From the dolphins media guide -
The most recent modification to the Dolphins’ logo was
made prior to the 1997 season. This marked just the third
logo change in the 36-year history of the franchise, and
the first since 1972.
The original logo featured the dolphin jumping in front
of a sunburst using the team’s base colors (aqua, coral
and white). In 1972, the dolphin was repositioned in front
of the sunburst and the aqua color was strengthened. In
1997, the traditional logo and colors were kept as a base,
while the sunburst on the logo was accentuated and the
dolphin was strengthened with a stronger definition of its
shape. In addition, the sunburst was more prominently
displayed with the elimination of the hashmarks around
the sun’s perimeter, while the dolphin’s features were
accentuated by navy highlights.