A geostatistically based inverse model for three-dimensional variably saturated flow

1998 ◽  
Vol 12 (5) ◽  
pp. 285-298 ◽  
Author(s):  
Debra L. Hughson ◽  
T.-C. Jim Yeh
Keyword(s):  
Three Dimensional ◽  
Inverse Model ◽  
Saturated Flow

Numerical simulation of three-dimensional transient variably saturated flow

2012 ◽  
pp. 173-178
Author(s):  
D Caviedes-Voullième ◽  
P García-Navarro ◽  
J Murillo
Keyword(s):  
Numerical Simulation ◽  
Three Dimensional ◽  
Saturated Flow

scholarly journals On the coupled unsaturated–saturated flow process induced by vertical, horizontal, and slant wells in unconfined aquifers

2017 ◽  
Vol 21 (2) ◽  
pp. 1251-1262 ◽  
Author(s):  
Xiuyu Liang ◽  
Hongbin Zhan ◽  
You-Kuan Zhang ◽  
Jin Liu
Keyword(s):  
Unsaturated Zone ◽  
Horizontal Well ◽  
Unsaturated Flow ◽  
Three Dimensional ◽  
Water Volume ◽  
Saturated Flow ◽  
Flow Process ◽  
Pumping Tests ◽  
Screen Length ◽  
Unconfined Aquifers

Abstract. Conventional models of pumping tests in unconfined aquifers often neglect the unsaturated flow process. This study concerns the coupled unsaturated–saturated flow process induced by vertical, horizontal, and slant wells positioned in an unconfined aquifer. A mathematical model is established with special consideration of the coupled unsaturated–saturated flow process and the well orientation. Groundwater flow in the saturated zone is described by a three-dimensional governing equation and a linearized three-dimensional Richards' equation in the unsaturated zone. A solution in the Laplace domain is derived by the Laplace–finite-Fourier-transform and the method of separation of variables, and the semi-analytical solutions are obtained using a numerical inverse Laplace method. The solution is verified by a finite-element numerical model. It is found that the effects of the unsaturated zone on the drawdown of a pumping test exist at any angle of inclination of the pumping well, and this impact is more significant in the case of a horizontal well. The effects of the unsaturated zone on the drawdown are independent of the length of the horizontal well screen. The vertical well leads to the largest water volume drained from the unsaturated zone (W) during the early pumping time, and the effects of the well orientation on W values become insignificant at the later time. The screen length of the horizontal well does not affect W for the whole pumping period. The proposed solutions are useful for the parameter identification of pumping tests with a general well orientation (vertical, horizontal, and slant) in unconfined aquifers affected from above by the unsaturated flow process.

Quantifying the error level in computed magnetic amplitude data for 3D magnetization inversion

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. J75-J84 ◽  
Author(s):  
Camriel Coleman ◽  
Yaoguo Li
Keyword(s):  
Field Data ◽  
Regularization Parameter ◽  
Three Dimensional ◽  
Inverse Model ◽  
Magnetic Data ◽  
Total Field ◽  
Noise Estimate ◽  
Amplitude Inversion ◽  
Amplitude Data ◽  
Magnetic Amplitude

Three-dimensional inversion plays an important role in the quantitative interpretation of magnetic data in exploration problems, and magnetic amplitude data can be an effective tool in cases in which remanently magnetized materials are present. Because amplitude data are typically calculated from total-field anomaly data, the error levels must be characterized for inversions. Lack of knowledge of the error in amplitude data hinders the ability to properly estimate the data misfit associated with an inverse model and, therefore, the selection of the appropriate regularization parameter for a final model. To overcome these challenges, we have investigated the propagation of errors from total-field anomaly to amplitude data. Using parametric bootstrapping, we find that the standard deviation of the noise in amplitude data is approximately equal to that of the noise in total-field anomaly data when the amplitude data are derived from the conversion of total-field data to three orthogonal components. We then illustrate how the equivalent source method can be used to estimate the error in total-field anomaly data when needed. The obtained noise estimate can be applied to amplitude inversion to recover an optimal inverse model by applying the discrepancy principle. We test this method on synthetic and field data and determine its effectiveness.

scholarly journals On Coupled Unsaturated-Saturated Flow Process Induced by Vertical, Horizontal and Slant Wells in Unconfined Aquifers

2016 ◽  
Author(s):  
Xiuyu Liang ◽  
Hongbin Zhan ◽  
You-Kuan Zhang ◽  
Jin Liu
Keyword(s):  
Unsaturated Zone ◽  
Horizontal Well ◽  
Unsaturated Flow ◽  
Three Dimensional ◽  
Early Time ◽  
Saturated Flow ◽  
Flow Process ◽  
Pumping Tests ◽  
Screen Length ◽  
Unconfined Aquifers

Abstract. Conventional models of pumping tests in unconfined aquifers often neglect the unsaturated flow process. This study concerns coupled unsaturated-saturated flow process induced by vertical, horizontal, and slant wells positioned in an unconfined aquifer. A mathematical model is established with special consideration of the coupled unsaturated-saturated flow process and well orientation. Groundwater flow in the saturated zone is described by a three-dimensional governing equation, and a linearized three-dimensional Richards' equation in the unsaturated zone. A solution in Laplace domain is derived by the Laplace-finite Fourier transform and the method of separation of variables. It is found that the unsaturated zone has significant effects on the drawdown of pumping test with any angle of inclination of the pumping well, and this impact is more significant for the case of a horizontal well. The effects of unsaturated zone on the drawdown are independent of the length of the horizontal well screen. For the early time of pumping, the water volume drained from the unsaturated zone (W) increases with time, and gradually approaches an asymptotic value with time progress. The vertical well leads to the largest W value during the early time, and the effects of the well orientation become insignificant at the later time. The screen length of the horizontal well does not affect W for the whole pumping period. The proposed solutions are useful for parameter identification of pumping tests with a general well orientation (vertical, horizontal, and slant) in unconfined aquifers affected from above by the unsaturated flow process.

A generalized Ross method for two- and three-dimensional variably saturated flow

2013 ◽  
Vol 54 ◽  
pp. 67-77 ◽  
Author(s):  
Yuanyuan Zha ◽  
Liangsheng Shi ◽  
Ming Ye ◽  
Jinzhong Yang
Keyword(s):  
Three Dimensional ◽  
Saturated Flow
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