By Ne-Zheng Sun
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This e-book systematically discusses easy suggestions, concept, resolution equipment and purposes of inverse difficulties in groundwater modeling. it's the first ebook dedicated to this topic.
The inverse challenge is outlined and solved in either deterministic and statistic frameworks. quite a few direct and oblique tools are mentioned and in comparison. As a useful gizmo, the adjoint nation procedure and its purposes are given intimately. For a stochastic box, the utmost chance estimation and co-kriging ideas are used to estimate unknown parameters. The ill-posed challenge of inverse answer is highlighted in the course of the entire booklet. the significance of knowledge assortment method is specifically emphasised. along with the classical layout standards, the relationships among choice making, prediction, parameter id and experimental layout are thought of from the viewpoint of prolonged identifiabilities. the matter of version constitution id can also be thought of.
This publication can be utilized as a textbook for graduate scholars majoring in hydrogeology or similar topics. it's also a reference ebook for hydrogeologists, petroleum engineers, environmental engineers, mining engineers and utilized mathematicians.
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Additional info for Inverse Problems in Groundwater Modeling
2) Explain the relationship between model calibration and parameter identification. (3) Explain the relationship between forward and inverse problems. 2. 1) to fit these data to determine K. 3) to fit these data to determine a and b. 3. 2. t EXISTENCE Intuitively, existence of an inverse solution appears to be no problem at all, since the physical reality must be a solution. In practice, however, the observation error (or noise) of state variables cannot be avoided. As a result, an accurate solution of an inverse problem may not exist.
Sun, Inverse Problems in Groundwater Modeling © Springer Science+Business Media Dordrecht 1999 40 Chapter 3 where M can be seen as a mapping which transfers each preimage pEP into an unique image U E U. Here, P and U are function spaces called parameter space and state space, respectively. Generally, parameter p can vary only in a subset Pad C P, which is called the admissible set of parameter p. For all p E Pad, the corresponding range of M(P) is denoted by M(Pad), which is a subset of state space U.
It is partia11y characterized by its first two moments, the mean (or drift) and the covariance function. Low order polynomials or other simple functions with a few undetermined coefficients can be used to represent the unknown drift and· covariance function. Thus, the unknown parameter is parameterized by these coefficients. A detailed discussion of the stochastic field method will be given in Chapter 7. (6) Geological Structure Method This method of parameterization was presented recently by Sun et al.