3D mapping is very challenging in the underwater domain, especially due to the lack of high resolution, low noise sensors. A new spectral registration method is presented that can determine the spatial 6 DOF transformation between pairs of very noisy 3D scans with only partial overlap. The approach is hence suited to cope with sonar as the predominant underwater sensor. The spectral registration method is based on Phase Only Matched Filtering (POMF) on non-trivially resampled spectra of the 3D data.Two extensive sets of experiments are presented. First, evaluations with simulated data are done where the type and amount of noise can be controlled and the ground truth transformations between scans are known. Second, real world data from a Tritech Eclipse sonar is used. Concretely, 18 sonar scans of a large structure in form of a flood gate and a lock in the river Lesum in Bremen are used for 3D mapping. In doing so, the spectral registration method is compared to two other methods suited for noisy 3D registrations, namely Iterative Closest Point (ICP) and plane-based registration. It is shown that the spectral registration method performs very well in terms of the resulting 3D map as well as its runtimes.