The benefits of Latin Hypercube Sampling in sequential simulation algorithms for geostatistical applications

Abstract

Sequential simulation is an extensively used algorithm for geostatistical simulations, especially the sequential Gaussian algorithm. This algorithm assumes a multivariate Gaussian model. This assumption is very convenient as it allows the local uncertainty model or conditional cumulative distribution function (ccdf) to be inferred through a few parameters given by simple kriging. The set of simulated values are drawn through Monte Carlo methods, randomly sampling the ccdf L times. In theory, this method characterises the space of uncertainty as the number of realisations increases. In practice, the number of realisations necessary varies according to the characteristics of the conditioning data. It is important that the L simulations appropriately describe the space of the uncertainty according to the objective addressed. However, in some situations, the number of simulations needs to be large, making the procedure computationally intense and time-consuming. This paper presents a more efficient strategy to generate the local ccdf based on the Latin Hypercube Sampling (LHS) technique. The objective is to replace the Monte Carlo simulation method by the LHS in order to improve the efficiency of the sequential Gaussian simulation algorithm. The use of the modified algorithm has shown that the space of uncertainty related to the random variable being modelled was obtained faster than by traditional Monte Carlo simulation for a given degree of precision. This approach also ensures that the ccdf is better represented in its entirety. This is illustrated using a case study from a Brazilian iron ore deposit.

Keywords

SEQUENTIAL GEOSTATISTICAL SIMULATION SEQUENTIAL GAUSSIAN SIMULATION LATIN HYPERCUBE SAMPLING NUMBER OF REALISATIONS CONDITIONAL CUMULATIVE DISTRIBUTION FUNCTION UNCERTAINTY EFFICIENCY

Get full access to this article

View all access options for this article.

References

Alabert

: ‘Stochastic imaging of spatial distributions using hard and soft information’, unpublished master dissertation, Stanford University, Stanford, CA, USA, 1987.

Deutsch

C. V.

and Journel

A. G.

: ‘GSLIB: geostatistical software library and user's guide', 2nd edn, 345; 1998, New York, Oxford University Press.

Godoy

M. C.

: ‘The effective management of geological risk in long-term production scheduling of open pit mines', unpublished doctoral dissertation, University of Queensland, Brisbane, Old, Australia, 2002.

Isaaks

E. H.

: ‘The application of Monte Carlo methods to the analysis of spatially correlated data', unpublished doctoral dissertation, Stanford University, Stanford, CA, USA, 1990.

Isaaks

E. H.

and Srivastava

: ‘Introduction to applied geostatistics‘, 561; 1989, New York, Oxford University Press.

Journel

A. G.

: ‘Modeling uncertainty: some conceptual thoughts‘, in ‘Geostatistics for the next century‘, (ed. Dimitrakopoulos

), 30–43; 1994, Dordrecht, Kluwer Academic Publishers.

Journel

A. G.

and Huijbregts

C. J.

: ‘Mining geostatistics‘, 600; 1978, London, Academic Press.

Koppe

V. C.

, Gambin

, Costa

J. F. C. L.

, Koppe

J. C.

, Fallon

and Davies

: ‘Análise de incerteza associada à determinação da velocidade de onda sônica em dep6sitos de carvão obtida por perfilagem geofisica - Newland coal mine - Australia', in Proc. III Cong. Brasileiro de Mina A Céu Aberto and Proc. III Cong. Brasileiro de Mina Subterrânea, Belo Horizonte, Brasil, September 2004, IBRAM, CD ROM.

Khosrowshahi

, Shaw

W. J.

and Yaetes

G. A.

: ‘Quantification of the risk using simulation of the chain of mining - case study at Escondida copper, Chile‘, in ‘Ore body modelling and strategic mine planning: uncertainbty and risk management models‘, (ed. Dimitrakopoulos

), Spectrum Series Vol. 14, 21–29; 2005, Carlton South, Vic., AusIMM.

10.

Matheron

: ‘The intrinsic random functions and their applica-tions', Adv. AppL Prob., 1973, 5, 439–468.

11.

McKay

M. D.

, Beckman

R. J.

and Conover

W. J.

: ‘A comparison of three methods for selecting values of input variables in the analysis of output from a computer code', Technometrics, 1979, 21, 239–245.

12.

Metropolis

and Ulam

: ‘The Monte Carlo method', J. Am. Stat. Assoc., 1949, 44, 335–341.

13.

Pilger

, Costa

J. F.

and Koppe

: ‘Improving the efficiency of the sequential simulation algorithm using Latin Hypercube Sampling', in Proc. 7th Int. Geostatistics Cong., (ed. Deutsch

and Leuangthong

), Vol. 2, 989–998; 2005, Dordrecht, Springer.

14.

S. F. dos Santos: ‘Redução da incerteza associada a modelos estocásticos de facies através do condicionamento a dados de produção', unpublished MSc dissertation, Universidade Federal do Espírito Santo, Vitoria, ES, Brazil, 2002.

15.

Verly

: ‘Estimation of spatial point and block distributions: the multiGaussian model', unpublished doctoral thesis, Stanford University, Stanford, CA, USA, 1984.