Introduction
Diamond, as a lustrous precious stone, has human fascination since historical times. In India, well known epics - the Ramayana and the Mahabharata have mention of ornaments of diamonds. India continued to have dominant position in diamond mining and trade till beginning of the 18th century. But, mining of the diamond on large scale started with real 'rush' in the last quarter of the 19th century in South Africa. The 'rush' in gradual process founded the basis for the modern scientific methods of exploration. Kimberlite was identified as the primary source. Index minerals were identified as exploration tools. Thermodynamics of diamonds and host-rock-mineral-entities and association helped in re-establishing the relation between the host rock and diamonds. Mineralogical assemblage, geophysical signatures and geochemical attributes of the primary rock become the implements for integrated approach in prospecting. Airborne surveys and remote sensed data were inducted in the search process. By now, there are sufficient numbers of discoveries world-over to establish the pattern of distribution in tectonic set-up and localisation in plate-tectonics model. The broad outlines used in exploration for primary source of diamonds can be summarised in the following lines :

Kimberlite Emplacement Model: Theoritical facts

• World over, majority of the kimberlites are emplaced in ancient cratonic blocks (Clifford,1966) or where Archaean basement is underlain by deep lithospheric keels (Haggerty, 1986) .
• Productive or diamond bearing kimberlites are emplaced in areas where surface heat flow is generally less than 40 Mw/m². This condition is suitably available in majority of the cratonic blocks.
• Ascent of kimberlite melt is from upper mantle but below the graphite-diamond stability surface (i.e., where pressure >45 to 60 Kb = 150-200 km depth and temperature from 900º to 1300º C ).
• The melt intrudes through pre-existing deep-seated faults / fractures, which have their roots in upper mantle.
• The deep-seated faults and deep-seated fractures are well depicted on the imageries in the form of lineaments traversing hundreds of kilometers.
• After reaching the lower level of the upper crust, the melt finds a number of shallow faults / fractures in its way. The melt intrudes into these weak zones of varied orientation in the form of cones and dykes.
• The kimberlites are usually localised in zones of high magmatic permeability and repetitive basic and ultrabasic magmatic activity (Kaminsky et al., 1995).
• The kimberlites occur in clusters and such clusters make a field (of 1 to 50 or more bodies Janse,1984, Mitchell,1986) and a set of fields a province.
• Mantle-xenoliths and xenocrysts, along with diamonds, are inducted into the accelerated-ascent of melt from the upper mantle environment and diamond stability zone.

Fig.1 : The idealised model for kimberlite emplacement in a cratonic block.
The above stated facts could serve as conceptual model or exploration model in search of the locales of the primary sources for diamonds. A detailed account on conceptual facts in diamond exploration and identification of prioritised zones in India was dealt in the compilation work of Satyanarayana, 2000.

With the advent of GIS technology with tessellation and vector encoding, the integrated approach in search of the primary sources for diamond also get a boost in identification of statistically derived favourable zones from the overlaid predictive thematic layers. The present work constitutes an analysis for mineral targeting in 2953 sq km area falling in the Narayanpet Kimberlite Field, southern India, where integration of evidence maps is attempted on 'Index Overlay Model' coupled with 'Bayesian Probability Principle' in a vector GIS.

Narayanpet Kimberlite Field
The Geological Survey of India since 1984-85 has been discovering kimberlite bodies in Maddur-Narayanpet area (Nayak et al., 1987: Sarma,1990; Rao, 1995), Mahboobnagar district of Andhra Pradesh. Till date more than 30 kimberlite bodies have been located, now this area which is designated as 'Narayanpet Kimberlite Field (NKF) (Satyanarayana et al., 1997)' is a promicing zone for kimberlites after the well-known 'Wajrakarur Kimberlite Field (WKF)' in Dharwar Craton. The NKF measures about 60 km x 40 km in western part of Mahboobnagar district, Andhra Pradesh and eastern part of the adjoining Gulberga district, Karnataka. The kimberlites of both the fields have broad similarities in mineralogical, petrological characters and major element chemistry, but there are subtle differences in REE distribution, indicator minerals and mantle nodules (Rao et al., 2001). The kimberlites of both NKF and WKF are in similar tectonic set-up, and of contemporary ages (Anil Kumar et al., 1993).

Geology
The area comprises broadly Archaean gneisses, migmatites and granites with enclaves of schistose rocks, Proterozoic granitic intrusives and sediments of Bhima Group and Cretaceous Deccan Basalts. Emplacement of kimberlites of the NKF is noticed in the gneisses and granites (Rao et al., 1998). For prognostication purpose, the geology is simplified into three litho-domains i.e., gneissic domain, granitic domain and basalt domain.

Tectnoic Elements
A number of faults, fractures and lineaments of varied dimensions, in different orientation related to different tectonic events are recorded in the area. Some of these are occupied by basic (including ultrabasic) intrusives, pegmatites, quartzo-feldspathic veins, younger acidic intrusives etc.. These intrusives are suggestive of zones of magmatic permeability and repetitive basic and ultrabasic magmatic activity in the area. The various tectonic elements of this area are grouped into E-W, NE-SW, N-S, NW-SE sets on the basis of their orientation.

Geophysical Surveys
Multidisciplinary studies involving detailed satellite imagery, aerial photo interpretation and ground geophysical surveys were initiated in the NKF to locate new kimberlite occurrences. Regional gravity and magnetic surveys carried out (Reddy et al., 2001) and interpretation of satellite and aerial photo data distincty brought out the co-axial relations existing between geophysical anomaly linears and major lineaments / faults (Rao, 2001). The computer based dataset for the present work is derived from the analogue maps generated during the actual surveys and field activities in the NKF.

Present Work

Methodology
The present GIS Project involves the following stages :

1. Data capture from analogue maps
2. Derivation of theme based evidence maps
3. Spatial analysis using Bayesian Probability Principle coupled with Index Overlay Model for mineral targeting

Data Capture: Approach in search of new targets in an area is mostly based on the philosophy of 'known to unknown'. In this respect the first step was to bring out all the appropriate data together into GIS database. The foresaid maps were digitised into a GIS software 'Arc/Info version 8.2'. The software captures data into workspace-coverage storage model.

Two types of datasets i.e., evidence set and over plotting set, are delineated among the captured spatial dataset. The evidence spatial dataset comprising those discrete geographic objects evidencing the causative role in the emplacement process or defining the signatures of probable locales of kimberlite and allied rocks in NKF. And thus they are of predictor nature in prognostication process. The spatial database from the evidence set are :

1. Lithology
2. Structure - faults/fractures and lineaments,
3. Gravity contours interpreted to high and low axes - represented as lines,
4. Ground magnetic contours interpreted to high and low anomalies - represented as lines
   
   The other set represents the existing kimberlite prospects in the NKF: The database of 33 discrete known bodies of kimberlite and allied rocks.
   
   
   Fig.2 : The Narayanpet Kimberlite dataset.

The dataset was captured, populated with attribute values, assigned Polyconic projection with map-centre of the mosaic of four 1:50,000 topobases as origin of co-ordinate axes, edge-matched and mosaiced, thereby, all the themes were brought to a common reference system. This fascilitated overlaying and over plotting of spatial databases for GIS analysis. Study of over-plotted digital maps is helpful in revealing the pattern of occurrence, field controls on known bodies and theoretical understanding of emplacement model for known bodies.

Visual analysis in understanding the pattern of distribution of kimberlites in NKF aided in understanding the controls on kimberlite emplacement. Small outcrops of geographic object like kimberlite - represented by points on the digital map may have three fundamental distribution patterns i.e., a) Complete spatial randomness, b) Clustered pattern and c) Regular pattern. The kimberlites of WKF and NKF represent a clustered pattern. Each cluster has limited aerial spread and the spread of kimberlites of NKF is in the form of an ellipse. On the whole, the ellipse precisely defines the kimberlite points. The major axis of this elliptical distribution suggests a probable E-W control on the kimberlite emplacement. But the ellipse has a considerably broad secondary axis perpendicular to the major axis, which suggests role of additional controls besides the E-W control.


Fig.3 : An ellipse define overall distribution of kimberlites of NKF



Fig.4 : Lithological domains and distribution of kimberlites of NKF
Over-plotting of the kimberlite occurrences on the generalised lithological domains (comprising gneisses, diapiric granites and Deccan Basalt ) brings out a modified distribution pattern influenced by the litho-domains. Though the number of known kimberlite occurrences is almost equal in gneiss and granite (17 and 16 respectively), the controls on distribution pattern in these two lithological domains is attributed to different sets of faults. The major axis of orientation of the kimberlite distribution is E-W in gneissic domain, whereas it is NNW-SSE in granitic domain.

Most of the theoretical concepts of kimberlite emplacement hold good for the NKF. The emplacement model for kimberlites emphasises - clustering in a form of 'nest of crustal faults and fractures' in proximity of a mega lineament. The mega lineament in NKF is traced from the Cuddapah Basin to the east that extends hundreds of kilometres in E-W disposition. It is thus obvious that the linear geographic objects like faults, lineaments and gravity axes have controls on the pattern of distribution of kimberlites. The directional sets of feature-elements have different degree of controls, i.e., from significant to least significant.

Derivation of theme based evidence maps: GIS provides unlimited opportunities to make observations on over-plotted thematic maps, delineation of predictive features and understanding their role in identification of prognostication zones. Following the understanding of the cause and effect relationships, the second phase in an analysis process, is to manipulate the data so as to derive theme base evidence maps. Table 1 gives the details of the need for manipulation, the analysis tool applied in spatial data manipulation and its objective as a part of prognostication over the Narayanpet dataset:


Table 1 : Manipulation, a chain of operations to make the data usable in analysis process

Operation	The need for manipulation	Analysis Tool	Objective of spatial data manipulation
A	Orientation of a predictive feature has differential control over target objects	Subsetting	a. a). Spatial and attribute sub-sets for fault objects having orientations : EW, NS, NW and NE. b). Sub-set of Litho-domain specific gravity objects (see Operation No. C)
B	To measure proximal distances between the known target objects and the predictive feature (linear objects).	Proximity/Near	This is a fact-finding stage to establish the measured closeness of target objects and predictive feature objects.
C.	Intersection point of gravity linearss and litho-domains as a control on target objects.	Intersect: input map = gravity line map and operation map = litho-domain polygon map	Nodes develop at intersection points in gravity line map. Tabular merger of two attribute tables takes place. This activity enables selection of gravity lines which falls in spatial continuum of a specific litho-domain.
D.	The statistical common distance which will define the prognosticated zone around predictive & sub-set feature.	Statistical summary tool Case item = orientation,Stat. function = mean of values in distance field	This is to acquire the mean of the measured closeness values of target objects and predictive feature objects derived by the operation No. B.
E.	Defining a zone around a predictive line feature which may be the zone of influence for prognostication.	Proximity/ Buffer Buffer distance = the statistical mean obtained from operation D	This is to achieve a well defined zone of prognostication for each input subset maps.
F.	Study of Bayesian Probability of a zone and score assignment on relative expectancy from the zone.	Creation of a score field in subset map and score calculation	Relative scores for defined zones on evaluated expectancy from the respective zones.

A chain of operations through near, buffer and statistics reporting tools are utilised to establish the precisely defined proximity between the predictive features of different themes and locales of any economic consequence (target). 'Near tool' - provides opportunity to define the closest nearness in quantitative terms, between the predictive line features (for present study faults & lineaments and interpreted gravity linears) and the target point objects (kimberlites). Using the 'summary statistical' tool - 'mean' for a specified case item (in present study fault_orientation for sub-sets of fault maps and gravity_orientation in granitic - and gneissic - domain sub-set maps) are acquired to establish the mean of the closest-distances between emplaced kimberlites and each causative sub-set line maps.

For the present study, magnetic low and high map, sub-set maps for faults-lineaments and domain gravity axes are buffered (both sided, and round buffer) with the value of statistical mean for orientation class of their nearest kimberlites data extracted from the near operation.



Fig.5 : Faults and lineament map is being prepared for analysis. Sub-set are created and proximity zone around subset features are defined.



Fig.6 : Litho-contact between the two domains and gravity line intersection has also a control. Subsets and proximity zone around gravity lines are defined accordingly.



Fig.7 : Proximity zone around magnetic low and high and kimberlite overplot
Spatial analysis using Bayesian Probability Principle coupled with Index Overlay Model for mineral targeting: 'Index overlay model' (Bonham-Carter, 1996 and Westen, 1997) is selected for analysis with the Narayanpet evidence dataset. The procedure of the model is that each class of a predictive map is given different score as well as each predictive thematic map itself receives different weight. Before integration into a multi thematic map, each class or sub-set of a thematic map was weighted, ranking on a suitability scale (0 - 9, maximum 10 weighted classes). The spatial association between known occurrence and the predictive datasets are used to workout weights, which were applied to predictive areas with similar characteristics to the known occurrence.

On account of standardising the weights for classes or sub-sets of a theme or for inter-thematic maps, factor (f) of 'posterior probability' upon 'prior probability' on the notion of Bayesian Probability Principle were undertaken. Prior probability is the ratio of known kimberlites (33) upon area (NKF). The expression for prior probability is the unbiased distribution of kimberlites per sq km area. Meaning thereby, the factor of prior probability is an expression of predictability at a point in the area when none of the thematic controls of predictive maps are taken into account. Whereas, posterior probability is the ratio between circumscribed kimberlite bodies upon summed up area of the predictive zone (inside of the buffered zone). Thus, the posterior probability is a biased probability for a specific case. With the bias of known controls on the emplacement of kimberlites, there is always an improved degree of predictability for a point within the predictive zone. Assuming a common weight base (= 2) for the outside the predictive zone, the weight (integer) for inside is subscribed (Table-2) by multiplying weight base and probability factor (f). Thematic integration of subsets was carried out followed by integration into a multi thematic map i.e., the subset-evidences together make a factor map. Addition of weights and normalisation was carried out in a newly created field in attribute table. Finally combining by union algorithms the three factor maps, namely- 1. fault and lineament factor map, 2. gravity factor map and 3. magnetic factor map result into the favourability map.

Table-2 : Kimberlite proximity respective scores for Thematic Evidence Dataset

Sl.No.	Theme	Sub-set theme	Mean distance of the nearest kimberlites	Posterior probability (kimberlites in the zone/area of the zone = x) X / Prior probability (33/2953 = 0.01117)	Score		Map Weight
A.	Faults	E-W Faults	1485m	13/675.6 sq km	1.7	3+2*=5	4
		NE-SW Faults	1345m	8/534.3 sq km	1.34	1+2*=3
		N-S Faults	1751m	9/269.6 sq km	2.98	6+2*=8
		NW-SE Faults	1307m	21/913.7 sq km	2.05	4+2*=9#
B.	Gravity	Gravity Axes in Granitic Domain		13/764.7 sq km	1.5	3+2*=5	2
		E-W Axes	2093m
		N-E Axes	1562m
		NW-SE Axes	1255m
		Gravity Axes in Gneissic Domain		17/680 sq km	2.24	5+2*=7
		E-W Axes	922m
		N-E Axes	1263m
		NW-SE Axes	2106m
C.	Magnetics		1441m	17/775.3	1.96	4+2*=6	1

* Prior probability of whole area or Dharwar Craton. # Relatively higher score is prescribed than the ratio. This is for highest upper crustal perforation along the set of faults (NW-SE) and the zone around has maximum number of kimberlite localised.
The favourability map generated on the combine of the Bayesian Probability Principle and Index Overlay Model, is a decision support map. The merit of the model could be realised when this map at decision making stage was over-plotted with kimberlite occurrence map in ARCMAP of ARCGIS Version 8.2, for each selection of a set of polygons qualifying a normalised weighted value or range of value one can have 'selection by location' of the kimberlite bodies falling within concerned polygons. A degree of confidence can be expressed in terms of known kimberlites falling within area acquired by the polygons. So, at a decision making stage, for each unique normalised weight classes the decision maker have both figures - statistically summed up area and improved confidence level (Table-3, column-e).

Table-3 : Computation of Degree of Confidence in Indexed Classes

Indexed weight class	Area withi n the range of Zones (sq km)	No. of kimberlites	Kimberlites/Zone area (c/b)	Posterior probability / prior probability or d / 0.01117	Probable decision
A	B	C	D	E	F
9	0.49	0	0	3.40	Extensive and detailed close grid/GPS based ant hills, soil chem.sampling, and ground geophysical studies.
>=8	79.69	3	0.0376
>=7	262.39	10	0.03811
>=6	480.09	17	0.0354	3.17	-Do-on wide grid, stream sediment sampling, Air borne Geophy.
>=5	1116.99	26	0.0232	2.08	Stream sediment sampling (sss)
>=4	2129.02	33 0.01550	1.39	Reconnoitry sss

For example, polygons selected for high range of weights (8 to 9) make patches, having a total area of 80 sq km, which contain 3 known kimberlite bodies in it. A higher ratio 3 nos/80 sq km (target area) upon 33 nos/2953 sq km (project area) propose an improved degree of confidence in the zone which is higher by 3.37 times from prior probability.

Conclusion
A chain of operations on near, buffer and statistics reporting tools are utilised to establish the precisely defined proximity between the predictive features of different themes and zones of any economic consequence.

Using the proximity figures and sub-thematic weights resulted from proximity and probability driven analysis approach in working out a model for the Narayanpet Kimberlite Field could be applied on the whole to the Dharwar Craton for locating new 'nest of faults and fractures' along mega-lineaments with any yield expectancy zones around them for kimberlites or related rocks.

Most appreciating aspect of the model is the factor - 'degree of confidence in a class or predictability of a class' of the final favourability map, which prompts a prospector or a decision making authority to arrive at a right kind of decision.

The model is for close observation in light of new discovery in the NKF in recent years. In light of the fact that kimberlites of the NKF are in similar tectonic set-up with age-wise contemporaneous to WKF (~1100 Ma, Radiometric dating of the bodies), the model has a scope to improve and widen its application throughout the Dharwar Craton, which depicts heat flow regime of < 40 Mw/ m2 (Heat flow map of India, after Ravi Shanker, 1988) that is favourable for diamond stability.

Acknowledgement
The authors are thankful to Director General, Geological Survey of India and DeputyDirector General, Geological Survey of India , Training Institute for granting permission to publish this paper. The authors are also thankful to s/Shri S.V.Stayanaraya, Director and K.R.P.Ra, Geologist (Sr.) of Geological Survey of India, Training Institute for valuable suggestions.


Fig. 9 : The favourability map showing selection of 3 nos. kimberlites in expectancy zone > = 8 and the summary statistics reports the summed up area for the Indexed classes.
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