Where in the United States is there a measurable evidence that the continents are moving relative to one another

the san andreas fault line

Californian San Andreas fault continents is moving relative to one another.

Explanation:

California is between two plates namely the Northern American Plate and the Pacific Plate that are moving slowly past each other. The Pacific plate moves in the northwest direction at the rate of 46 mm/year with reference to the Northern American Plate.

It is believed that the motion was triggered by the strike-slip earthquake that occurred on the fault San Andreas. The fault by nature is a transform fault which extends approximately 1200 kilometer through California. There are three segments dividing the faults each with different degree of earthquakes.