Geology topics

Li Zheng

Publications and source records attributed to Li Zheng.

3 recordsLinked to original sources

USGS2002

Steady shape analysis of tomographic pumping tests for characterization of aquifer heterogeneities

Hydraulic tomography, a procedure involving the performance of a suite of pumping tests in a tomographic format, provides information about variations in hydraulic conductivity at a level of detail not obtainable with traditional well tests. However, analysis of transient data from such a suite of pumping tests represents a substantial computational burden. Although steady state responses can be analyzed to reduce this computational burden significantly, the time required to reach steady state will often be too long for practical applications of the tomography concept. In addition, uncertainty regarding the mechanisms driving the system to steady state can propagate to adversely impact the resulting hydraulic conductivity estimates. These disadvantages of a steady state analysis can be overcome by exploiting the simplifications possible under the steady shape flow regime. At steady shape conditions, drawdown varies with time but the hydraulic gradient does not. Thus transient data can be analyzed with the computational efficiency of a steady state model. In this study, we demonstrate the value of the steady shape concept for inversion of hydraulic tomography data and investigate its robustness with respect to improperly specified boundary conditions.

Water Resources Research↗

USGS2000

Estimating the theoretical semivariogram from finite numbers of measurements

We investigate from a theoretical basis the impacts of the number, location, and correlation among measurement points on the quality of an estimate of the semivariogram. The unbiased nature of the semivariogram estimator ŷ ( r ) is first established for a general random process Z( x ). The variance of ŷ Z ( r ) is then derived as a function of the sampling parameters (the number of measurements and their locations). In applying this function to the case of estimating the semivariograms of the transmissivity and the hydraulic head field, it is shown that the estimation error depends on the number of the data pairs, the correlation among the data pairs (which, in turn, are determined by the form of the underlying semivariogram γ( r )), the relative locations of the data pairs, and the separation distance at which the semivariogram is to be estimated. Thus design of an optimal sampling program for semivariogram estimation should include consideration of each of these factors. Further, the function derived for the variance of ŷ Z ( r ) is useful in determining the reliability of a semivariogram developed from a previously established sampling design.

Water Resources Research↗

USGS2000

Estimating the variance and integral scale of the transmissivity field using head residual increments

A modification of previously published solutions regarding the spatial variation of hydraulic heads is discussed whereby the semivariogram of increments of head residuals (termed head residual increments HRIs) are related to the variance and integral scale of the transmissivity field. A first‐order solution is developed for the case of a transmissivity field which is isotropic and whose second‐order behavior can be characterized by an exponential covariance structure. The estimates of the variance σ Y 2 and the integral scale λ of the log transmissivity field are then obtained via fitting a theoretical semivariogram for the HRI to its sample semivariogram. This approach is applied to head data sampled from a series of two‐dimensional, simulated aquifers with isotropic, exponential covariance structures and varying degrees of heterogeneity (σ Y 2 = 0.25, 0.5, 1.0, 2.0, and 5.0). The results show that this method provided reliable estimates for both λ and σ Y 2 in aquifers with the value of σ Y 2 up to 2.0, but the errors in those estimates were higher for σ Y 2 equal to 5.0. It is also demonstrated through numerical experiments and theoretical arguments that the head residual increments will provide a sample semivariogram with a lower variance than will the use of the head residuals without calculation of increments.

Water Resources Research↗