(2) D Hint: $S_{1}$ represents the interior (including the circumference) of the circle: $(x-5)^{2}+(y-5)^{2} \leqslant$ 49, with an area of $49 \pi$. $S_{2}$ represents the interior (including the circumference) of the circle: $(x-50)^{2}+(y-50)^{2} \leqslant$ 4998, with an area of $4998 \pi$. Therefore, the area ratio is $102: 1$.
(2) If the sets are:
$$
\begin{array}{l}
S_{1}=\left\{(x, y) \mid \lg \left(1+x^{2}+y^{2}\right) \leqslant 1+\lg (x+y)\right\}, \\
S_{2}=\left\{(x, y) \mid \lg \left(2+x^{2}+y^{2}\right) \leqslant 2+\lg (x+y)\right\},
\end{array}
$$

then the ratio of the area of $S_{2}$ to the area of $S_{1}$ is ( ).
(A) $99: 1$
(B) $100: 1$
(C) $101: 1$
(D) $102: 1$