SPECTRAL AND BISPECTRAL ANALYSIS FOR SINGLE-INPUT AND MULTIPLE-INPUT NONLINEAR PHREATIC AQUIFER SYSTEMS

In general, stochastic partial differential equations and/or boundary conditions describing flow in phreatic aquifers are nonlinear. This pa per uses second-order perturbation to approximate the response of a ph reatic aquifer system subject to multiple random inputs. The approach is equivalent to assuming quadratic nonlinearities in the original non linear phreatic aquifer system. Using frequency domain representations , the resulting model is decomposed into linear and nonlinear (quadrat ic) frequency response functions (FRF). For Gaussian input, the respon se of a nonlinear phreatic aquifer system is non-Gaussian and is typic ally skewed. Thus the variance spectrum is insufficient to describe th e response process. The bispectrum, defined as the Fourier transform o f the third-order cumulant sequence, represents the distribution of sk ewness with frequency and further serves as a measure of the nonlinear ity of the system. Given input processes of aquifer recharge and strea m stage fluctuations, the linear and quadratic FRF are used to constru ct the spectrum and bispectrum of the response process. The role of no nlinearity in a stream-aquifer system is examined.