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