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All the graphics I've seen showing epicenters with a hypocenter (labeled focus in the graph below) appear to show that epicenters are always directly above their related hypocenters. Is this correct?

3D slice of Earth showing a Earthquake with the related fault, epicenter, and hypocenter

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By definition, the answer is yes:

epicenter, the point on the earth's surface vertically above the focus of an earthquake, or the Hypocenter

according to Merriam-Webster or a many other sources.

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  • $\begingroup$ Yes to the question - by definition :-) :-) $\endgroup$ – winwaed Jun 9 '14 at 18:45
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Generally defined, an epicentre is just a projection of the hypocentre (aka focus), on the nearest outer surface of the body in which the seismic source occurs.

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