  In this paper, we study the geometry of trisections on certain rational
elliptic surfaces. We utilize Mumford representations of semi-reduced divisors
in order to construct trisections and related plane curves with interesting
properties explicitly. As a result we are able to construct new examples of
Zariski pairs. Especially, we show the existence of a family of Zariski pairs
that degenerate to the same conic-line arrangement.
