| One of the aims of geostatistics is to integrate information of very different nature, such as well logs, a geological scenario and a geophysical impedance cube, into a consistent numerical model. Of particular interest is the geological scenario and more generally the structural model that links local data together in space. The geological scenario is usually integrated into the 3D numerical model using a sequential simulation algorithm. Sequential simulation, in the simple case of indicator variables, involves the estimation of several increasingly complex indicator conditional expectations. If high order statistics, higher than order two, are to be accounted for, the estimation of these conditional expectations is made difficult by the huge number of parameters to be estimated. Casting the problem into the framework of reproducing kernel Hilbert spaces, we propose a method for determining the best estimator of a conditional expectation. An important property of the proposed estimator is that its complexity does not depend on the complexity of the conditioning event, hence allowing performing sequential simulation without relying on the Markov hypothesis typically called for to limit the size of the conditioning event.; Integrating the structural model (layering, faults, etc.) into the final numerical model requires geostatistical routines that can operate directly on the data structure used to represent the structural model. While many CAD programs are currently capable of modeling complex geometries and topologies, no available geostatistics toolkit provides algorithm implementations that are independent of the data structure used to represent the simulation grid. The GsTL library capitalizes on the advent of generic programming to provide a comprehensive set of geostatistics routines which can be applied on any type of grid data-structure. Two applications of GsTL are presented: the use of a GsTL simulation routine on two different Gocad data structures, and the design of a new geostatistics software. S-GeMS, entirely built on the GsTL library. S-GeMS is a cross-platform software and offers the more common geostatistics algorithms, such as kriging of one or more variables, sequential and multiple-point simulations. Its source code is made available to everyone to study, modify and redistribute. |
