“…After the pioneering development of three dimensional HT models and simulations by Yeh and Liu [2000] and Zhu and Yeh [2005] and laboratory experiments by Liu et al [2002], numerous HT studies have been conducted using numerical models [Bohling et al, 2002;Xiang et al, 2009;Cardiff et al, 2009;Cardiff and Barrash, 2011;Liu and Kitanidis, 2011], controlled sandbox experiments Illman et al, 2007Illman et al, , 2008Illman et al, , 2010Yin and Illman, 2009;Berg and Illman, 2011a;Liu and Kitanidis, 2011], and field pumping tests [Bohling et al, 2007;Illman et al, 2009;Huang et al, 2011;Brauchler et al, 2011;Berg and Illman, 2011b, 2015Cardiff et al, 2009Cardiff et al, , 2012Cardiff et al, , 2013a. Among the various studies, steady state Cardiff et al, 2009], temporal moment Yin and Illman, 2009], transient Liu et al, 2007], travel time [Brauchler et al, 2011], and oscillatory pressure signal [Cardiff et al, 2013b] data have been inverted to map heterogeneity patterns. Compared to hydraulic parameters estimated via traditional approaches, such as kriging of local-scale data or effective parameters by treating the aquifer to be homogeneous, Illman et al [2010] and Illman [2011a, 2015] found that hydraulic parameters estimated through HT are significantly better in predicting drawdown responses.…”