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?
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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.
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.