Multivariate grid-free geostatistical simulation with point or block scale secondary data

Abstract

A novel grid-free geostatistical simulation method (GFS) allows representing coregionalized variables as an analytical function of the coordinates of the simulation locations. Simulation on unstructured grids, regridding and refinement of available realizations of natural phenomena including, but not limited to, environmental systems are possible with GFS in a consistent manner. The unconditional realizations are generated by utilizing the linear model of coregionalization and Fourier series-based decomposition of the covariance function. The conditioning to data is performed by kriging. The data can be measured at scattered point-scale locations or sampled at a block scale. Secondary data are usually used in conjunction with primary data for the improved modeling. Satellite imaging is an example of exhaustively sampled secondary data. Improvements and recommendations are made to the implementation of GFS to properly assimilate secondary exhaustive data sets in a grid-free manner. Intrinsic cokriging (ICK) is utilized to reduce computational time and preserve the overall quality of the simulation. To further reduce the computational cost of ICK, a block matrix inversion is implemented in the calculation of the kriging weights. A projection approach to ICK is proposed to avoid artifacts in the realizations around the edges of the exhaustive data region when the data do not cover the entire modeling domain. The point-scale block value representation of the block-scale data is developed as an alternative to block cokriging to integrate block-scale data into realizations within the GFS framework. Several case studies support the proposed enhancements.

Geological Objects and Physical Parameter Fields in the Subsurface: A Review

“…The use of point-based parameterizations is also much studied in computational physics under the term "meshless methods", see for instance Liu and Gu (2005). In the practice of geostatistical methods, the values m k are generally modeled on a Cartesian grid, but recent papers also discuss about the application of geostatistics on unstructured grids (Gross and Boucher 2015;Manchuk et al 2005;Zaytsev et al 2016), or directly on points (Zagayevskiy and Deutsch 2016). A major interest of these methods is to estimate or simulate values directly on the physical modeling support, and also to use adaptive resolution depending on the local information density and on the sensitivity between the model parameters and the physical process.…”

Strategies to access web-enabled urban spatial data for socioeconomic research using R functions

“…These databases are obtained by either primary data online surveys (Wright 2005;Chang et al 2006;Howard et al 2015;Siewert and Udani 2016) or secondary official and non-official registers. Secondary data are "ready-made" statistical variables originally collected by persons other than the researchers, for a different purpose than the ones of corresponding investigation (Atkinson and Brandolini 2001;Westling et al 2009;Zagayevskiy and Deutsch 2016).…”