Thanks to Ron Blakely's website at Northern Arizona I get to show some really neat renderings of what the earth's surface looked like at various intervals in geologic time. I'm not a geologist so I'd love to be corrected on the details and the placement of the X-marks-Durham.
Rendering of the continents about 500 million years ago (mya). Click to enlarge but you can make out the Durham X near the island arc to the lower left.
When the North American (top) and Euro-African(bottom) plates began to come together around 350 mya they thrust the old island arc onto the American continent. Shown above is the collision, which took place near the equator (imagine it running horizontally through the middle of the picture).
In the Triassic period, around 250 mya, the two continental plates that had come together to form Pangaea and the Appalachians began to tear apart. This tearing sheared apart the mountain range and created basins including what we now call the Durham Triassic basin.
By 180 mya the two continental plates tore apart completely and began moving away from each other to take up their current positionsacross the Atlantic Ocean. Over time, as North America slowly drifted northwest away from the equator, erosion destroyed much of the mountain range near Durham and the accumulating pressure of millions of years of piled sediment turned the bottom of the Triassic basin into mudstone and sedimentary rock of all kinds.