Over the life of a mine it is often necessary to drill additional holes to address new, or changing, objectives. Most previous algorithms proposed for this purpose have aimed at reducing the block model uncertainty and enhancing the value of the drilling information as their objective functions, and have paid little or no attention to improving the accuracy of the ore/waste classification. In this paper the authors have used the misclassification probability parameter to define an objective function for the optimization of the location of additional drill holes. Using the simulated annealing method, the efficiency of the proposed objective function has been validated and proven in optimally locating additional drill holes for an application in a phosphate mine. An advantage of this objective function, compared with the usual ones, is that in addition to having a direct relationship to the kriging variance, it depends highly on the estimated and cut-off grades; the greater the difference between these grades, the less will be the misclassification probability. Since these two grades remain unchanged as the number of the drill holes increases, the only way to reduce the misclassification probability is to reduce the estimation variance by drilling the additional drill holes in appropriate locations.
AartsE. & KorstJ. (1989). Simulated Annealing and Boltzmann Machines. New York, NY: Wiley. 272 pp.
2.
AnnelsAlwyn E., 1996. Mineral Deposit Evaluation: A Practical Approach. CHAPMAN &HALL, P. 436.
3.
ArmstrongM. (1983). Comparing drilling patterns for coal reserve assessment. Proc. Aust. Inst. Min. Metall., 288, 1–15.
4.
AspieD. & BarnesR. J. (1990). Infill-Sampling Design and the Cost of Classification Errors. Mathematical Geology, 22(8), 915–932.
5.
BurgerH.; and BirkenhakeF., 1994. Geostatistics and the polygonal method: A re-examination. In: International Association for Mathematical Geology (IAMG 95) Annual Conference, pp.50–55.
6.
BrusD. J. & HeuvelinkG. B. M. (2007). Optimization of sample patterns for universal kriging of environmental variables. Geoderma, 138(1–2), 86–95.
7.
ChouD. & SchenkD. E. (1983). Optimum Locations for Exploratory Drill Holes. International Journal of Mining Engineering, 1, 343–355.
8.
ChristakosG. & OleaR. A. (1992). Sampling design for spatially distributed hydrogeologic and environmental processes. Advanced Water Resources, 15, 219–237.
9.
ChristakosG. & KillamB. R. (1993). Sampling design for classifying contaminant level using annealing search algorithms. Water Resourses Research, 29(12), 4063–4076.
10.
CressieN. (1991). Statistics for Spatial Data. New York: Wiley. 900p.
11.
DasA. C. (1950). Two-dimensional systematic sampling and the associated stratified and random sampling. Sankhya, 10, 95–108.
DebbaP., CarranzaE. M., SteinA., & MeerF. (2009). Deriving Optimal Exploration Target Zones on Mineral Prospectivity Maps. Mathematical Geosciences, 41(4), 421–446.
14.
DeutschC. V. & JournelA. G. (1992). GSLIB: geostatistical software library and user's guide. Oxford University Press.
15.
DeutschC. V. (1993). Kriging in a Finite Domain. Mathematical Geology, 25(1), 41–52.
16.
DeutschC. V. (1996). Correcting for negative weights in ordinary kriging. Computers & Geosciences, 22(7), 765–773.
17.
Drewk J., 1974. Estimation of Petroleum Exploration Success and the Effects of Resource Base Exhaustion via a Simulation Model. U.S. Geol. Survey Bull. v. 1328, 25p.
18.
EnglundE. J. & HeraviN. (1993). Conditional simulation: practical application for sampling design optimization. In SoaresA. (Ed.), Geostatistics Troia ‘92 (pp. 613–24). Dordrecht: Kluwer.
19.
FroylandG., Menabde1M., StoneP., HodsonD., 2004. The Value Of Additional Drilling To Open Pit Mining Projects. In: Proceedings of Orebody Modeling and Strategic Mine Planning - Uncertainty and Risk Management, Perth, pp. 169–176.
20.
GershonM., AllenL. E., & ManleyF. (1998). Application of a new approach for drillholes location optimization. International Journal of Mining, Reclamation and Environment, 2, 27–31.
21.
GershonM. E. (1983). Optimal Drillhole Location Using Geostatistics. Atlanta, GA: SME-AIME.
22.
GoriaS., ArmstrongM., & GalliA. (2001). Quantifying The Impact of Additional Drilling on an Openpit Gold Project. Cancun, Mexique: Proceedings of the International association for mathematical geology.
23.
GoriaS., ArmstrongM., & GalliA. (2002). Using a Bayesian approach to incorporate new information when estimating resources. Berlin: Proceedings of the International association for mathematical geology.
24.
HaselA. A. (1938). Sampling error in timber surveys. Journal of Agricultural Research, 57, 713–736.
25.
HassanipakA. A. & SharafodinM. (2003). GET: A Function for Preferential Site Selection of Additional Borehole Drilling. Exploration Mining Geology, 13, 139–146.
26.
HedarA. & FukushimaM. (2002). Hybrid simulated annealing and direct search method for nonlinear unconstrained global optimization. Optimization Methods and Software, 17, 891–912.
27.
HernandezJ. & EmeryX. (2009). A geostatistical approach to optimize sampling designs for local forest inventories. Canadian Journal of Forest Research, 39(8), 1465–1474.
28.
IsaaksE. H. & SrivastavaR. M. (1989). An introduction to applied geostatistics (p. 561). New York, NY: Oxford University Press.
29.
YenJ., LiaoJ.C., LeeB. and RandolphD., 1998, A hybrid approach to modeling metabolic systems using a genetic algorithm and simplex method. In: Proceedings of the 1995 IEEE 7th International Conference on Tools with Artificial Intelligence 28, pp. 173–191.
30.
JournelA. G. and HuijbregtsCh. J., 1978, Mining Geostatistics. Academic Press, New York/London, pp. 458, 462-4.
31.
KelleyC. T. (1999a). Detection and remediation of stagnation in the Nelder-Mead algorithm using a sufficient decrease condition. SIAM Journal on Optimization, 10, 43–55.
32.
KelleyC. T., 1999b. Iterative Methods for Optimization. SIAM Frontiers in Applied Mathematics 18, Philadelphia, PA.
33.
KimY.C., MyersD.E. and KundsonH.P., 1977. Advanced Geostatistics in Ore Reserve Estimation and Mine Planning. US Department of Energy, October.
34.
KimY. C., MartinoF., & ChopraI. (1981). Application of geostatisticsin a coal deposit. Mining Engineering, 33(11), 1476–1481.
KochG.S.Jr, and LinkR.F., 1974. A Mathematical Model to Guide the Discovery of Ore Bodies in a Coeur d'Alene Lead-Silver Mine. U.S. Bur. Mines Rept. Inv. 7989, 43 p.
37.
KvasnickaV. & PospichalJ. (1997). A hybrid of simplex method and simulated annealing. Chemometrics and Intelligent Laboratory Systems, 39, 161–173.
38.
LeeY.-M. & EllisJ. H. (1997). Estimation and simulation of lognormal random fields. Computers & Geosciences, 23(1), 19–31.
39.
LuoR., HuangY., LiangX., LuoJ., & CaoY. (2013). Optimization of the seismic processing phase-shift plus finite-difference migration operator based on a hybrid genetic and simulated annealing algorithm. Petroleum Science, 10(2), 190–194.
40.
MahalanobisP. C. (1940). A sample survey of the acreage under jute in Bengal. Sankhys, 4, 511–530.
41.
MalmqvistK., MalmqvistL., & ZwiefelH. (1980). Computer Simulation of Simulation for Deep-Seated Orebodies in Mining Districts. Econ. Geol., 75, 927–935.
42.
NelderJ. A. & MeadR. (1965). A simplex method for function minimization. The Computer Journal, 7, 308–313.
43.
QahwashA.-L. A. (1987). An optimal algorithm for drilling strategy. Energy, 12(6), 423–425.
44.
OleaR. (1999). Geostatistics for Engineers and Earth Scientists (p. 328). Holland: Kluwer Academic Publishers.
45.
QuenouilleM. H. (1949). Problems in plane sampling. Annals of Mathematical Statistics, 20, 355–375.
46.
PautschG. R., BabcockB. A. and BreidtF., 1998. Optimal Sampling under a Geostatistical Model. http://purl.umn.edu/18424.
47.
PeredoO. & OrtizJ. M. (2011). Parallel implementation of simulated annealing to reproduce multiple-point statistics. Computers & Geosciences, 37(8), 1110–1121.
48.
PilgerG. G., CostaJ. F. C. L., & KoppeJ. C. (2001). Additional Samples: Where they should be Located. Natural Resources Research, 10(3), 197–207.
49.
RogersonP. A., DelmelleE. M., BattaR., AkellaM. R., BlattA., & WilsonG. (2004). Optimal sampling design for variables with varying spatial importance. Geographical Analysis, 36, 177–194.
50.
SinclairJ. & BlackwellG. H. (2002). Applied mineral inventory estimation (p. 381). London: Cambridge University Press.
51.
SaikiaK.; SarkarB.C., 2006. Exploration drilling optimization using geostatistics: a case in Jharia Coalfield, India. Applied Earth Science (Trans. IMM B)115(1), pp. 13–22.
52.
SavinskiiI. D. (1965). Probability Tables for Locating Elliptical Underground Masses with a Rectangular Grid. New York, NY: Consultants Bureau. 110 p.
53.
SchuenemeyerJ. H., BawiecW. J., & DrewL. L. (1980). Computational Methods for a Three-Dimensional Model of the Petroleum-Discovery Process. Computers and Geosciences, 6, 323–360.
54.
ShiehS. S., ChuJ. Z., & JangS. S. (2005). An interactive sampling strategy based on information analysis and ordinary kriging for locating hot spot regions. Mathematical Geology, 37(1), 29–49.
55.
SimbahanG. C. & DobermannA. (2006). Sampling optimization based on secondary information and its utilization in soil carbon mapping. Geoderma, 133(3–4), 345–362.
56.
SingerD. A., and WickmannF. E., 1969. Probability Tables for Locating Elliptical Targets with Square, Rectangular, and Hexagonal Point-Nets. Pennsylvania State Univ., Mineral Sci. Expt.Sta., Spec. Pub. 1–69, 100 p.
57.
ShuryginA. M. (1976). The Probability of Finding Deposits and Some Optimal Search Grids. Math Geol., 8, 323–330.
58.
SoltaniS. & HezarkhaniA. (2009). Additional exploratory boreholes optimization based on three-dimensional model of ore deposit. Archives of Mining Sciences, 54, 495–506.
59.
SoltaniS., HezarkhaniA., Erhan TercanA., & KarimiB. (2011a). Use of genetic algorithm in optimally locating additional drill holes. Journal of Mining Science, 47(1), 62–72.
60.
SoltaniS. & HezarkhaniA. (2011b). Determination of realistic and statistical value of the information gathered from exploratory drilling. Natural Resources Research, 20(4), 207–216.
61.
Soltani-MohammadiS., HezarkhaniA., & Erhan TercanA. (2012). Optimally locating additional drill holes in three dimensions using grade and simulated annealing. Journal of the Geological Society of India, 80(5), 700–706.
62.
Soltani-MohammadiS., AmniehH. B., & BahadoriM. (2012). Investigating ground vibration to calculate the permissible charge weight for blasting operations of Gotvand-Olya dam underground structures. Archives of Mining Sciences, 57(3), 687–697.
63.
SoltaniS. & HezarkhaniA. (2013a). Proposed algorithm for optimization of directional additional exploratory drill holes and computer coding. Arabian Journal of Geosciences, 6(2), 455–462.
64.
Soltani-MohammadiS. & HezarkhaniA. (2013b). A Simulated Annealing-Based Algorithm to Locate Additional Drillholes for Maximizing the Realistic Value of Information. Natural Resources Research, 22(3), 229–237.
65.
SouzaL. E., CostaJ. F., & KoppeJ. C. (2004). Uncertainty estimate in resources assessment: a geostatistical contribution. Natural Resources Research, 13(1), 1–15.
66.
SzidarovszkyF. (1983). Multiobjective Observation Network Design for Regionalized Variables. International Journal of Mining Engineering, 1, 331–342.
67.
Van GroenigenJ. W. & SteinA. (1999a). Spatial simulated annealing for constrained optimization of spatial sampling schemes. Journal of Environmental Quality, 27, 1078–86.
68.
Van GroenigenJ. W., SideriusW., & SteinA. (1999b). Constrained optimisation of soil sampling for minimisation of the kriging variance. Geoderma, 87, 239–259.
69.
Van GroenigenJ. W. (2000). The influence of variogram parameters on optimal sampling schemes for mapping by kriging. Geoderma, 97, 223–236.
70.
VerlyG. (2005). Grade Control Classification of Ore and Waste: A Critical Review of Estimation and Simulation Based Procedures. Mathematical Geology, 37(5), 451.
71.
WaltonD. R. & KauffmanP. W. (1982). Some Practical Considerations in Applying Geostatistics to Coal Reserve Estimation. Dallas, TX: SME-AIME.
72.
WebsterR. and OliverM. A.,2007. Geostatistics for Environmental Scientists Wiley.
73.
WillamP.C1978. Exploration And Mining Geology. John Wiley & Sons, Inc. 430–432.
74.
WuJ., ZhengC., & ChienC. C. (2005). Cost-effective sampling network design for contaminant plume monitoring under general hydrogeological conditions. Journal of Contaminant Hydrology, 77, 41–65.
75.
XiaY.-M., ZhangG.-Q., NieS.-J., BuY.-Y., & ZhangZ.-H. (2011). Optimal control of cobalt crust seabed mining parameters based on simulated annealing genetic algorithm. Journal of Central South University of Technology, 18(3), 650–657.
76.
ZubrzyckiS. (1958). Remarks on random, stratified and systematic sampling in a plane. Colloquium Mathematicum, 6, 251–264.
