Conditional Simulation of Random Fields with Bivariate Gamma Isofactorial Distributions
- PDF / 535,981 Bytes
- 27 Pages / 432 x 648 pts Page_size
- 48 Downloads / 278 Views
Conditional Simulation of Random Fields with Bivariate Gamma Isofactorial Distributions1 Xavier Emery2 This work focuses on a random function model with gamma marginal and bivariate isofactorial distributions, which has been applied in mining geostatistics for estimating recoverable reserves by disjunctive kriging. The objective is to widen its use to conditional simulation and further its application to the modeling of continuous attributes in geosciences. First, the main properties of the bivariate gamma isofactorial distributions are analyzed, with emphasis in the destructuring of the extreme values, the presence of a proportional effect (higher variability in high-valued areas), and the asymmetry in the spatial correlation of the indicator variables with respect to the median threshold. Then, we provide examples of stationary random functions with such bivariate distributions, for which the shape parameter of the marginal distribution is half an integer. These are defined as the sum of squared independent Gaussian random fields. An iterative algorithm based on the Gibbs sampler is proposed to perform the simulation conditional to a set of existing data. Such ‘multivariate chi-square’ model generalizes the well-known multigaussian model and is more flexible, since it allows defining a shape parameter which controls the asymmetry of the marginal and bivariate distributions. KEY WORDS: Gaussian random fields, multigaussian distribution, multivariate Chi-square distribution, Gibbs sampler, destructuring effect.
INTRODUCTION Geostatistical simulation is commonly used in ore reserve evaluation to calculate the tonnages and grades above one or several cutoffs, in petroleum engineering and groundwater hydrology to study the permeability of a reservoir or an aquifer, and in environmental applications to assess whether the unsampled value of a contaminant exceeds a given threshold or not. This approach requires modeling the attribute under study by a random function and defining its spatial distribution. Many algorithms for simulating continuous attributes rely on the well-known multigaussian model. However, the mathematical convenience of this model is balanced by several limitations. In particular, the spatial distributions of the indicators are symmetrical around the median threshold and the extreme high and low values 1Received
18 July 2003; accepted 24 September 2004. of Mining Engineering, University of Chile, Avenida Tupper 2069, Santiago, Chile; e-mail: [email protected]
2Department
419 C 2005 International Association for Mathematical Geology 0882-8121/05/0500-0419/1
420
Emery
do not cluster in space (Goovaerts, 1997, p. 290). Other random function models are needed when such properties are not suited to the attribute at hand. For instance, one may resort to object-based models, substitution random functions, tessellations, truncated Gaussian or plurigaussian models (Chil`es and Delfiner, 1999, p. 449; Lantu´ejoul, 2002; Armstrong and others, 2003). This work deals with another random function model
Data Loading...
