The GRF (Gräfenberg) seismic array in Germany is located at epicentral distances immediately before the PKP caustic B generated by underground nuclear explosions on the French atolls Mururoa and Fangataufa in the South Pacific. I use the large-amplitude PKP waveforms to improve the locations of underground explosions near these French atolls. The core phases are investigated using theoretical seismograms calculated with an extended reflectivity method. Near the caustic range, the waveforms are strongly distance dependent due to a rapid decrease in PKPdiff amplitudes before the caustic B. On the basis of their different slownesses, beam-forming and velocity-spectral (vespagram) analyses are used to identify PKPdiff, PKIKP, and PKiKP, which arrive within a few seconds of each other. Amplitudes and travel times of the weak secondary arrivals PKIKP and PKiKP are measured from the corresponding beams using a matched-filter technique. Theoretical seismograms show a change in the amplitude ratio PKIKP/PKPdiff by a factor of 2 for explosions separated by 30 km. This distance-dependent amplitude ratio is tested as a discriminant for closely spaced explosions using 31 Mururoa and five Fangataufa events. On average, the observed amplitude ratios agree with the theoretically expected amplitude-ratio behavior with distance. A combined analysis of travel time and amplitude data indicates that the investigated Mururoa explosions were detonated beneath a relatively large area of the atoll (ca. 80%), whereas on Fangataufa, explosion epicenters were concentrated within a small portion of the island. This finding contrasts the ISC/PDE epicenter determinations, which, due to insufficient station coverage, locate the majority of the explosions outside of the rim of the atolls.