“…Such effects have been observed in nearly all rock types and an incomplete listing of contributions where such nonlinear effects have been observed includes those for igneous and metamorphic hard rocks (e.g., Birch, 1960Birch, , 1961Blake et al, 2013;Cheng and Toks€ oz, 1979;Cholach et al, 2005 Stanley, 2003;Goddard, 1990;Kern, 1982;Lyakhovsky et al, 1997;Todd and Simmons, 1972), sandstones (e.g., Christensen and Wang, 1985;Gomez et al, 2010;Jones and Nur, 1983;Khazanehdari and McCann, 2005;Khazanehdari and Sothcott, 2003;Lo et al, 1986;Prasad and Manghnani, 1997;Sayers, 2002;Sayers et al, 1990;Smith et al, 2010;Wyllie et al, 1958;Xu et al, 2006), carbonates (e.g., Alam et al, 2012;Azeemuddin et al, 2001;Fabricius et al, 2008;Melendez Martinez and Schmitt, 2013), and mudstones (Freund, 1992;Kwon et al, 2001;Sayers, 1999). Many workers have focused on different ways to describe this nonlinearity including the use of curve fitting (Carcione and Tinivella, 2001;Eberhart-Phillips et al, 1989;Freund, 1992;Khaksar et al, 1999;Kirstetter et al, 2006;Prasad and Manghnani, 1997;Prikryl et al, 2005;…”