Improved method for hydrochemical exploration of mineral resources

Vietnam Journal of Earth Sciences 39(2), 167-180, DOI: 10.15625/0866-7187/39/2/9703 167 (VAST) Vietnam Academy of Science and Technology Vietnam Journal of Earth Sciences Improved method for hydrochemical exploration of mineral resources Nguyen Van Luyen*1, Oleg G. Savichev1, Viktor A. Domarenko2, Quach Duc Tin3 1Department of Hydrogeology, Engineering Geology and Hydrogeoecology, Tomsk Polytechnic University, Tomsk, Russian Federation 2Department of Geoecology and Geochemistry, Tomsk Polytechnic University, Tomsk, Russian Federation 3Department of the Science, Technology and International Cooperation, General Department of Geology and Minerals of Vietnam (GDGMV) Received 09 January 2017. Accepted 10 April 2017 ABSTRACT The article deals with a method for hydrochemical exploration and poorly studied areas based on the simulation and statistical modeling of the hydrochemical field. The peculiarity of the method is a prospecting area spotting under the following conditions: (1) the maximal ratio between river basin in the Riverhead without evident channel network and the total river basin; (2) the river network and tectonic deformations maximum; (3) presence of low-flow rate sections with relatively sharp breaks in grade of the water surface (outflow of rivers from mountainous areas onto the sub-mountain plain, extended sections of channel multi-branching). A sampling of 2-3 samples of surface water, 2-3 samples of river bed sediments, and 2-3 samples of ground water is taken at prospective sections and contiguous terri- tories and the chemical composition determined. The geo-informational analysis and obtained data are used to deter- mine the parameters of the model of the area under study, a predictive assessment of the hydrochemical indicators for prospective sections is carried out, and a detailed examination is planned and performed. The expected reduction in the cost of exploration compared to currently used methods is approximately 20%. Keywords: Hydrochemical exploration, hydrochemical background, anomaly. ©2017 Vietnam Academy of Science and Technology 1. Introduction1 The discovery of hydrochemical anomalies is one of the most important stages of geo- chemical exploration for mineral resources and solving a range of geo-ecological tasks (environmental impact assessments for con- struction, setting permitted water pollution *Corresponding author, Email: Luyennv@mail.ru  levels, and others), and typically comprises the taking and subsequent analysis of a large number of samples of water, bed sediment, soil, rock, and vegetation at points on a regu- lar grid. For example, in the Russian Federa- tion, the current recommendation when con- ducting geochemical surveys on a scale of 1:200.000 is to take samples each 4 km2 with the potential for increasing density to 1 point Nguyen Van Luyen, et al./Vietnam Journal of Earth Sciences 39 (2017) 168 per 1-2 km2 (Requirements, 2002). The volume of samples increases significantly when performing work at a high level of de- tail, which results in the time and expenditure needed to perform the work increasing to the point that profitability is lost. But that is only a part of the problem in increasing the general effectiveness of predictive and exploratory geological and geo-ecological works, the key factor for resolution of which is improving the (express or implied) geochemical models on which any hydrochemical study method is based. A fairly complete survey of such models, methods, and methodologies for hydrochemi- cal exploration of mineral resources is provid- ed in the literature (Barsukov et al., 1981; Ko- lotov, 1992; Kraynov, Ryzhenko, Shvets, 2004; Kopylova, Guseva, 2014; Domarenko, 2012; Polikarpochkin, 1976; Shvartsev et al., 2005). Without repeating previous publica- tions, we note that two main concepts are typ- ically considered. The first comprises the presence of a sufficiently strong source from some geological epoch (usually of trans- magmatic origin) forming the primary geo- chemical halo. This source is typically camou- flaged by the formation of various origins forming the medium for the secondary geo- chemical halo but may be detected if there is a certain ratio of erosion and accumulative pro- cesses. Where there is a significant prevalence of the first (erosion) and an insufficiently “strong” source of chemical elements and compounds, geochemical anomalies are not formed or are concentrated in the crust with- out the formation of a mineral resource depos- it, and where the second (accumulative pro- cesses) prevails, the geochemical halo is spa- tially limited and/or very difficult to detect. In this case, hydrochemical exploration is limited to studying the hydraulic erosion formations and tracing migratory water flows, which of- ten involve the migration of chemical ele- ments in suspension and the movement of stream sediments, or, somewhat more rarely - in solution (Shvartsev S.L et al., 1997). The most obvious example of the use of this kind of approach is the exploration for placer gold deposits in river valleys (Domarenko, 2012; Lavyorov, Patyk-Kara, 1997). The second concept assumes that even ab- sent a single source it is possible that accumu- lative processes may prevail over migratory processes, which (if maintained over an ex- tended period of geological time) may result in the formation of geochemical anomalies, including the formation of mineral resource deposits (Shvartsev S.L, 2008). This preva- lence is most commonly due to relatively sud- den global or regional changes in geochemical conditions on a geological time scale, signifi- cantly more rarely it is the result of modern processes (many geologists effectively view the latter case as a variation of remote location of the principal source and transformation of the geochemical halos (Lavyorov, Patyk-Kara, 1997; Mezhelovsky et al., 2001; Levashov et al., 2010). In both cases, the hydrochemical study methodology is based on consideration of ge- ochemical processes and includes planning and conducting sampling, laboratory work, and assessment of “background” and “anoma- lous” concentrations, as a rule in accordance with the accepted a priori law of the distribu- tion of probabilities. Usually, this is normal (Gaussian) or log-normal distribution and the key rule for detecting anomalies is exceeding the interval limits (E((С))–k((С)); E((С))+ k((С))), where E((С)) is the expected value of function (С) of concentra- tion С (including case (С)=С); ((С)) is the standard deviation of (С); k - inverse nor- mal distribution at the level of significance  (The Instruction, 1965; Perelman, 1979; Davis, 1986). Differences between the ap- proaches described above are mainly found in the choice of environmental components stud- ied, the form of migration of their chemical Vietnam Journal of Earth Sciences 39(2), 167-180 169 elements, and density of the sampling grid, which depend on the scale of exploration. The authors’ work under consideration at- tempts to: (1) build a simulated statistical model of the formation of hydrochemical anomalies that is not contrary to either con- cept and (2) to use the model as the basis for the development of a hydrochemical explora- tion method capable of reducing the volume of sampling without reducing effectiveness. 2. Theory and Basic model A mathematical model is a convenient tool for studying reality, based on taking key pa- rameters and the relationships between the parameters that define a system as a whole and disregarding other factors on the basis of error analysis of the related elements and rela- tionships. This definition is also simultaneous- ly a formulation of the limits on use of mod- els: (1) if there are changes in the system as a complex of defined functions corresponding to the structure formed in the specified condi- tions - a set of elements (at the level of physi- cal development or conceptualization) and the relationships between them, then the model used to study it must also be changed; (2) modelling is no different from guesswork if the error in determining modelling parame- ters is comparable to or greater than the error in predictive estimates made using the mod- els. Correspondingly, these limits also formu- late the main principles of modeling: (1) the probability the model is not adequately realis- tic is more than zero; (2) the adequacy of the model is evaluated for the weakest link (Loucks D.P et al., 2005). The hydrochemical study process often us- es some simplified mass transfer equations, which in one-dimensional form may be writ- ten as follows:  Cf x CD xx Cv t С         , (1) where С - substance concentration in the water medium; t and x - time and space coor- dinates; v - velocity of flow; D - hydrodynam- ic dispersion coefficient; f(C) - a function characterising hydrochemical processes in the system and the introduction of substances from outside the system (Kraynov, Ryzhenko, Shvets, 2004; Lerman, 1979; Lekhov, 2010; Benedini, Tsakiris, 2013). Equation (1) is usually used in conjunction with a flowchart of initial and boundary conditions and certain simplifications. These conditions very com- monly follow two options, when considering: (1) a thermodynamic model, provided f(C)=0; (2) a hydrodynamic stationary model with maximum simplification f(C)=0 or f(C)= -kCC (kC - a parameter essentially corresponding to specific speed of change С), which, in turn, is additionally simplified by excluding either diffusion or advective components. Another extremely important aspect of simulation modeling is the choice of means of description D. Typically it is oriented on eval- uating the parameters of equation (2): vDD m   , (2) where Dm - molecular diffusion coefficient;  - dispersion parameter (dispersive-ness pa- rameter). In many cases where hydrodynamic models are used, D is taken as a constant, while f(C)=0, which effectively corresponds to the propagation of flow disturbance an un- limited distance and liquidation (or substantial weakening) of the impulse source. However, if it is considered in general as a non-linear function of С, then given the results of studies of heat disturbance propagation in a non- linear environment (Martinson L.K et al., 1996), it is possible to note the ability to local- ize increased substance concentrations within a limited spatial area due to volume absorp- tion, when the "warming wave" is replaced by a "cooling wave" changing the direction of the. For the studied element and other chemi- cal elements also, the resulting concentration gradient is an important factor in the for- mation of the geochemical barrier, which cre- Nguyen Van Luyen, et al./Vietnam Journal of Earth Sciences 39 (2017) 170 ates a stronger spatial localization effect for high concentrations in the geological medium. A similar effect is displayed in the for- mation of the structure section of peat depos- its when significant changes in humidity occur at the boundaries of active and inert layers that have a non-linear relationship with hy- draulic conductivity, hydrodynamic dispersion of dissolved salts and the function f(C) (Savi- chev O.G, 2015). It can be amplified by a sig- nificant reduction in oxygen access and, as a result, a change in the redox conditions, re- moval of low-solubility compounds by both chemical reaction and absorption processes involving the generation of a layer preventing substance diffusion and the infiltration of at- mospheric precipitation (Shvartsev S.L, 2015; Lasaga A.C, 1995). This effect can also be preserved after very significant environmental changes (according to (Gamov M.I et al., 2012), when the upper and lower boundaries of coal seams are often characterized by the presence of layers with a higher content of a range of chemical elements). Analysis of hydrochemical and hydrologi- cal monitoring observations of Eurasian rivers (Fadeev et al., 1989; Savichev, Nguyen, 2015) indicate that substance concentration С in wa- ter flows is related to water discharge Q. The nature of this relationship may be shown upon analysis of the system of standard differential equations describing changes over time of С and Q: Ck dt dC C  , (3) Qk dt dQ Q  , (4) Where kC and kQ - specific velocity of change in substance concentration and water discharge, respectively. The ratio of kC and kQ is generally a function of water mass and tem- perature travel, which means (5) can be written. 2 0 10 k Q C Q Qkk k k     , (5) Where k0, k1, k2 - empirical coefficients; Q0 - water discharge corresponding to certain initial conditions. In the light of the above, and using chain rule differentiation of the complex function, we obtain equation (6):    120 21 kk XkkXZ exp , (6) Where Z=C/С0 and X=Q/Q0 - modular co- efficients of concentration and water flow rate; С0 - the substance concentration corre- sponding to certain initial conditions. If the ratio of kC and kQ changes little over time, ex- pression (6) takes on a power-law relationship of C to Q, which is widely used in hydro- chemistry and close in significance to the in- direct indicators of substance migration in water used in geochemistry (Savichev O.G, 2010-2015). Equation (6) enables a description of the temporal changes in the chemical composition of natural waters relating to the corresponding fluctuations in water runoff at a specific out- flow but is difficult to apply without addition- al conditions for describing the spatial chang- es. In the latter case, it appears better to use expression (7), which was derived in (Savi- chev O.G et al., 2014) as a result of resolving a simplified equation for substance travel pri- marily due to advective transfer, provided the drainage basin of a river with area F can be presented as part of an annulus with an angle at centre  and radius L, and the water mass movement is from the edge sector to towards the centre of the reference circle. 3 0 0 00 k UU U F F Y Y CC    ,, , (7) Where C0 and Y0 - characteristic substance concentrations for the period of time under consideration and depth of runoff from a river basin with area F; C0,U and Y0,U - substance Vietnam Journal of Earth Sciences 39(2), 167-180 171 concentration and depth of runoff from the section of the river basin with area FU at an upper course without a pronounced channel; k3 - coefficient reflecting the conditions for transfer from the run off layer to the reference average depth of flow and the chosen time scale. Assuming that the geochemical anoma- ly is situated in the inaccessible territory at the river source, the use of equation (7) with known values for C0 allows a significant re- duction of time and effort in the process of determining C0,U (Savichev O.G et al., 2005). The presence of a large number of factors and the nature of the processes whereby geo- chemical anomalies are formed means that concentrations of substances in the geological medium can be treated as random amounts, the behavior of which can be described by one of the laws of the probability distribution. In geochemical practice, as noted above, normal and lognormal distributions are most com- monly used for these purposes. However, a number of other approaches should not be overlooked, e.g., proposals to use gamma dis- tribution when describing hydrochemical run off (Dolgonosov B.V et al., 2015). However, the most logical and, simultaneously, simple choice is lognormal distribution, on the basis of the following assumptions (Savichev O.G, 2010, 2015). (1) Consideration is given to the water- rock system formed under the influence of natural and anthropogenic factors over the course of a statistically homogeneous period. Individual components of this system are in quasi-equilibrium and characterized by Ns chemical reactions, which, subject to (Garrels R.M et al., 1965; Grenthe I et al., 1997), may be combined into a single overall reaction cor- responding to equations (8, 9):       0 1 T N i iT KTRG s lnln , (8)   sN j jjy CbbC lnln 0 , (9) Where GT and К0T - the overall change in Heimholtz free energy and the overall equilib- rium constant at a given temperature Т; Пi - the overall production of active components involved in each reaction; Cy - the concentra- tion of the target substance; b0, bj are con- stants. (2) The total quantity of substance Ns+1 is highly significant, which with consideration for the law of large numbers allows the prob- ability distribution for ln C (and the character- istic time of transformation of the substance subject to (3)) to be treated as normal, and for the concentration С, log-normal. (3) The expected value of E(C), based on (6, 9) provided probability Ns-1 is approxi- mately constant, approximates to the geomet- rical mean Сg, and the standard deviation (subject to Taylor series expansion) - to func- tion of С0 and coefficient of water discharge variation Cv (Q):          QCvCkkQCvCkkC g  10010 (10) Absent data on timed water discharges (or average daily discharges in overwetting zone), the annual water runoff coefficient of varia- tion, calculated empirically depending on the area of the drainage basin F and the average specific discharge MQ,a can be used in formula (10) as a first approximation. In particular, with consideration for the formula of S.N. Kritsky and M.F. Menkel (following (Chebo- taryov N.P, 1962)), expression (10) takes the form:   270060 4 , , , aQ g MF Ck C   . (11) Where k4 - empirical coefficient. Summarizing the data, we note three key aspects of the simulated statistical hydro- chemical model under consideration. First, the parameters С0 and Q0 in (5-7, 9) may be inter- preted as the expected value of substance con- centrations and water flow rates. However, Nguyen Van Luyen, et al./Vietnam Journal of Earth Sciences 39 (2017) 172 С0Сg, and Q0Qa, where Сg - the geometric mean; Qa - the arithmetic mean. Absent ob- servational data, the geometric mean value of Сg, can be estimated in the assumption that for a statistically homogeneous period the ex- pected value of the hydrochemical run off G0 from a unit of area of the drainage basin with a pronounced channel network (at each mo- ment of time G=CQ) should not vary signifi- cantly, that is: 00    F G dt d . (12) or 14 4  k aQsg aQ k aQ sg aQ sQ sgg MCM M C M M CС ,, , , , , , , (13) Where MQ,a and MQ,s- the arithmetic mean water runoff module at the present time, and at the commencement of functioning of the studied geosystem; Сg and Сg,s - the geometric mean substance concentrations corresponding to MQ,a and MQ,s. Second, the deviation of substance concen- tration from С0 is determined: (а) in time - by fluctuations in water runoff according to (6); (b) in space - by the degree of drainage of the territory with higher substance content (C0,U) in various components of the river network. Where k3 is a positive value, the latter is di- rectly proportional to the area of the drainage basin from a river source without a pro- nounced channel FU according to (7), as well as the contiguousness of the river network and tectonic structures, which can be estimated by variations P(rf)-P(r)P(f), where: P(r) - drain- age network density, equivalent to the proba- bility of channel migration of surface waters; P(f)- density of distribution of tectonic faults within the river basin; P(rf) - probability of the river network and tectonic faults coinciding. Third, subject to (Alekseyenko V. A et al., 2005), the background concentration of sub- stances in a body of water (in water or bed sediment) may be treated as an expected value and estimated by determining the confidence interval for the geometric mean after exclud- ing anomalous concentrations Cex. The latter are estimated in accordance with condition (14), and an integrated procedure for deter- mining hydrochemical background and anom- alies:     QCvkkCС gex  101  , (14) Where  - the normal distribution quantile with probability /2;  - the significance lev- el. Subject to a minimum margin of error in determining water discharges and substance concentrations in the water medium, and the recommendations of (Rozhdesvensky, Chebo- tarev, 1974), it is appropriate to take =5%, respectively - 2. Thus, the model of hydrochemical pro- cesses in the supergene zone in general de- scribed by the equations (6-9, 13-14), allows describing a condition and long-term changes of system “water - rock”. This model corre- sponds to the key concept: the hydromineral complex is the genetically connected associa- tion of connections of the chemical elements formed in a direction to equilibrium in the system “water - rock” and controllable by wa- ter flow intensity (as the factor determining time and conditions of such interactions) (Kopylova Yu. G at el, 2014; Udodov P.A at al., 1962; Shvartsev S.L, 2005, 2008). 3. Results 3.1. Method of hydrochemical exploration for mineral resources Adaptation of the simulated statistical hy- drochemical model described above to hydro chemical study practices with consideration for previous research (Savichev et al, 2015) enabled the formulation of the following prin- cipal provisions and phases of a method of hydrochemical exploration for mineral re- sources in poorly or unstudied inaccessible territories: Geo-informatic analysis of the studied ter- ritory is carried out to determine the following parameters: Vietnam Journal of Earth Sciences 39(2), 167-180 173 - Determination of sections with a relative- ly weakly pronounced channel network, de- termination of their area FU and the total area of the drainage basin F; - Determination of the denseness of the river network P(r) - ratio of channel network length to area of the river basin, density of tectonic fault distribution P(f) - ratio of total length of faults (according to geological map) to area of drainage basin under consideration, probability of coincidence of the river net- work and tectonic faults P(rf) - ratio of the length of the river network coincidence with tectonic faults (subject to map scale and dou- bled margin of error in determining distance using the map) to the area of the drainage ba- sin and calculation of differences P(rf)- P(r)P(f); - As a first approximation, the N1 sections with maximum FU/F and P(rf)-P(r)P(f) val- ues are taken as the most promising for explo- ration; the perspective of sections is assessed from the viewpoint of the first concept (strong source); - N2 low-flow sections with relatively sharp changes in water surface grade (river outflow from mountains to plain, sections with extensive braiding) are determined; the perspective of these sections is assessed from the standpoint of both concepts (strong source and accumulative processes prevailing over substance migration); - A list N3 of prospective sections is formed following the rule: N3= N1 + N2, (15) Where  - expert evaluation of the desira- bility of performing exploratory works at the N2 sections based on the results of analysis of the location of resources formed under similar geographical conditions (analogy principle); for each N3 water flow: - The depth of runoff Y or specific dis- charge MQ (where possible, the coefficient of the water discharge variation Cv(Q)) is deter- mined for the drainage basin as a whole, for the section of the drainage basin without a pronounced channel network, and for other territories using the methods accepted in hy- drogeological practice (Mujumdar P.P et al., 2012); where it is not possible to reliably de- termine the change in water runoff layer for the territory, Y/Y0=1 is applied; - The period of time  in which the water runoff is approximately equal to the long-term average is determined, with CCg; - 2-3 water samples and 2-3 bed sediment samples, and if possible 2-3 water samples from the aquifer drained as much as possible by water flow are taken during the period . At least one sample (No.1) from each of the indicated components (surface water, bed sed- iment, groundwater) must be situated on the section with a relatively weakly pronounced channel network FU, one sample (No.2) from the outflow forming the boundary of area F. Efforts should be made to ensure that the samples are taken at sections of the drainage basin with differing water surface grades. Sample No.3 may be taken from a section with relatively sharp changes in grade. The water and bed sediment samples shall be tak- en and their chemical composition determined in accordance with regulatory documents, for example, in the Russian Federation in accord- ance with (Requirements to manufacture.); - For known values of concentrations С1, С2 (С3) and the corresponding values of drainage basin area F1, F2 (F3) back-calculation using formula (7) determines the coefficient k3; - The geometrical mean value of concen- tration Cg is calculated in the outlet of the drainage basin with area F using formula (13) and standard deviation using formulas (10, 11); - Concentration C0,U is calculated at the drainage basin section at the river source without a pronounced channel and/or for sec- tions with a sharp change in grade (for con- centrations С2, С3 and Cg); if the derived value of C0,U conforms to condition (14), the said Nguyen Van Luyen, et al./Vietnam Journal of Earth Sciences 39 (2017) 174 section is deemed to have maximum prospec- tive in terms of mineral resource exploration; if condition (14) is not met, expert evaluations of the value of C0,U at which the section is considered to have prospective may be used (for example, by analogy); - Detailed geological and geochemical studies of the designated sections with high C0,U values are planned and conducted with a greater sampling frequency of river bed sedi- ments and other environmental components; - The data obtained is used to calculate the geometric mean and standard deviation and test condition (14); a geological-economic assessment of the territory is performed in the event of anomalous concentrations. Partial testing of the method was per- formed using data on the chemical composi- tion of Northern Vietnamese water flows (Bac Kan province, Cho Don district, Red River and Thai Binh River drainage basins, namely the interfluvial area of major tributaries - the Gam River and Cau River). The geological structure of the studied area involves three structural levels lying on the pre-Paleozoic granite-metamorphic foundation of the lower structural stage and not penetrated within the area (Figure 1). The middle structural level is formed from large graben syncline with Or- dovician-Silurian and Devonian sedimenta- tion. The graben syncline structure is compli- cated by sub-isometric depressions filled with upper Triassic deposits in the south-western area of the territory. The sedimentation is penetrated by varied, complex structured in- trusions of gabbro-granite series from the up- per Paleozoic and Meso-Cenozoic stages of tectonic-magmatic activation. Tectonic struc- tures of various ages and orientations create a mosaic/block structure in the district and are the main factor favoring development of the river network in the territory. The district metals profile is determined by a significant quantity of occurrences and small deposits of lead, zinc, iron, manganese, apparently strati- form (Dao Manh Tien, 1984). The main study targets are: the Cau river: (section of upper stream) - a large tributary of the Hong River system; the Pho Day river (tributary of the Hong river) and its tributary the Pho Day river; the Ta Dieng river, which flows into the Ba Be lake; the Ban Thi river (tributary of the Gam river) and its tributary the Che Ngu river (Figure 1). Nguyen Van Luyen took 10 river water samples from a layer 0.3-0.5 m below the surface on 14-16 February 2015 (with the concurrent measuring of water temperature, specific electrical con- ductivity, and pH) using specially prepared containers. Laboratory work was performed at the accredited hydrochemical laboratory of Tomsk Polytechnic University (state accredi- tation number No. ROSS RU. 0001.511901 of 12.07.2011). The specific electrical conduc- tivity, permanganate demand, pH, and con- centrations of Ca2+, Mg2+, Na+, K+, HCO3–, CO32–, CO2, Cl–, SO42–, Si, NH4+, NO2–, NO3–, PO43–, Fe, Zn, Cd, Pb, Cu, Al in the samples were determined. According to a considered method on a digital map (in a format of MapInfo) of scale 1: 50.000 total areas F of river basins and sec- tions with a relatively weakly pronounced channel network FU have been determined. Calculation of extent of tectonic faults and sites of concurrences of river valleys and tec- tonic faults is executed on a digital geological map of scale 1:200.000 (concurrence was es- timated on a curve bending around which was carried out on meanders of the river in view of an error of definition of a map distance at a rate of 0.5 mm in the specified scale). As a result of the study, the results of which are described in more detail in the work of O. G. Savichev and Nguyen Van Luyen (Savichev O.G et al., 2015), it was proven that the highest concentrations of Zn and Pb were found in the waters of the River Ban Thi and upper part of the Day river (where the Cho Dien deposit was previously discovered at Ban Thi with Pb+Zn reserves of approximate- Vietnam Journal of Earth Sciences 39(2), 167-180 175 ly 10 million tons with a content of 3-24%, and the Bang Lung deposit with reserves of more than 5 million tons, Pb content up to 9.5% and Zn up to 4.25%). These sections coincide with Devonian deposits, intensive tectonic faults, and are characterized by the highest values of FU/F and P(rf)-P(r)P(f), with the strongest association with the ratio FU/F found for lead, and for the difference P(rf)-P(r)P(f) - with Zn (Figure 2, 3). Figure 1. Geological structure of study area 1:200,000 (according to (Nguyen Kinh Quoc. 2001)), as amended), showing surface water hydrodynamic observation points (1): I - Undiscriminated Quaternary; II - Van Lang for- mation (upper subformation); III - Van Lang formation (lower subformation); IV - Van Lang formation (Phia Bioc complex); V - Van Lang formation (Nui Chua Complex); VI - Khao Loc formation; VII - Mia Le formation; VIII - Pia Phuong formation (subformation: a - upper; b - lower); IX - Phu Ngu formation (subformation: a - upper; b - middle; c - lower) Nguyen Van Luyen, et al./Vietnam Journal of Earth Sciences 39 (2017) 176 Figure 2. The relationship between (С)Zn and (С)Pb concentration and the ratio of the overall drainage basin area F and area of the upper without river network FU (Zn=228.6(F/FU)-1,35; the trend line: solid line of blue square - Ф(I)=C(Zn)Y/YU= 1575,540(F/FU)-3,140, R2=0,83; broken brown lines Ф(I)=C(Pb)Y/YU = 95,211(F/FU)-2,422, R2=0,63 correlation ratio R2=0,39; Pb=63.6(F/FU)-1,81; R2=0,73; critical value taken as Rlim2=0,36) (according to (Statistical data of the People’s Committee of Cho Don District), disregarding sample NM03, taken next to a factory); dotted line indicates trend; line colour corresponds to colour of Zn and Pb symbols Figure 3. The relationship between Zn and Pb concentrations and the difference in probability of intersecting a tec- tonic fault P(rf) and derived value P(r) and P(f) (Zn=4.9(P(rf) - P(r)P(f))+13.8; R2=0.81; Pb=0.6(P(rf) - P(r)P(f))+1.6; R2=0.68; Rlim2=0.36) (according to (Statistical data of the People’s Committee of Cho Don District), disregarding sample NM03, taken next to a factory); dotted line indicates trend; colour of line corresponds to colour of Zn and Pb symbols 0 2 4 6 8 10 12 14 0 20 40 60 80 100 0 5 10 15 Ф( II), мк г/д м3 Ф( I), мк г/д м3 F/FU Ф(I) Ф(II) 0 1 2 3 4 5 0 1 2 3 4 0.0 0.2 0.4 0.6 0.8 1.0 Pb , m g/k g Zn , m g/k g P(r|f), км/км2 Zn Pb Vietnam Journal of Earth Sciences 39(2), 167-180 177 Thus, changes of concentration Zn and Pb in river waters of researched territory as a whole are well described by the equation (7). Thus the maximal concentration Zn and Pb are observed on sites of known ore display of these metals for which ratio F/FU is minimal, and difference P(rf)-P(r)P(f) is maximal. The physical sense of the received result con- sists the probability of formation of geochem- ical anomalies essentially increasing at the presence of a source of substance (access to which is realized on tectonic faults) and con- cerning low water migration. In result of such site accumulation of substance prevails in comparison with its carrying out. If similar situation is observed under rather constant conditions or the gradual reduction in intensi- ty of water exchange during enough long time then it can lead to accumulation of the sub- stance in the increased or high concentration. Certainly, it is only one of variants of the suc- cession of events, but as has shown the analy- sis of the received data, its probability in some cases allows to use ratio F/FU and P(rf)- P(r)P(f) as criteria of geochemical explora- tion for mineral resources. 4. Discussions Thus, one of the key factors in the for- mation of the chemical composition of natural and natural-anthropogenic water is the intensi- ty of water exchange, regulating the time and conditions of interactions in "water-rock" sys- tem (Lerman, 1979; Kraynov, Ryzhenko, Shvets, 2004; Shvartsev, 2008). The most im- portant characteristics of the water exchange rate (in terms of its effect on the chemical composition of water) are the module of a water flow (water flow per unit time per unit area) and modular water flow rates (the ratio of water flow at a particular time or on aver- age over a period of expectation). The relationship between the modular co- efficients of concentration and water flow rate looks as the function of the gamma distribu- tion (6). But the most part of observations usually corresponds to the recession curve, which looks as the inverse power dependence. A similar relationship is characteristic for the geometric mean hydrochemical indices, but with the norm (term average value) of module water flow. The most significant changes in the chemical composition of natural waters occur at the stage of the slope, subsurface and groundwater flow when the depending on the speed of movement of water generated the set of basic chemical reactions and physical- chemical processes, determining hydrochemi- cal "background". At the stage of streamflow, this complex may vary, but not so much. Moreover, the standard deviation of hydro- chemical indicators in direct proportion to the respective geometric mean and coefficient of variation of water flow (10). The latter value is inversely proportional to the area of the catchment (11). Respectively, it can be con- cluded that the variability of the concentration of the solutes decreases somewhat for large water bodies (both surface and underground) compared with smaller. Another aspect of the impact of water flow on the chemical composition of wa- ter is to increase the content of substances at levels: (1) strengthening of the conjuga- tion of the river network and tectonic dis- turbances; (2) decreasing in the ratio of general catchment area (in the numerator) for its part in the origins of the river with- out the expressed channel network (the denominator). Both features characterize the conditions of interaction of water with the rock (with primary aluminosilicate minerals and products of chemical reac- tions). Analysis of the data revealed a sta- tistically significant relationship between the conditional probability confinement river network to tectonic disturbances P(r|f) and the concentrations of substances in river waters and sediments, and also found an association between the condi- Nguyen Van Luyen, et al./Vietnam Journal of Earth Sciences 39 (2017) 178 tional probability P(r|f) and empirical probability concentrations (Figure 4). Sat- isfactory convergence of the measured and calculated concentrations of Zn and Pb in river waters and sediments is achieved by using dependence (7). Figure 4. The relationship between the empirical probability of Zn concentrations in bed sediments and the condi- tional probability P(r|f); P(Zn)=86.433P(r|f), R2=0.53 In general, the catchment areas of the riv- ers studied, where mining is carried out lead- zinc ores, items with elevated concentrations of Zn, Pb, and some other elements are asso- ciated, on the one hand, to the overlapping portions of the river network, part of the wa- tercourses which is confined to the tectonic faults controlling the placement of lead-zinc occurrences and deposits, due to increased removal of chemical elements from the ore bodies. On the other hand, the increase in the concentrations of these elements with respect to the local geochemical background in gen- eral, the higher the larger the poorly drained catchment area in the vicinity of the manifes- tations and the closer is an anomaly of the enterprises for extraction and processing of ores. Depending on the distribution of chemical elements in the water objects at different dis- tances from the extraction sources and the enrichment of lead and zinc ores, the correla- tion coefficients between the conditional probability P(r|f) and the content of heavy metal elements can be varied as: (1) Zn in riv- er waters 0,730.16; (2) Zn in extracted water from sediments 0,700.16; (3) Pb in river wa- ters 0,440.18; (4) Pb in extracted water from sediments 0,690.16. The high values are mainly found in the area near the mining areas. Generally, the probability of detection of anomalous concentrations of Pb and Zn in sediments and river waters between the rivers Lo and Cau increased providing the rate of conjugation of the river network and tectonic disturbances P(r|f) more 0,6 km/km2, а the ratio of the catchment area and the upper part without the expressed channel network F/FU. 5. Conclusion A simple simulated statistical model of the hydrochemical field is proposed, with the fol- lowing key aspects: (1) concentrations of sub- stances in surface and ground water, and river bed sediment are generally treated as random values subject to a lognormal probability dis- tribution; (2) the hydrochemical background 0.0 20.0 40.0 60.0 80.0 100.0 0.0 0.2 0.4 0.6 0.8 1.0 P (Zn ), % P(r|f), km/km2 Vietnam Journal of Earth Sciences 39(2), 167-180 179 is taken as the expected value of the indicator for a section with approximately homogene- ous geological landscape and hydrological conditions and calculated as the geometric mean; (3) fluctuations in concentrations rela- tive to the background values have a non- linear correlation with the modular coefficient of water flow, and the standard deviation is directly proportional to the hydrochemical background and coefficient of variation of the water runoff. A method for hydrochemical exploration and poorly studied areas is proposed on the basis of this model. The distinguishing feature of this method is the determination of pro- spective sections using the following criteria: (1) maximum ratio of the area of the drainage basin at a river source without a pronounced channel network to the total area of the drain- age basin; (2) maximum association of the river network with tectonic faults; (3) pres- ence of low-flow rate sections with relatively sharp water surface grade changes (outflow of rivers from mountains to plain, extensive sec- tions with braiding). 2-3 surface water sam- ples, 2-3 river sediment samples, and 2-3 ground water samples are taken at promising sections and contiguous territories, and the chemical composition determined. 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