Is it possible to realize $K3$ surface as a ramified double cover of rational elliptic surface? If so, is there way to see an elliptic fibration structure on $K3$ from such cover? It seems to me one can use the divisor $6H - 2E_{1} - \cdots - 2E_{9}$ and the class $3H - E_{1} - \cdots - E_{9}$ in two fold cover gives the fiber class in $K3$?