已知集合$${{S}_{1}}=\left { \left( x,  y \right)\left\textbar{} {{\log }_{2}}\left( 1+{{x}^{2}}+{{y}^{2}} \right)\leqslant 1+{{\log }_{2}}\left( x+y \right) \right. \right }$$，并且集合  $${{S}_{2}}=\left { \left( x,  y \right)\left\textbar{} {{\log }_{\frac{1}{2}}}\left( 2+{{x}^{2}}+{{y}^{2}} \right)\geqslant -2+{{\log }_{\frac{1}{2}}}\left( x+y \right) \right. \right }$$，则$${{S}_{2}}$$与$${{S}_{1}}$$的面积比为．
选项为:A:$$2:1$$  B:$$4:1$$  C:$$6:1$$  D:$$8:1$$  请回答其中一个选项.