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Applied Stochastic Hydrogeology$
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Yoram Rubin

Print publication date: 2003

Print ISBN-13: 9780195138047

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780195138047.001.0001

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Fundamentals of Stochastic Site Characterization

Fundamentals of Stochastic Site Characterization

Chapter:
2 (p.13) Fundamentals of Stochastic Site Characterization
Source:
Title Pages
Author(s):

Yoram Rubin

Publisher:
Oxford University Press
DOI:10.1093/oso/9780195138047.003.0007

A few schematic representations of heterogeneous geological formations are depicted in figure 2.1. These and similar types of images, often encountered in geological site investigations, demonstrate the complexity of subsurface geology. Each image shows several blocks, all nearly homogeneous in terms of some physical or chemical property z, but with possibly strong variations in properties in between. The patterns of spatial variability shown in these images are difficult to capture in the absence of a large number of measurements adequately distributed over the domain. However, the high cost of procuring such databases renders deterministic image reconstruction an elusive goal, one which is largely abandoned in favor of approaches which try to formulate the laws which govern the pattern of spatial variability. These models are known as space random functions (or SRFs, for short). Besides deconstructing complex spatial variability patterns into simple, quantitative laws, SRFs can be used to construct images which have these spatial laws in common, and to estimate z at specific locations. Constructing a SRF for a spatially variable z is based on analysis of z measurements. The goal of that analysis is to reduce the ensemble of measurements to a few useful statistics which capture mathematically the pattern of spatial variability. A few statistics were found to be very useful for exposing the laws of variability, and will be explored in detail. The data analysis includes single (univariate), two-point (bivariate), and multipoint (multivariate) analyses. Univariate analysis focuses on the same-point statistical behavior of the variable z, regardless of the behavior of its neighbors. It answer questions such as “What is the average value of Z?” or “What are the chances that Z will exceed 1000 units?” Bivariate and multivariate analyses explore the simultaneous behavior of z at two or more locations. They provide tools which answer questions such as “What is the likelihood that a region of high permeability will stretch between the contamination source and some environmentally sensitive target?” or “What is the probability to observe z larger than 1500 units at x given that a value of 1300 was measured 5 meters away from x?”

Keywords:   Alluvial fan, Bedsets, Central moments, Deconditioning, Facies, Hierarchy, Indicators, Lithofacies, Microscale

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