The propagation of an oceanic rift is an important tectonic problem, with a bearing on the reorganization of plate motion and on the early opening of oceanic basins. At the propagating rift at 95°30′W near the Galapagos Islands, we can use magnetic methods to determine the tectonic origin of a set of important sea floor features. The observed 27 km offset between the axes of the propagating rift and the dying rift presents us with an ideal situation, in which the oceanic crust created by the opposing systems has been magnetized in opposite directions. The normally magnetized crust of the propagating rift tip penetrates into older crust, which created when the earth's main field was reversed. A combined Deep Tow and Sea Beam investigation at 95°30′W on the Cocos-Nazca spreading center has revealed the crustal contact between the propagating rift and the dying rift systems. The inherent magnetic labelling of the crust has been recovered by performing inversions on the gridded representations of the observed magnetic field and bathymetry, working in the Fourier domain. The result is a gridded rock magnetization distribution. The inversion of the surface data covers a large area, 6000 km 2, and demonstrates close agreement with magnetization amplitudes of rock samples at existing dredge sites. In general, the propagating rift process appears to be much more orderly than the dying rift process. The magnetic polarity transition widths are narrower, and the boundaries have fewer undulations than the dying rift, which appears to be quite episodic in behavior. The average propagation rate is 52 mm/yr, compared to the average spreading half-rate of 29 mm/yr. The locations of the boundaries suggest that the acceleration to the normal spreading rate on the propagation rift requires about 250, 00 years. The inversion of the Deep Tow data, near the sea floor, provides a high resolution definition of the tip of the propagation rift, at 2°38.1t'N, 95°30.0′W.