Scale dependence of the hydraulic properties of a 1 fractured aquifer estimated using transfer functions

We present an investigation of the scale dependence of hydraulic 3 parameters in fractured media based on the concept of transfer functions (TF). 4 TF methods provide an inexpensive way to perform aquifer parameter es5 timation, as they relate the fluctuations of an observation time series (hy6 draulic head fluctuations) to an input function (aquifer recharge) in frequency 7 domain. Fractured media are specially sensitive to this approach as hydraulic 8 parameters are strongly scale dependent, involving non-stationary statisti9 cal distributions. Our study is based on an extensive data set, involving up 10 to 130 measurement points with periodic head measurements that in some 11 cases extend for more than 30 years. For each point, we use a single-porosity 12 and dual-continuum TF formulation to obtain a distribution of transmissiv13 ities and storativities in both mobile and immobile domains. Single-porosity 14 TF estimates are compared with data obtained from the interpretation of 15 over 60 hydraulic tests (slug and pumping tests). Results show that the TF 16 is able to estimate the scale dependence of the hydraulic parameters, and 17 it is consistent with the behavior of estimates from traditional hydraulic tests. 18 In addition, the TF approach seems to provide an estimation of the system 19 variance and the extension of the ergodic behavior of the aquifer (estimated 20 in approximately 500 m in the analyzed aquifer). The scale dependence of 21 transmissivity seems to be independent from the adopted formulation (sin22 gle or dual-continuum), while storativity is more sensitive to the presence 23 of multiple continua. 24