## Geometric reconstructions of continents

Although approximate reconstructions can be performed manually by moving models of continents

Geographical pole-

-Axis of rotation

^^ Pole of rotation Angle of rotation

Great circle or Equator of rotation Small circles or latitudes of rotation

Figure 3.1 Euler's theorem. Diagram illustrating how the motion of a continent on the Earth can be described by an angle of rotation about a pole of rotation.

across an accurately constructed globe (Carey, 1958), the most rigorous reconstructions are performed mathematically by computer, as in this way it is possible to minimize the degree of misfit between the juxtaposed continental margins.

The technique generally adopted in computer-based continental fitting is to assume a series of poles of rotation for each pair of continents arranged in a grid of latitude and longitude positions. For each pole position the angle of rotation is determined that brings the continental margins together with the smallest proportion of gaps and overlaps. The fit is not made on the coastlines, as continental crust extends beneath the surrounding shelf seas out to the continental slope. Consequently, the true junction between continental and oceanic lithosphere is taken to be at some isobath marking the midpoint of the continental slope, for example the 1000 m contour. Having determined the angle of rotation, the goodness of fit is quantified by some criterion based on the degree of mismatch. This goodness of fit is generally known as the objective function. Values of the objective function are entered on the grid of pole positions and contoured. The location of the minimum objective function revealed by this procedure then provides the pole of rotation for which the continental edges fit most exactly.

Figure 3.2 Fit of the continents around the Atlantic Ocean, obtained by matching the 500 fathom (920 m) isobath (redrawn from Bullard et al., 1965, with permission from the Royal Society of London).

Figure 3.2 Fit of the continents around the Atlantic Ocean, obtained by matching the 500 fathom (920 m) isobath (redrawn from Bullard et al., 1965, with permission from the Royal Society of London).