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Application of the convolution equation to stream‐aquifer relationships
Author(s) -
Hall Francis R.,
Moench Allen F.
Publication year - 1972
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr008i002p00487
Subject(s) - aquifer , geology , convolution (computer science) , hydraulic head , impulse response , groundwater flow equation , flow (mathematics) , stream function , mathematics , mathematical analysis , soil science , mechanics , geotechnical engineering , groundwater flow , geometry , computer science , groundwater , physics , machine learning , artificial neural network , vorticity , vortex
Flow and head variations in stationary linear stream‐aquifer systems are obtained through application of the convolution equation. Four highly idealized cases involving finite and semi‐infinite aquifers, with and without semipervious stream banks, are considered. Equations for the instantaneous unit impulse response function, the unit step response function, and the derivative of the unit step response function are given for each case. Head fluctuations in the aquifer due to an arbitrarily varying flood pulse are obtained for the cases involving a finite aquifer with and without a semipervious stream bank. Flow in and out of the aquifer at the stream bank is determined for the same cases and demonstrates the value of the convolution equation in evaluating the base flow. Head variations, and to a lesser extent flow variations, are apparently relatively insensitive to variations in aquifer diffusivity.