A method is described for determining the elastic-rebound strain increments associated with earthquakes occurring on a particular fault. For a given sequence of earthquakes, a graph of the accumulated increments so determined plotted against time represents the actual fault movement during the interval covered by the sequence. The method also provides a means for determining whether or not a chosen sequence of earthquakes represents movements of a single fault structure. In this way it becomes possible to discover faults which otherwise may escape detection. Evidence of this kind is offered which indicates that the Tonga-Kermadec and South American sequences of earthquakes originate on great faults which dip under the continental masses. The faults are approximately 2500 km. and 4500 km. in length respectively. Their transverse dimensions are approximately 900 km. each. They both extend to a depth of approximately 650 km.—more than one tenth of the radius of the earth. The oceanic deeps associated with these faults are surface expressions of the downwarping of their oceanic blocks. The upwarping of their continental blocks have produced islands in the Tonga-Kermadec region and the Andes Mountains in South America.