-transformed uni-element contents based on rock type at/near each sample site. Data subset A pertains to sample sites (*n*=38) underlain by the Aroroy Diorite, while data subset B pertains to sample sites (*n*=97) underlain by dacitic/andesitic rocks (Fig. 2). Data subset A also pertains to sample catchment basins underlain mostly by the Aroroy Diorite, while data subset B also pertains to sample catchment basin underlain mostly by dacitic/andesitic rocks (i.e. the Mandaon, Sambulawan and Lanang Formations). As illustrated in Figure 2, subdividing a stream sediment geochemical data set according to rock type at/near each sample site is intuitive and, therefore, preferable to the applications of certain analytical techniques requiring that data under examination follow a normal or lognormal distribution (e.g. analysis of probability plots; Sinclair 1983). That is because (a) data on rock type at/near each sample site are collected routinely during geochemical surveys and (b) many workers have demonstrated that geochemical data invariably show neither normal nor lognormal distributions (e.g. Vistelius 1960; McGrath & Loveland 1992; Reimann & Filzmoser 2000).

The boxplots of log_{e}-transformed uni-element contents in data subsets A and B (Fig. 3) show that stream sediments in sample catchment basins underlain mostly by the Aroroy Diorite have rather lower concentrations of each of the elements under study than stream sediments in sample catchment basins underlain mostly by dacitic/andesitic rocks. The boxplots (Fig. 3) illustrate also that, if the individual uni-element data are not subdivided as shown in Figure 2, differences in empirical frequency distributions of data in subsets A and B are likely to undermine estimation of local background uni-element contents per stream sediment sample catchment basin via either the multiple regression technique or the analysis of weighted mean uni-element contents of lithological units.

The multiple regression analysis performed on each of the two subsets of the data is forced through the origin (i.e. setting *b _{o}*=0) so that the problem of matrix singularity is avoided and Equation (4) is determinate. In addition, because the uni-element data are log

_{e}-transformed, the regression coefficients (

*b*) of each of the

_{j}*j*(=1,2,…,

*m*) independent variables (i.e. lithological units represented as areal proportions in individual sample catchment basins) are usually positive and readily interpretable as the geometric mean of uni-element contents of individual lithological units. Likewise, because the uni-element data are log

_{e}-transformed, the value of

*M*for each of the

_{j}*j*(=1,2,…,

*m*) lithological units (represented by their areas in individual sample catchment basins) can be interpreted as the weighted geometric mean of uni-element contents of individual lithological units.

The estimates of *b _{j}* and

*M*for each of the lithological units represented by data subset A are given in Table 2. Note that the sample catchment basins for stream sediment data subset A are underlain by at least one of the three lithological units listed in Table 2. The values of either

_{j}*b*or

_{j}*M*in data subset A show that the Aroroy Diorite, compared to the Mandaon and Sambulawan Formations, has the lowest geometric means of concentrations of most elements; whereas, the Mandaon Formation, compared to the Aroroy Diorite and Sambulawan Formation, has the highest geometric means of concentrations of most elements, particularly As. However, Table 2 shows that, for the Mandaon and Sambulawan Formations the values of

_{j}*b*are mostly higher than the corresponding values of

_{j}*M*; whereas, for the Aroroy Diorite the values of

_{j}*b*and

_{j}*M*are more-or-less similar.

_{j}The estimates of *b _{j}* and

*M*for each of the lithological units represented by data subset B are given in Table 3. Note that the sample catchment basins for stream sediment data subset B are underlain by at least one of the six lithological units listed in Table 3. The values of

_{j}*b*in data subset B show that, among the lithological units, the alluvial deposits have the lowest geometric means of concentrations of most elements, followed by the Nabongsoran Andesite. In contrast, the values of

_{j}*M*in data subset B show that the Nabongsoran Andesite and the alluvial deposits have more-or-less similar geometric means of uni-element contents as those of the other lithological units. Table 3 furthermore shows that (a) for each of the lithological units, except the Nabongsoran Andesite and alluvial deposits, the values of

_{j}*b*and

_{j}*M*are more-or-less similar and (b) among the lithological units, excluding the alluvial deposits, the Mandaon Formation seems to be the most enriched in As.

_{j}Depending on the element and lithological unit examined, there are either weak or strong discrepancies between *b _{j}* and

*M*(Tables 2 and 3). A plausible explanation for the discrepancies between

_{j}*b*and

_{j}*M*can be deduced by plotting the values of

_{j}*b*–

_{j}*M*versus the percentages of individual lithological units in the total area covered by the sample catchment basins (Bonham-Carter

_{j}*et al*. 1987). For data subset A (Fig. 4a), the values of

*b*–

_{j}*M*are positive and the absolute differences between

_{j}*b*and

_{j}*M*are large (i.e.|

_{j}*b*–

_{j}*M*| >0.5) if lithological units occupy less than 7% of the total area covered by the sample catchment basins. For data subset B (Fig. 4b), the values of

_{j}*b*–

_{j}*M*are mostly negative and the absolute differences between

_{j}*b*and

_{j}*M*are large (i.e.|

_{j}*b*–

_{j}*M*| >0.5) if lithological units occupy less than 5% of the total area occupied by the sample catchment basins.

_{j}A *t*-test on the differences between *b _{j}* and

*M*was further performed by using the number of subset samples used to derive them and the estimates of their dispersions (see Bonham-Carter

_{j}*et al*. (1987) for estimation of dispersion of

*M*). For data subset A (Fig. 5a), most of the

_{j}*t*-values for the differences between

*b*and

_{j}*M*for most elements exceed the critical

_{j}*t*-value at

*p*=0.001 (i.e. 99.9% significance level) particularly if lithological units occupy less than 8% of the total area covered by the sample catchment basins. For data subset B (Fig. 5b), most of the

*t*-values for the differences between

*b*and

_{j}*M*for most elements exceed the critical

_{j}*t*-value at

*p*=0.001 particularly if lithological units occupy less than 3% of the total area occupied by the sample catchment basins. These results indicate that, for the pairs of

*b*and

_{j}*M*with

_{j}*t*-values exceeding the critical

*t*-value, the differences between

*b*and

_{j}*M*are statistically significant particularly if lithological units occupy, on average, less than 6% of the total area covered by the sample catchment basins.

_{j}Figures 4 and 5 show that for data subset A the values of *b _{j}* are mostly over-estimated and the for data subset B the values of

*b*are mostly under-estimated if lithological units occupy, on average, less than 6% of the total area covered by the sample catchment basins. The plots in Figures 4 and 5 suggest, therefore, that estimates of

_{j}*M*are generally more robust than estimates of

_{j}*b*. Thus, the values of

_{j}*M*(Tables 2 and 3) and Equation (6) were used further in the case study in order to obtain values of

_{j}*Y*

_{i}

^{′}, which represent local background uni-element contents of stream sediments due to lithology in individual sample catchment basins.

## DERIVATION AND STANDARDIZATION OF UNI-ELEMENT RESIDUALS

The values of *Y*_{i}^{′}, obtained via the analysis of weighted mean uni-element contents of lithological units, were subtracted from the corresponding measured uni-element contents of stream sediment samples in order to obtain uni-element residuals, which are either positive or negative. A positive residual can be interpreted as enrichment of uni-element contents of stream sediments due to anomalous sources (e.g. mineral deposits), while a negative residual can be interpreted as depletion of uni-element contents of stream sediments due to certain intrinsic geochemical processes or anthropogenic factors. Because there are two subsets of data from which values of *Y*_{i}^{′} were obtained, then there are also two subsets of uni-element residuals. The magnitude of individual uni-element residuals in one subset cannot be compared to the magnitude of individual uni-element residuals in the other subset because they have been derived using different empirical relationships between measured stream sediment uni-element contents and areas of lithological units in sampled catchment basins (as depicted by different values of *M _{j}*). Supposing that rate of weathering and erosion everywhere in a small district, such as Aroroy, is uniform would imply that there must be a proper but simple way that allows comparison of magnitude of uni-element residuals, for the purpose of classification or ranking of anomalies, in all subsets (i.e. the whole set) of the geochemical data.

In order that uni-element residuals and, thus, uni-element anomalies in both data subsets can be compared and analysed as one data set, the uni-element residuals in data subset A and in data subset B were standardized into *Z*-scores. One standardization algorithm for obtaining *Z*-scores makes use of classical statistics in CDA, thus: *Z _{ij}* represents the standardized uni-element residuals for sample

*i*in data subset

*j*,

*R*the uni-element residuals for sample

_{ij}*i*in data subset

*j*,

*R*values and

_{ij}*SDEV*the standard deviation of

_{j}*R*values. Another standardization algorithm for obtaining

_{ij}*Z*-scores makes use of robust statistics in EDA (Yusta

*et al*. 1998), thus:

*Z*represents the standardized uni-element residuals for sample

_{ij}*i*in data subset

*j*,

*R*the uni-element residuals for sample

_{ij}*i*in data subset

*j*,

*R*values and

_{ij}*IQR*the inter-quartile range of

_{j}*R*values. The

_{ij}*IQR*is equivalent to the absolute difference between the 1st quartile (or 25th percentile) and the 3rd quartile (or 75th percentile) of a set of values.

Table 4 shows the results of standardization of uni-element residuals based on robust statistics (median, *IQR*) in EDA (Equation (8)) and on classical statistics (mean, standard deviation) in CDA (Equation (7)). On the one hand, depending on the element examined in data subset A, the EDA-based standardization results in a 0 to 25% increase in the number of positive residuals and in a 0 to 18% decrease in the number of negative residuals. In addition, depending on the element examined in data subset B, the EDA-based standardization results in 0 to 11% increase or decrease in the number of positive residuals and in 0 to 10% decrease or increase in the number of negative residuals. Moreover, depending on the element examined in data subsets A and B, the EDA-based standardization results in a median 0% increase or decrease in the number of positive residuals and in a median 0% increase or decrease in the number of negative residuals. On the other hand, depending on the element examined in data subset A, the CDA-based standardization results in 11 to 23% decrease in the number of positive residuals and in 9 to 21% increase in the number of negative residuals. In addition, depending on the element examined in data subset B, the CDA-based standardization results in 4 to 68% decrease in the number of positive residuals and in 8 to 82% increase in the number of negative residuals. Moreover, depending on the element examined in the whole data set, the CDA-based standardization results in a median 16% decrease in the number of positive residuals and in a median 14% increase in the number of negative residuals.

Table 4 shows, therefore, that the CDA-based standardization of uni-element residuals in individual subsets of geochemical data is unsatisfactory for the purpose of comparing uni-element anomalies in data subsets and, thus, for classifying uni-element anomalies based on a single set of standardized uni-element residuals. The CDA-based standardization is unsatisfactory, at least in this case study, probably because a subset of uni-element residuals is likely to be composed of several outliers (i.e. uni-element residuals are probably due to various factors, one of which could be mineral deposits) and because the mean and standard deviation in classical statistics are non-resistant to outliers. For example, Bonham-Carter & Goodfellow (1984) found that uni-element residuals lack spatial autocorrelation, indicating that they have large deviations from their central tendency. However, the median and the *IQR* are, unlike the mean and the standard deviation, respectively, resistant and robust measures of central tendency and departure from central tendency of values in a data (sub)set containing at most 25% of outliers (Tukey 1977).

Therefore, the EDA-based standardization (i.e. Equation (8)) was applied to uni-element residuals in data subsets A and B in order to obtain a single set of standardized uni-element residuals. Figure 6 shows the spatial distributions of the whole set of measured As values and the whole set of standardized As residuals. In contrast to the spatial distributions of the measured As values (Fig. 6a), the spatial distributions of the standardized As residuals show not only enrichment of As along the north–NW trend of the epithermal-Au deposits but also enrichment of As in the eastern parts of the area underlain by the Aroroy Diorite (Fig. 6b). These results demonstrate the value of estimating and then removing local background uni-element contents attributable to lithology from measured uni-element contents of stream sediments in order to enhance anomalies. The standardized uni-element residuals were then subjected to downstream dilution correction in order to further enhance and identify significant anomalies.

## DOWNSTREAM DILUTION CORRECTION OF UNI-ELEMENT RESIDUALS

The magnitude of uni-element residuals (i.e. *Y*_{i} – *Y*_{i}^{′}) is controlled by downstream dilution due to mixing of stream sediments from various and mostly non-anomalous sources in a sample catchment basin (Hawkes 1976), thereby obscuring contributions of anomalous sources. Equation (3) is applicable for downstream dilution correction of unit-element residuals if the assumption of exposed mineral deposits of a unit area of 1 km^{2} (i.e. *A _{a}* = 1 km

^{2}) per sample catchment basin is more-or-less valid. This is not the case, however, in the case study because the sizes of most (i.e. 105 out of 135) of the sample catchment basins are less than 1 km

^{2}(see Fig. 1b or 2); that is, they vary from 0.09 to 2.66 km

^{2}with 0.64 km

^{2}as median and 0.24 km

^{2}as

*MAD*(i.e. median of absolute deviations of values from their median; Tukey 1977). In addition, by using Equation (3) to correct uni-element residuals for downstream dilution, it can be argued that estimates of local background uni-element contents (i.e.

*Y*

_{i}

^{′}) are added back. Rose

*et al*. (1979, p. 399) point out that the term

*A*is much larger than

_{i}*A*. Thus, by assuming, in each sample catchment basin, small exposed anomalous sources of unit area of 1 ha (i.e.

_{a}*A*= 0.01 km

_{a}^{2}), which is 9 × to 265 × smaller than the size (

*A*) of any sample catchment basin in the study area,

_{i}Carranza & Hale (1997) made the same assumption of a unit size of exposed anomalous sources in every sample catchment basin and used the same relation in Equation (9) in order to correct uni-element residuals for downstream dilution. Note, however, that downstream dilution correction via either Equation (3) or (9) neglects contributions from overbank materials, assumes lack of interaction between sediment and water and that rate of weathering and erosion is uniform in each sample catchment basin (cf. Hawkes 1976). Nevertheless, considering that sizes of sample catchment basins differ and that sizes of anomalous sources (if present) probably differ from one catchment basin to another, dilution-correction of uni-element residuals is warranted despite limitations of the model.

## CLASSIFICATION OF UNI-ELEMENT ANOMALIES

Because dilution-corrected uni-element residuals are plausibly due to various factors (e.g. presence of mineralization), a data set of such variables is likely to represent multiple populations. Analysis and classification of anomalies in geochemical data sets containing multiple populations can be accomplished via application of, for example, probability plots (Sinclair 1974, 1991). However, identifying population break points in a probability plot can be highly subjective, requires experience and, thus, is not a trivial task. In addition, the application of probability plots assumes that the data under examination exhibit normal or lognormal distribution, whereas many workers havedemonstrated that geochemical data invariably show neither normal nor lognormal distributions (e.g. Vistelius 1960; McGrath & Loveland 1992; Reimann & Filzmoser 2000). Accordingly, in the past, analysis and classification of anomalies in dilution-corrected uni-element residuals were based on visual inspections of spatial distributions of percentile-based classes of such variables (Bonham-Carter & Goodfellow 1986; Bonham-Carter *et al*. 1987; Carranza & Hale 1997). Although percentiles of values in any data set are robust despite their empirical frequency distributions, visual inspection of spatial distributions of percentile-based classes of dilution-corrected uni-element residuals is also arguably subjective. Estimation of threshold based on robust statistics in EDA, such the upper whisker or the upper inner fence of a boxplot and the median+2*MAD* (Reimann *et al*. 2005), was also not considered here because of the following reasons. Although a boxplot-defined threshold is robust if a data set contains less than 10% outliers (Reimann *et al*. 2005), the study area is highly mineralized (Mitchell & Balce 1990; Mitchell & Leach 1991) and more than 10% of the stream sediment samples in the study area represent significant anomalies (JICA-MMAJ 1986; Carranza 2004). In addition, although a median+2*MAD* threshold is robust if a data set contains at least 15% outliers (Reimann *et al*. 2005), the choice of what multiple of *MAD* (e.g. 2) is optimal for setting a threshold is also arguably subjective just as in the application of classical statistics in CDA (e.g. mean+2*SDEV*). It is proposed and demonstrated here that, because several other workers have postulated that the spatial distributions of stream sediment geochemical data are multifractals (Bölviken *et al*. 1992; Cheng *et al*. 1996; Cheng 1999; Agterberg 2001; Rantitsch 2001; Li *et al*. 2002, 2003; Shen & Cohen 2005), objective analysis and classification of anomalies in dilution-corrected uni-element residuals can be achieved via application of the C-A fractal method (Cheng *et al*. 1994). Recently, Carranza (2008, 2009) has demonstrated that, in mapping of stream sediment anomalies, the C-A fractal method outperforms the median+2*MAD* and mean+2*SDEV* methods of identifying threshold.

The concept of C-A fractal method (Cheng *et al*. 1994) can be summarized as follows. In a study area, geochemical concentration levels (* v*) and the cumulative areas (

*) enclosed by each geochemical concentration level (i.e.*

**A***(≥*

**A***)) are plotted along the x-axis and y-axis, respectively, of a log–log graph. A C-A plot describes not only the empirical frequency distributions of geochemical concentration levels but also the spatial distributions and geometrical properties of the features defined by different geochemical concentration levels. Concentration-area plots invariably satisfy certain power-law functions, which are depicted as straight lines (or line segments) on a log–log graph. If, on the one hand, a C-A plot can be depicted by one straight line, then it probably represents a fractal distribution of geochemical background. If, on the other hand, a C-A plot can be depicted by at least two straight-line segments, then the rightmost straight-line segment (i.e. highest concentration values) probably represents a fractal distribution of geochemical anomalies, whereas the straight-line segment(s) to the left probably represent(s) a multifractal distribution (or intertwined fractal distributions) of geochemical background. Agterberg (2007) has shown that geochemical anomalies with Pareto distribution plot as a straight-line segment on the right-hand side of a C-A plot. Accordingly, the breaks in slopes of straight-line segments fitted through a log–log plot of the C-A relationship represent threshold values of different ranges or populations of concentration values in a geochemical data set. These different populations would represent different background and anomalous geochemical processes, one of which could be mineralization.*

**v**The C-A fractal method for analysis and classification of geochemical anomalies was developed using lithogeochemical data (Cheng *et al*. 1994), although it has been applied to analysis and classification of anomalies in continuous field models of stream sediment geochemical data (Cheng *et al*. 1996; Cheng 1999) and in catchment-based discrete field models of stream sediment geochemical data (Carranza 2008, 2009). In this study, the C-A fractal method (Cheng *et al*. 1994) was also applied to analyse and classify anomalies in standardized dilution-corrected uni-element residuals portrayed as catchment-based discrete field models. In this case, uni-element residuals (* v*) and areas (

*) of sample catchment basins associated with standardized dilution-corrected uni-element residuals equal to and greater than*

**A***are plotted on a log–log graph. However, negative standardized dilution-corrected uni-element residuals cannot be represented in a log–log graph of the C-A relation (i.e. negative values do not have logarithms), although this is not a concern because negative standardized dilution-corrected uni-element residuals can be considered to represent background populations and, thus, can be excluded in the analysis and classification of high background to anomalous populations in positive standardized dilution-corrected uni-element residuals. The results of C-A fractal analysis are shown for As, which is a pathfinder element for epithermal-Au deposits.*

**v**The log–log graph of the C-A model for positive standardized dilution-corrected As residuals can be fitted with three straight-line segments (Fig. 7a), indicating the presence of (at least) three populations that can be separated by threshold values at the breaks in slopes of the straight-line segments. These three populations, from lowest to highest values, are considered to represent high background, low anomaly and high anomaly of As. The three thresholds obtained from the log–log graph, and a threshold of zero dilution-corrected As residual to represent upper limit of background, are used to display the spatial distributions of the background and anomalous populations of standardized dilution-corrected As residuals (Fig. 7b). The spatial distributions of the classes of standardized dilution-corrected As residuals derived by the C-A fractal method (Fig. 7b) show a set of low and high anomaly sample catchment basins along the north–NW trend of the epithermal-Au deposits and a set of mostly low anomaly sample catchment basins in the eastern sections of the area underlain by the Aroroy Diorite. Whereas the former set of anomalies can be readily regarded as significant, the latter set of anomalies cannot be readily regarded as significant or non-significant without considering other uni-element anomalies. The C-A fractal method was also applied to separate background and anomalies in the dilution-corrected residuals of Cu, Zn, Ni, Co and Mn, so that analysis of multi-element anomalies can be performed.

## MODELLING OF MULTI-ELEMENT ANOMALIES

### Analysis of multi-element associations

Based on the dilution-corrected residuals of all elements under study, an anomalous multi-element stream sediment geochemical signature reflecting presence of mineralization was determined from via principal components (PC) analysis. It was deemed important to select a subset of ‘highly-enriched’ samples based on the dilution-corrected uni-element residuals because results of PC analysis tend to be dominated by non-anomalous populations. Applications of different selection criteria to a set of dilution-corrected uni-element residuals would result in different subsets of ‘highly-enriched’ samples, each of which is likely to yield different results in PC analysis. Criteria for selecting a subset of ‘highly-enriched’ samples can be based either on results of classification of uni-element anomalies or on some ‘expert’ knowledge and/or a-priori information (say, from an orientation survey). However, it was not intended here to obtain different subsets of ‘highly-enriched’ according to different selection criteria and then to study how sensitive the results are to the choices made. This leaves an outstanding question of how best to select ‘highly-enriched’ samples open for investigation. Whatever criterion is or criteria are applied to select ‘highly-enriched’ samples, the *n*>10*v* rule-of-thumb relation between number of samples (*n*) and number of variables (*v*) to be used in multivariate data analysis must be followed (Howarth & Martin 1979; Howarth & Sinding-Larsen 1983).

Based on the *n*>10*v* rule (with *v*=6 elements), the preceding results of classification of uni-element anomalies and a criterion that a ‘highly-enriched’ sample is one with anomalous dilution-corrected residuals for at least one of the elements under study, a subset of *n*=93 ‘highly-enriched’ samples was obtained for PC analysis. However, histograms and boxplots of dilution-corrected uni-element residuals in the ‘highly-enriched’ samples (not shown here) indicate the presence of multiple populations, extremely low and high values, and non-normal empirical frequency distributions of these data. These characteristics of the dilution-corrected uni-element residuals in the ‘highly-enriched’ samples undermine reliable estimation of the Pearson correlation matrix to be used as starting point of the PC analysis. Alleviating the effects of these data characteristics by log-transformation is not possible due to the presence of negative values. Therefore, it was decided to assign descending ranks of 93 to 1 (i.e. considering 1 as the lowest rank) to descending dilution-corrected uni-element residuals and tied ranks were averaged. A Spearman rank correlation matrix was then computed for the rank-transformed dilution-corrected uni-element residuals and this was used in the PC analysis (George & Bonham-Carter 1989; Carranza & Hale 1997). Table 5 shows the results of the PC analysis.

The PC1, accounting for *c*. 34% of the total variance, represents a Co-Zn-Mn association reflecting plausibly metal-scavenging by Mn-oxides in the drainage environments in most parts of the area; Cu, Ni and As have antipathetic, weak sympathetic and very weak sympathetic relations, respectively, with this multi-element association. The PC2, accounting for *c*. 22% of the total variance, represents a Ni-Cu-As association having an antipathetic relation with Mn and thus reflects plausibly an anomalous multi-element association. The association between Cu and As in PC2 reflects plausibly enrichment of these elements in stream sediments due to weathering and erosion of anomalous sources containing sulphide (chalcopyrite and arsenopyritic) minerals, which generally characterize the mineralogy of epithermal-Au deposits in the area. The association of Ni with Cu and As in PC2 can be ascribed to the dacitic/andesitic rocks that host the epithermal-Au deposits in the area. The PC3, accounting for *c*. 17% of the total variance, represents an As-dominated multi-element association and reflects plausibly the presence of epithermal-Au deposits. The PC4, accounting for *c*. 14% of the total variance, represents an antipathetic relation between an As-Mn-Cu association and a Co-Ni association; the former is possibly due to metal-scavenging by Mn-oxides in some parts of the area while the latter is possibly due to lithologies with slightly more mafic compositions that are not represented in the analysis because they are not mappable at the scale of the lithological map shown in Figure 1. The last two PCs, together accounting for *c*. 13% of the total variance, are not easily interpretable in terms of geological significance.

The presence of two anomalous multi-element associations, represented by PC2 and PC3, in the ‘highly-enriched’ samples is possibly due to differences in mobility of As, Cu and Ni in the surficial environments. Thus, the PC2 and PC3 scores were analysed further in order to determine if they represent significant anomalies. Because the loading on As in PC3 is negative, the PC3 scores are negated (i.e. multiple by −1) so that high negated PC3 scores represent As anomalies. The PC2 and negated PC3 scores are attributed to the sample catchment basins, which are then subjected to the C-A fractal method for separation of background and anomalous multi-element populations. On the one hand, the spatial distributions of the PC2 scores, representing a Ni-Cu-As association, show a NW-trending zone of low and high anomalies following roughly the north–NW trend of the epithermal-Au deposits (Fig. 8a). The low and high anomalies of the PC2 scores seem to decay from the southeastern parts to the northwestern parts of the area. This implies that the Ni-Cu-As association is controlled by topographic elevation (see Fig. 1b). On the other hand, the spatial distributions of the negated PC3 scores, representing an As-dominated multi-element association, show a north–NW -trending zone of low to very high anomalies following closely the north-northwest trend of the epithermal-Au deposits (Fig. 8b). This implies that the As-dominated multi-element association is controlled by mineralization, although there is also a north-trending zone of low to high anomalies of negated PC3 scores in the eastern parts of the area where epithermal-Au deposits are not known to occur.

The apparent similarity and difference between the spatial distributions of anomalous PC2 and negated PC3 scores may be explained as follows. On the one hand, the low and high anomalies of PC2 scores along a zone following roughly the trend of the epithermal-Au deposits plausibly represent weathered materials derived from mineralized outcrops, which have been transported downstream and farther away from the deposits. On the other hand, the low, high and very high anomalies of negated PC3 scores along a zone following closely the trend of the epithermal-Au deposits plausibly represent weathered materials derived from mineralized outcrops, which have been transported downstream but not farther away from the deposits. Thus, anomalies of either PC2 scores or negated PC3 scores are both significant to certain extents, although anomalies of PC2 scores are possibly due to ‘allochthonous’ epithermal-Au deposits while anomalies of negated PC3 scores are possibly due to ‘autochthonous’ epithermal-Au deposits. Because of the apparent similarity between the spatial distributions of anomalous PC2 and negated PC3 scores, it is appealing to integrate such variables into a single variable representing an As-Ni-Cu association reflecting the presence of epithermal-Au deposits. A simple multiplication can be applied to integrate the PC2 and negated PC3 scores, although this creates false anomalies from PC2 and negated PC3 scores that are both negative. This problem is overcome by first re-scaling the PC2 and negated PC3 scores linearly to the range [0,1] and thereafter performing multiplication on the re-scaled variables. The resulting integrated As-Ni-Cu scores are then attributed to the sample catchment basins for the application of the C-A fractal method to separate background and anomaly. Cheng *et al*. (1997) have also applied PC analysis to surficial sediment (till, soil and humus) geochemical data prior to application of the C-A fractal method to map multi-element anomalies.

The spatial distributions of integrated As-Ni-Cu scores (Fig. 9) show adjoining high and very high anomalies, which coincide with or are proximal to most epithermal-Au deposits. Most of the high anomalies of PC2 scores in the southeastern quadrant of the area (Fig. 8A) have been downgraded in importance (i.e. they now map as low anomalies as shown in Figure 9), but many of the low and high anomalies of both PC2 and negated PC3 scores in the northwestern quadrant of the area (Fig. 8b) have been upgraded in importance (i.e. they now map as high anomalies as shown in Figure 9). In addition, many of the low anomalies of negated PC3 scores in the eastern parts of the area (Fig. 8b) have been enhanced. Combining the PC2 (Ni-Cu-As) and negated PC3 (As) scores into integrated As-Ni-Cu scores has an overall positive effect in this case study and is therefore defensible.

### Screening of multi-element anomalies

The presence of stream sediment uni-element or multi-element anomalies does not always mean the presence of mineral deposits, so it is necessary to apply certain criteria for screening or prioritization of anomalies prior to any follow-up work. Criteria for screening or prioritization can be related to indicative geological features of the mineral deposit type of interest or to factors that could influence localization of stream sediment anomalies. The criteria applied to screen or prioritize stream sediment anomalies can differ depending on whether the area being examined is a ‘brownfield’ (i.e. where a number of mineral deposits have already been discovered) or a ‘greenfield’ (i.e. where mineral deposits have not been discovered yet).

In a brownfield area, the significance of multi-element stream sediment anomalies can be screened relative to sample catchment basins that either contain discovered mineral deposits or are situated at some distances downstream of discovered mineral deposits. That is because stream sediments in those sample catchment basins are probably anomalous due to materials derived from discovered mineral deposits by certain geogenic or anthropogenic processes. Thus, in a brownfield area, the significance of multi-element stream sediment anomalies in sample catchment basins can be screened by using binary presence/absence of anomalies due to discovered mineral deposits (cf. Bonham-Carter *et al*. 1988). Accordingly, a binary anomaly map (Fig. 10a) was created by assigning a score of 1 to sample catchment basins that contain or are within *c*. 2 km downstream of each of the known epithermal-Au deposits and by assigning a score of 0 to the remaining sample catchment basins. The downstream distance limit is based on findings in similar climatic regions that trace-metal (e.g. As) anomaly dispersion trains reach at least 2 km downstream from epithermal-Au deposits (cf. Fletcher 1996; Williams *et al*. 2000; Leduc & Itard 2003; Ashley *et al*. 2007).

In either a brownfield area or a greenfield area, the significance of multi-element stream sediment anomalies can be screened relative to faults/fractures because (a) such geological features are common loci of many types of mineral deposits, whose element contents find their way into streams due to geogenic or anthropogenic processes and (b) the presence of such geological features indicates enhanced structural permeability of rocks in the subsurface, which facilitates upward migration of groundwaters that have come into contact with and have leached substances from buried mineral deposits. Thus, in either a brownfield area or a greenfield area, the significance of multi-element stream sediment anomalies in sample catchment basins can be screened by using fault/fracture density as a criterion (cf. Carranza & Hale 1997). Accordingly, a map of fault/fracture density per sample catchment basin (Fig. 10b) was created in a raster-based GIS by calculating the ratio of number of pixels representing faults/fractures in a sample catchment basin to the total number of pixels in that sample catchment basin. Most of the epithermal-Au deposits in the study area are situated in sample catchment basins with moderate to high fault/fracture density (Fig. 10b).

In order to screen the significance of multi-element anomalies shown in Figure 9, two analyses were performed – one for a brownfield model and another for a greenfield model. For the brownfield model, the integrated As-Ni-Cu scores (Fig. 9) and fault/fracture densities (Fig. 10b) of sample catchment basins were used as independent variables and the binary anomalies scores (Fig. 10a) were used as dependent variable in logistic regression analysis and the output regression scores obtained for every sample catchment basin were subjected to classification via the C-A fractal method. This analysis is akin to the multiple linear regression analysis performed by Bonham-Carter *et al*. (1988), although it was preferred to use logistic regression analysis here because (a) it is appropriate when the dependent variable is binary and (b) it makes no assumption about the frequency distribution of data of independent variables (Rock 1988). For the greenfield model, assuming that there are no discovered mineral deposits in the study area, the products of integrated As-Ni-Cu scores and fault/fracture density were obtained per sample catchment basin and then were subjected to classification via the C-A fractal method.

For the brownfield model, the classification of the logistic regression scores via C-A fractal analysis results in many highly significant anomalies aligned nicely along north-northwest trend of the epithermal-Au deposits (Fig. 11). For the greenfield model, the classification of the products of integrated As-Ni-Cu scores and fault/fracture density via C-A fractal analysis results in many significant and highly significant anomalies following closely the north–NW trend of the epithermal-Au deposits (Fig. 12). The differences between the two models of significant anomalies are mainly due to the differences between the methods and criteria applied in each analysis as discussed above. Nevertheless, the results shown in Figures 11 and 12 both indicate clearly that most anomalies of integrated As-Ni-Cu scores in the western half of the study area (see Fig. 9) are significant. Both models also suggest that most anomalies of integrated As-Ni-Cu scores related to the Aroroy Diorite in the eastern half of the study area (see Fig. 9) are non-significant (i.e. most of them are background as shown in Figures 11 and 12). This latter result implies that the Aroroy Diorite is possibly non- or weakly-mineralized.

The apparent strong spatial association of the brownfield model of significant anomalies (Fig. 11b) with the epithermal-Au deposits in the study area implies that application of the logistic regression technique discussed here is likely to yield significant stream sediment anomalies that can be used as guides toward undiscovered deposits in a brownfield area. The apparent strong similarity of the greenfield model of significant anomalies (Fig. 12b) to the brownfield model of significant anomalies (Fig. 11b) implies that application of the simple technique of multiplying derivative data representing anomalous multi-element associations with fault/fracture density is likely to yield significant stream sediment anomalies that can be used as guides toward undiscovered mineral deposits in a greenfield area. However, each of the techniques used here in order to obtain a model of significant stream sediment anomalies may or may not be the most optimal way of integrating spatial data based on sample catchment basins (e.g. fault/fracture density per sample catchment basin) in order to screen or prioritize the significance of stream sediment anomalies in either a brownfield or greenfield area, respectively. Other techniques of spatial data integration and other criteria for screening/prioritizing anomalies may be more optimal, but they must be investigated in every case of catchment basin analysis of stream sediment anomalies.

## DISCUSSION AND CONCLUSIONS

There are various factors that influence variation in stream sediment background uni-element contents. For example, it has been shown in some case studies that drainage sinuosity (Seoane & De Barros Silva 1999), which is mainly a geogenic factor, and selective logging (Fletcher & Muda 1999), which is an anthropogenic factor, can influence the variability of background uni-element contents of stream sediments. Nevertheless, a universal factor of variation in stream sediment background uni-element concentration is lithology. Estimation and removal of local background uni-element contents of stream sediments due to lithology from measured stream sediment uni-element contents is vital to the recognition of significant geochemical anomalies.

The results of the case study demonstrate that significant uni-element and multi-element anomalies can be extracted from stream sediment geochemical data through a 5-stage GIS-based methodology involving: (1) estimation of local background uni-element contents due to lithology per sample catchment basin; (2) removal of estimated local background uni-element contents due to lithology from measured uni-element contents, which results in uni-element residuals; (3) dilution-correction of uni-element residuals using a modified formula from the relation proposed by Hawkes (1976); (4) modelling of uni-element and/or multi-element anomalies via application of the concentration-area fractal method; and (5) screening of significant anomalies by integration of spatial data representing factors that could influence the occurrence and/or localization of stream sediment geochemical anomalies.

Consideration of the area of influence of every stream sediment sample location – its catchment basin – is the key in stages (1), (3) and (5). In stage (1), more robust estimates of local background uni-element contents due to lithology can be obtained by using areas of lithological units per sample catchment divided by the total area of sample catchment basins (in the ‘weighted means’ technique) instead of using areal proportions of lithological units per sample catchment basin (in the multiple regression technique). In stage (3), dilution-correction of uni-element residuals is based on area of sample catchment basins plus an assumption of a small unit area of exposed anomalous sources (e.g. mineral deposits). Correction for downstream dilution using either Equation (3) or (9) (i.e. based on the assumption of a unit area for exposed anomalous sources contributing to uni-element contents of stream sediments), is appropriate for analysis of anomalies in stream sediment geochemical data in areas where there are some known occurrences of mineral deposits of interest. In areas where there are no known occurrences of mineral deposits of interest, it would be more prudent to calculate productivity (Moon 1999) or ‘stream-order-corrected’ residuals (Carranza 2004) because these techniques do not require assumption of unit area of exposed anomalous sources contributing to stream sediments. Certainly, the downstream dilution-correction model based on the idealized relation proposed by Hawkes (1976), which is adopted in the case study, does not apply universally. However, the idealized formula proposed Hawkes (1976) shows reasonable agreement between theory and prediction of known porphyry copper deposits in his study area.

Prior to stage (4), if dilution-corrected uni-element residuals are derived from a number of subsets of stream sediment geochemical data based on, say, rock type at or near each sample site, then, for the standardization of dilution-corrected uni-element residuals per data subset in order to obtain a single set of dilution-corrected uni-element residuals for classification of anomalies, the application of robust statistics in EDA (Tukey 1977) should be preferred to the application of classical statistics in CDA. In stage (4), the results of the case study demonstrate that anomalies in dilution-corrected uni-element residuals and in derivative scores representing multi-element associations can be identified objectively by application of the C-A fractal method (Cheng *et al*. 1994). In stage (5), the area of individual sample catchment basins is further useful in screening of stream sediment anomalies by using fault/fracture density, which was estimated as the ratio of number of pixels representing faults/fractures in a sample catchment basin to number of pixels in that sample catchment basin. Other types of spatial data based on individual sample catchment basins can be useful in screening or prioritizing of stream sediment anomalies. For example, in another GIS-based case study, Seoane & De Barros Silva (1999) prioritized sediment sample catchment basins that are anomalous for gold by using catchment basin drainage sinuosity, which is estimated as the ratio of total length of streams within a sample catchment basin to the total distance between the start and end points of the main stream and its tributaries in that sample catchment basin. Finally, it is clear that GIS supplements EDA and C-A fractal analysis with tools for data manipulation, integration and visualization in order to identify and map catchment basins containing significant stream sediment anomalies.

## Acknowledgments

G. Bonham-Carter and an anonymous reviewer are thanked for their constructive comments on an early version of the paper.

- © 2010 AAG/Geological Society of London