A combined Deep Tow and Seabeam 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 observed 27-km offset between the axes creates an ideal solution for the application of magnetic methods. The normally magnetized crust of the propagating rift tip penetrates into older crust, which was created when the earth's main field was reversed. As the V-shaped structure of the rift clearly violates the conventional two-dimensional assumptions, a full three-dimensional analysis is required. In addition, the distorting influence of over 1000 m bathymetric relief must be removed from the observed field. Inversions have been performed 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 km2, 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 drying 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 propagating rift requires about 250,000 years. The inversion of the Deep Tow data, near the seafloor, provides a high-resolution definition of the location of the tip of the propagating rift, at 2¿38.1'N, 95¿30.0'W.