Discerning connectivity features and scaling behaviour of spatial random fields through the Method of Anchored Distributions (MAD).

点击翻译按钮获取中文摘要

Hydrogeolocial quantities like conductivity or transmissivity are usually hard to represent in a precise manner due to having both a high degree of spatial variability as well as exhibiting a scarcity of information. As a result these quantities are commonly modeled as random fields, which, under the assumption of a Gaussian process, are defined by their expectation value and their covariance function respectively the variogram. This variogram is usually parametrized by fitting a model functions to an experimental variogram derived from measurements of the conductivity. Typical variogram model include the exponential, Gaussian and the spherical variogram. Despite their differences these different functions can often be fitted to the experimental variogram with similar accuracy. This observation is substantiated by the fact that the choice of the aforementioned model functions often has little impact on subsequently performed flow and transport simulations. In this study we will however, investigate the two scenarios, where such variogram models can be mistaken for structurally different variogram models therefore leading to very different results.The first scenario is a comparison of a Gaussian random field with a Gaussian variogram function vs. a non-Gaussian random field with a high degree of connectivity of the extreme values of the field. It has been shown that such fields can have very similar variogram functions making them nearly indistinguishable based on the experimental variogram alone. Due to the different connectivity features the resulting flow and transport behavior will however, differ strongly.The second scenario is a comparison of Gaussian random fields having either an exponential or a so called truncated power-law variogram function. In analogy to above scenario both these fields have a similar variogram function but strongly differ with respect to the scaling behavior. Falsely ignoring this fact will leads to errors if data from different scales are assimilated or the so found results are transferred to other spatial scales.These two presented scenarios both share the fact, that, based on characterization of mean and variogram alone, they are hard to discriminate yet can lead to very different results if used for further analyses of the properties they represent. As a result it is necessary to use additional data in order to discern the original structure of the random field.In this study we will use the Method of Anchored Distributions, which is a novel tool for the inverse characterization of spatial random fields. The method is very versatile with respect to the used data, has a modular structure and does not assume any formal relationship between the target variable (log hydraulic conductivity) and the data used for the inversion process.