THE STATISTICAL MATHEMATICAL METHODS OF PROCESSING THE GRAVITY AND AIRBORNE GAMMA RAY SPECTRUM DATA FOR EVALUATING AND PROSPECTING MINERAL RESOURCES

1NGUYỄN TÀI THINH, 2NGUYỄN THẾ HÙNG

1Việt Nam Association of Geophysicists, 18 Hoàng Quốc Việt, Hà Nội;
 2Division of Geophysics, Km.9, Nguyễn Trãi Road, Thanh Xuân, Hà Nội.

Abstract: This paper presents a complex of methods of processing and analyzing the gravity and airborne magnetic-gamma ray spectrometer data, which are based on the methods of mathematical statistics for evaluation and prospecting of mineral resources. These methods are formed on the basis of results of researches and applications that were carried out by the authors in the Division of Geophysics during recent years.

The statistical methods of processing and analyzing the gravity and airborne gamma ray spectrometer data consists mainly of defining the statistical characteristics and the correlation functions of geophysical fields; applying the filtration for analyzing the geophysical field components; determining the multisignal anomalies by geophysical data; pattern recognizing by using sample mines and etc.. The used algorithms are mainly in softwares Coscad 8.0, Coscad 3D (Russian Federation, 2002), Potential Field (USA, 1995), ER Mapper (Australia, 1995), etc. in combination with some specific support softwares written by the authors.

In this paper the authors outline also some results, as an illustrating example of using the above mentioned complex of methods for processing and analyzing the gravity and airborne magnetic - gamma ray spectrometer data on scale of 1/50,000 applied in the Tiên Phước area, Quảng Nam Province to evaluate the perspective of mineral resources in this area. The results of processing allow to contour 4 primary gold perspective regions: Núi Nưa of Tiên Hiệp commune, Thôn Ba, Thôn Bốn of Trà Đốc commune, Vĩnh Ninh and the region of potassium feldspar perspective about east of Hưng Nhượng. The ground detailed assessment has showed some gold sulphide-quartz zones of large size and high gold concentration (about of 1.0 - 102 g/t Au).

The obtained in the Tiên Phước area results prove the reasonableness and the effectiveness of the complex of applicated methods.


I. INTRODUCTION

In Việt Nam, the gamma-ray spectrometer and gravimeter studies at the scale of 1/50,000 up to 1/25,000 have been carried out about over 100,000 km2, covering almost the region of from Thanh Hóa to Bình Thuận, Tây Nguyên area and some the mountainous area of North Việt Nam. The obtained data were analysed for different purposes in the time of report for the projects. Therefore, the exploitation and synthesis of information is still in the limited level.

The study for finding the methods of processing, analyzing airborne gamma-ray spectrometer and gravimeter data were started since 1995 by Nguyễn Tài Thinh, Nguyễn Thế Hùng, Đỗ Tử Chung, Võ Thanh Quỳnh, Nguyễn Tuấn Phong, Doãn Ngọc San,... The results of these studies were applied in different levels. Among them, the complex of methods of processing, analyzing the airborne gamma-ray spectrometer and gravity data for geological and mineral resource investigation on the basis of statistical mathematics, carried out by Nguyễn Tài Thinh, Nguyễn Thế Hùng and etc., has been widely used and get the active results in the geological interpretation and mineral exploration.

The results of analyzing the geophysical data by statistical maths during recent years play important role in the geological and mineral investigation, especially in the finding new deposits, such as uranium in Quảng Nam,  fluorite in Bình Định, magnesite in Gia Lai, gold and tin mines in Nghệ An, Quảng Bình, Huế, Lâm Đồng, etc. and many prospecting regions.

II. ESSENTIAL STATISTICAL PROCESSING METHODS 

1. Main parameters of gamma ray spectrometer anomaly

The statistical parameters used in the geological and mineral resource investigation are as follows:

- Relative radiation parameters (JK, JTh, JU): Radiation parts of the radioactive elements in total radiation field. This parameters represent the nature of radiation field.

- Ratio of contents of the radioactive elements: In the primary rocks the correlation between radioactive elements is nomal, so as the content ratios between them vary in a small range. But in the altered rocks these ratios change visibly. The ratios used in the processing are: qTh/qU; qK/qTh;  qU/qK

- Multi-component parameter (F): Multi-component parameter is calculated by the formula: F = qU.qK/ qTh            

Zones of high multi-component parameters often present altering rocks. For this reason the multi-component parameter is considered as prospective index.

- Dominal parameters: Di = qi.qi / qj.qK. The altered processes of the rocks will change the content of their radioactive elements. The content of some elements will increase while the content of some other decreases. Dominal parameters (DU, DTh, DK) allow to define these changes and calculated by formulae:

Above-based content Δqij  is calculated by:

Δqij   =  qi2 -  kij . qi

Where: Δqij - above-base content of the radioactive element - i; qi -  content of the radioactive element - i; kij - base value of the ratio of the element couple - i and - j.

2. Main statistical processing methods

 Basic statistical performances: The calculation of statistical feature of the gamma ray spectrometer and gravimeter data is a necessary step for defining the used methods and sequence of processing. The basic statistical performances include mathematical expectation, variances, standard deviation, asymmetries, variant range, gradient, radius of correlation … and other features, such as: autocorrelation function D(K, M); autocorrelation function between two fields B(m); autocorrelation and structure-correlation function RR(L);  spectrum analysis of the geophysical fields….

Separation of the field into the different components: Optimal filter: energy filter, Vine - Conmogorop filter; component analysis method.

Detection of multisignal anomaly: The use of autocorrelation and structural correlation functions (ACF và SCF) as above mentioned allows to detect the multisignal anomalies. In prospecting (exploratory) geophysics under weak anomaly it is accepted to count a signal which is commensurable on amplitude with a level of disturbance or is lower than this level and its authentic visual discovery is practically impossible.

Classification methods: K-mean classification method; Multi-dimensional Classifi-cation Method.

Method of pattern recognization: The problem is presented such as there should be recognized by pattern of the multi-signal anomalies based on the data set  F(i,j), i =,  j = , with size of M*N points, where M: number of points on profile, N: number of profiles.

We suppose that, the window size is of M*N points and inclination of zero, the mathematic model of field consists of signal (anomaly) A(i,j) and disturbance n(i,j). The disturbance conforms to p-dimensional standard distribution with p: dimensional average vector equal 0 and correlation matrix S.

Therefore it should be used statistic T2 and distribution of Fisher:


F =

Where :

  : valuation of different vectors of averages along the columns in the window;

    row vectors;

   

is valuation of total correlation matrix by columns and rows.                        


The hypothesis is considered as truth when  F < Flim, where Flim: critical value of Fisher distribution with freedom orders g1, g2:

          g=;  g= 2NM – N +M – P +1     

The truth of H0 - hypothesis confirms that, the centre of window is the same anomaly. By moving the window along all the profiles we should contour the anomalies in the investigation area.

III. SOME RESULTS APPLIED FOR EVALUATION OF PRIMARY GOLD PERSPECTIVE IN TIÊN PHƯỚC AREA, QUẢNG NAM PROVINCE

The Tiên Phước area is about of 1000 km2 in area, located in the Tiên Phước District, Quảng Nam Province. There are many geological investiagation and mineral resource evaluation projects in the scale of from 1:1,000,000 to 1:50,000 - whole area, up to 1:10,000 to 1:5,000 - in some localities.

In this area some mines of industrial value were discovered, such as the Bồng Miêu gold mines, that many years has been exploited, the Trà Dương gold mine and other primary gold occurrences, the Tiên An graphite mine, the Tiên Hiệp postassium feldspar mine, etc.. Almost geologists have been considering the Tiên Phước area as primary gold perspective place, but it still is not sufficiently evaluated because of the complicated topographical conditions, geological features, etc..

To evaluate the primary gold perspective of this area, the authors of this paper carried out the processing of the airborne gamma-ray spectrometer data obtained by the Division of Geophysics at 1/25,000 scale, basing on the complex of above mentioned methods.

1. Geological, geophysical, mineral features of Tiên Phước area

Geological and geophysical features: Geological formations in Tiên Phước area differ by their physical charateristics [8]. There are mainly metamorphic rocks of the Khâm Đức Formation (MP ), including biotite schist, graphite schist, feldspar quartz schist of the Lower Subformation, distributed in continuous bands, extending from the east to the west of the central part of the area. These rocks are characterized by the positive magnetic anomalies, low intensity ∆T = -30 ¸ 20 nT, rather high gamma spectrometer fields, of complex structure: Iγ = 3.5 ¸ 10 µR/h, qth = 10 ¸ 35 ppm, qu = 4 ¸ 13.5 ppm, qk = 0.5 ¸ 2.7 %, in special, rather high qth/qu and qu/qk ratios, while  qk/qth is lower: qth/qu = 3.0 ¸ 30; qu/qk = 5 ¸ 8; qk/qth < 0.2.

The amphibole schist, amphibole gneiss schist, biotite gneiss schist, biotite plagiogneiss of the Middle Subformation are located in the north and south area, differing from rocks of the Lower Subformation by complex variable magnetic fields ∆T = -140 ¸ 100 nT, rather low gamma spectrometer fields: Iγ = 1 ¸ 3 µR/h, qth= 3 ¸ 9 ppm, qu= 2 ¸ 4 ppm, qk = 0.25 ¸ 0.75 %.

Magmatism appears in the form of small-sized massifs, including: biotite-hornblende granodiorite of the Quế Sơn Complex (GDi/P2-T1 qs), located at the north and west peripheries in the form of small massifs, with magnetic field intensity ∆T = -40 ¸ 30 nT, rather high gamma spectrometer field: Iγ = 3 ¸ 7 µR/h, qth= 4 ¸ 20 ppm, qu = 4 ¸ 12.5 ppm, qk= 1.0 ¸ 2.5 %.

The dark-coloured porphyritic biotite granite of the Hải Vân Complex (G/aT3n hv) appears mainly in the south and northwest, characterized by the magnetic field ∆T = -160 ¸ 130 nT, low gamma spectrometer field: Iγ = 1 ¸ 1.5 µR/h, qth = 3 ¸ 5 ppm, qu = 2.5 ¸ 4.5 ppm, qk = 0.5 ¸ 1.5 %.

The porphyritic granosyenite, syenite rocks of the Măng Xim Complex are located in the northern periphery, having stable magnetic field ∆T = -10 ¸ 50 nT, rather high gamma spectrometer field, mainly of thorium, potassium component: Iγ = 3.5 ¸ 5 µR/h, qth = 5 ¸ 15 ppm, qu = 4 ¸ 6 ppm, qk = 1.0 ¸ 2.5 %.

The faults are clearly represented in the geophysical fields and of NW-SE, NE-SW, submeridional, subparallel trends. The special interest is in the II-order fault Long Bình - Núi Chè, of subparallel trend. It is expressed clearly in the magnetic field in the form of series of small-sized anomalies, which is the boundary between the northern positive and southern negative magnetic fields, as well as on the gamma spectrometer field. This is a thrust fault with the rising northern wing.

Primary gold mineralization:

 - Bồng Miêu gold mine: This mine was discovered before 1954. At present, the Bồng Miêu Gold Company is exploring and exploiting it.

According to the data of scale 1/10,000 of the № 501 Enterprise of the Central Việt Nam Geological Division, the Bồng Miêu gold mine comprises metamorphic rocks of the Lower Khâm Đức Subformation (MP 1) with biotite-garnet gneiss, amphibole gneiss schist, feldspar-sillimanite-quartz schist. These rocks form the Bồng Miêu anticlinal. The tectonic faults usually include the rising and subsiding processes, forming the anticlines, synclines and zones of breaking bearing quartz veins containing mineralization.

Along the faults are located mineral bodies consisting of gold-quartz veins of bed, lens and nest forms. The thickness of veins is about 10 cm to 4 m, extending about 3 km in the parallel direction. The mineralization control is the Bồng Miêu anticline, having 2 types of ore bodies: 1. Type of concordance between ore bodies and ore-bearing rocks; 2. Type of discordance between ore bodies and ore-bearing rocks.

The ore mineral composition is mainly of pyrite, galenite, hematite, chalcopyrite and pyrrhotine. The gold reserves of this mine is about 12,233 kg with average content of 14 g/t.

- Trà Dương gold mine: located in the southern part of the study area, discovered in 1990 year during the geological mapping of the Tam Kỳ - Hiệp Đức sheet-group at 1/50,000 scale. In the 1991, Mai Thất [4] carried out the study and detailed evaluation of this mine. The gold mine is situated in ancient metamorphic rocks of the Khâm Đức Formation. Analytical results show that the gold content is high, about of 0.8 up to 3.4 g/t. This mine is considered as of good prospect.

- Trà Giang gold mine: located in Trà My District, Quảng Nam Province, situated close to the southern part of area [7] (in the rural zone of the area).

The structure of the gold mine comprises biotite gneiss, biotite plagiogneiss, biotite-quartz schist of the Middle Khâm Đức Subformation (MP 2). The rocks are mainly altered by the chloritization process, penetrated by the diorite, quartz diorite, horblende granodiorite of the Trà Bồng Complex (Di-GD1/O-S tb). In the central part occur small massifs of  biotite granite, two-mica granite of the Bà Nà Complex (G/K bn).

The fault system is mainly in subparallel direction. The dip angle of the faults are of from 80 to 850. The width of cataclastic zones is about 70 to 100 m containing gold-sulphide quartz veins. These faults are the factor controlling and locating the gold ores, while the faults of NW-SE direction move the system of subparallel faults.

In the mine were detected 6 gold ore bodies, located in gold quartz dykes. The ore bodies are mainly of band and lens form, extending discontinuously in the range of from 50 to 300 m, the thickness varies from 0.2 to 1.2 m and located in the zone of chloritization, pyritization or along the strike of the schists. The ore mineral component includes pyrite, magnetite, chalcopyrite, galenite and sphalerite.

The gold content is about 2.4 to 75.5 g/t; silver content - 2.4 to 31.7 g/t. The supposed reserves for the gold: 3265 kg; for silver: 3265 kg.

Besides, during the investigation at the scale of 1/200,000 and 1/50,000 were discovered 4 primary gold occurrences in the Tiên Lập Commune, and 2 occurences in the Tiên Lanh Commune, near the left side of the Tranh River.

2. Some results of analysing the geophysical data for primary gold evaluation

For the primary gold evaluation of the Tiên Phước area, the authors have been carrying out the processing and analysis of the airborne gamma-ray spectrometer data by the above mentioned method system. To apply the method of pattern recognization 2 well-known primary gold mines were selected, namely Bồng Miêu and Trà Giang ones.

The signs used for pattern recognization are of 18 parameters: Iγ,  qTh, qU, qK, JK, JU, JTh­, F, ΔT, DK, DU, DTh, qTh/qU, qU/qK, qK/qTh, Δqkth, Δquk, Δquth.

In the results, 3 types of geophysical anomalies are contoured, representing different altered processes:

- 1st type of anomaly: including the anomalies of potassium nature, with low content of thorium, uranium: qk = 1.4 ÷ 2.2 %, Jk = 0.2 ÷ 0.4, qk/qth = 0.2 ÷ 0.4, qu = 3 ÷ 4.5 ppm, Ju = 0.3 ÷ 0. 45, qth = 2 ÷ 5 ppm, F = 1.0 ÷ 1.8. The anomalies of this type may be concerned with the sulphidization process (type 1a).

In some places, there are anomalies of high potassium and thorium contents: qk = 2 ÷ 4 %, qth = 15 ÷ 25 ppm, F =  0.6 ÷ 0.9. The anomalies of this type may be concerned with the pegmatite bodies of high potassium (type 1b).

- 2nd type of anomaly: The nature of this anomaly is mainly of potassium-uranium,  Ju –rather high, while thorium content and other parameters – lower. J = 2 ÷ 4 mr/h, qu  = 2 ÷ 4 ppm, sometimes 4 ÷ 6 ppm, qth = 2 ÷ 6 ppm, qk = 1.0 ÷ 1.6 %, Ju = 0.5 ÷ 0.76, Jth = 0.2 ÷ 0.45, jk = 0.2 ÷ 0.45, F = 0.6 ÷ 1.8, qk/qth = 0.2 ÷ 0.4, qu/qk = 6 ÷ 25, qth/qu = 2 ÷ 5. This type of anomaly may be concerned with the sulphide-quartz alteration.

- 3rd type of anomaly: The nature of this anomaly is mainly of thorium-uranium, while potassium parameter is lower. J = 3.5 ÷ 6.5 mr/h, qu = 5 ÷ 15 ppm, qth = 10 ÷ 25 ppm, Ju = 0.45 ÷ 0.7, Jth = 0.3 ÷ 0.6, qu/qk = 9 ÷ 15, qth/qu = 2 ÷ 3, F < 0.6. This type of anomaly may be concerned with the graphitization alteration.

 Synthesizing the results of pattern recognizing by Bồng Miêu, Trà Giang mines, defined geophysical anomalies and other geological data, we have contoured 6 perspective on primary gold  areas (Fig. 1), such as:

a. Bồng Miêu perspective area (I): covering almost the present Bồng Miêu gold mine and extending southward to Xeo Kcheo Village. The anomalies are distributed mainly at Núi Kẽm and Hố Gần sites, besides, there is a small area of 0.3 km2 at Xeo Kcheo, in 4 km south of Núi Kẽm and Hồ Gần mines, which has anomaly features like the above mentioned mines.

b. Trà Dương perspective area (II): extending in the subparallel direction from Trà Dương to Dương Yên, with 13 km in length, 2,8 km in width, located in the rocks of the Lower Khâm Đức Subformation, close to the northern edge of II-order Long Bình – Núi Chè fault. The fault system and zones of mylonites is very complicated.

Almost all the anomalies in this area belong to the 2nd type. The results of pattern recognization conform to Bồng Miêu mine with confidence probability of  > 80 %.

In this area the mineral evaluation at scale of 1/10,000 is carried out in an area of 10 km2 in Trà Dương Commune, besides, there is 1 gold occurence found in Dương Yên.

c. Núi  Nưa perspective area (III): extending in NE-SW direction along the fault of the same direction with 10 km in length from Hương Lam to Thôn Một, about 2 km in width. This perspective area is mainly located in the Lower Khâm Đức Subformation.

In this area are distributed anomalies of the 2nd type. The results of pattern recognization conform to Bồng Miêu mine with confidence probability of > 85 %, concentrated at 3 small sites, namely Hương Lam, Đèo Liễu and Thôn Một ones.

According to [1] 1 gold occurrence has been found at Thôn Một.


Figure 1. The result of mineral resource perspective evaluation of Tiên Phước area


d. Thôn Ba (Trà Đốc Commune) perspective area (IV): located in the south of the investigated area, extending in the subparallel direction of 8 km in length, 3 km in width, closer to southern edge of II-order Long Bình - Núi Che Fault. In the north of the area are distributed the rocks of the Lower Khâm Đức Subformation, whereas in the south there is the Middle Khâm Đức Subformation. The fault system is mainly of  NW-SE, NE-SW and subparallel directions.

In this area are distributed  the bands of 2nd and 1st anomaly types. The results of pattern recognization conform to Bồng Miêu mine with confidence probability of  > 85 %, whereas some places are conform to Trà Giang mine with confidence probability of  > 80 %.

e. Thôn Bốn (Trà Đốc Commune) perspective area (V): located close to the western edge of investigated area, extending in NW-SE direction, with the size of 11×4 km, close to the northern edge of the Long Bình - Núi Che Fault. In this area, the rocks belong mainly to the Lower Khâm Đức Subformation, in the centre appear magmatic massifs of the 2nd phase of Quế Sơn Complex. The fault system is rather complicated.

In this area the geophysical anomalies are mainly of 1st and 2nd types. The results of pattern recognization conform to Bồng Miêu and Trà Giang mines with confidence probability of  > 85 %, distributed almost at Thôn Bốn village and Núi Ba Mt.

h. Vĩnh Ninh (Tiên Lãnh Commune) perspective area (VI): located in the northwest of the area, of isometric form with the size of 5 × 4,5 km. The rocks belong mainly to the Lower and Middle Khâm Đức Subformations, located close to the eastern part the intrusive massif of Hải Vân Complex. The fault system is very complicated.

In this area are contoured the anomalies of magnetic field ∆T = -270 ¸ 185 nT, the gamma anomalies of 1st and 2nd types with high potassium content, probably concerned to potassium pegmatite bodies. The results of pattern recognization conform to Bồng Miêu mine with confidence probability of > 85 % and in some places to Trà Giang mine with confidence probability of  > 80 %.

In this area is discovered 1 gold occurrence close to the side of the Tranh River.

Besides, there are contoured 1 location of 3rd anomaly type, located in the same Hương Nhượng graphite mine and the 2 locations of 1st anomaly type with high potassium content, probably concerned to potassium pegmatite bodies, among them there is the location coinciding with the Tiên Hiệp potassium feldspar mine.

3. Results of detailed works

The authors carried out the detailed investigation in the 2 areas, namely Núi Nưa and Thôn Ba of Trà Đốc Commune, using geological observation, prospecting the heavy minerals in limited volume.

a. Results of Núi Nưa perspective area. The detailed work is carried out in an area of about 5 km2 per total 20 km2 of the whole Núi Nưa area.

  In this area there are mainly gneiss, biotite gneiss, biotite schist of the Khâm Đức Formation. The fault system is rather complicated, including tectonic mylonitization zones. The main direction of the faults is NW-SE and submeridional.

  In this area were discovered 3 zones of thermal alterion, extended in the NW-SE direction with the length of 300-750 m, the width of 30-100 m. The hydrothermal altering processes are usually the quartzitization, sericitization, beresitization. In the hydrothermal zones are located the sulphide quartz veins with the 10-50 cm thickness gold veinlets in submeridional or NW-SE direction. The average content of sulphide is about of 10 ÷ 12 %. The analytical results 7/20 samples have gold content of 12.5 ÷ 13.3 g/t, silver content of 20 ÷ 21 g/t.

Results of detailed works in Thôn Ba village (Trà Đốc Commune) perspective area. The detailed work is carried out in the area of about 6 km2 per 24 km2 of the whole Trà Đốc area. The results show that there are 3 hydrothermal zones, extended in 300-1000 m, the width varies from several to 50-70 m. In the altered zones there are systems of ore dykes of 1-2 m in thickness. The mineralization is mainly of gold sulphide quartzitization, the content of sulphide is high of 20-40 %. The main altering processes are quartzitization, sericitization, beresitization ....

  The main rocks are gneiss, biotite gneiss, biotite schist of Khâm Đức Formation. Besides, there are small massifs of biotite granite of the Hải Vân Complex, scatteredly distributed in the area. The fault system is rather complicated, including the mylonitization, cataclastic zones. The analytical results of 50 samples: 35 samples have gold content of  4 ÷ 102 g/t, silver content 9 ÷ 31 g/t.

IV. CONCLUSIONS

The mathematical methods of statistical processing the airborne gamma-ray spectrometer and gravimeter data for the geological and mineral investigation were applied in the Division of Geophysics in many years, a part of them has been used in prospecting a lot of important mineral mines. The results of data processing and the detailed work obtained in the Tiên Phước area, although with restricted volume and methods, show the objectiveness and the effectiveness of the presented method system.

The authors of this article hope that the obtained results may be applied in the other fundamental investigation fields, such as: evaluation of underground water resource, environmental fundamental investigation for the purpose of planning and sustainable socio-economic development.

This article is completed with the support of the basic research projects Nos. 7.200.06 and 7.201.06 

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