Independent Factor Simulation for Improved Multivariate Geostatistics

Abstract

Multivariate techniques aim to integrate multiple variables and/or data in the same framework to improve uncertainty assessment in high resolution geostatistical models. The necessity to build models that better quantify the uncertainty with limited data that are often collected with different data types has driven the latest developments in multivariate geostatistical modeling. The use of decorrelation techniques facilitates the modeling of equally sampled data, whereas cokriging is more suitable for unequally sampled data and in cases where different data types are considered. The emphasis of this thesis is on the challenges and gaps in current multivariate modeling workflows involving multivariate criteria and geostatistical cosimulation with cokriging. This thesis develops techniques that improve multivariate models of equally and unequally sampled data.

The first contribution of this thesis is on multivariate modeling of equally sampled data. An integrated framework that uses the projection pursuit multivariate transform in the context of estimation and local uncertainty assessment is proposed. Simulation of the independent factors is skipped and the local multivariate distributions are directly back-transformed for posterior uncertainty assessement. This framework provides a starting point for modeling more complicated multifactor and extreme value criteria. The applicability of the proposed methodology is shown in the context of exploration geochemistry with geochemical data collected in the Northwest Territories.

The second contribution of the thesis is the development of a methodology that combines the LMC and blind source separation theory for addressing the complexity and limitations of multivariate geostatistical workflows with the LMC and cokriging. The proposed methodology allows for independent simulation of the LMC factors with the most appropriate algorithm, improving variogram reproduction and facilitating model checking. As a consequence, this methodology offers a modern approach to the LMC that increases its applicability in geostatistical multivariate modeling. This methodology is applied in multivariate modeling of geochemical data.

Because the LMC factors have a single spatial covariance function, the most appropriate Gaussian simulation algorithm may be selected and applied to each factor independently. The third contribution of this thesis is to address the challenges of optimal selection of the simulation algorithm and provide practical recommendations based on different analyses with four common Gaussian simulation algorithms.