How the planet Earth evolves to its present form and how the interior of Earth affects its surface are still open questions. The main difficulty in probing the answer is the incomplete knowledge of Earth''s internal structures, especially at the ancient geological past. This book introduces a novel approach to reproduce the evolving interior of Earth, using a technique widely adopted in weather prediction. An inverse model based on this technique can crank the time machine backward, and reveal the Earth''s structure in the past. An example is the reconstruction of the so called Farallon plate (an oceanic plate that has almost entirely recycled into the interior of Earth) subducting beneath North America since the Cretaceous time when dinosaurs still roamed our planet. The inverse calculation indicates that this process strongly affected the surface evolution of North America, including formation of both its enigmatic inland sea once flooding half of the continent and the peculiar geology such as the Rocky Mountains and the Colorado Plateau.