A wide range of geophysical processes and rock properties has been described in fractal or scaling terms. For continental crust, well log susceptibilities, surface susceptibilities and aeromagnetic fields all tend to support a model for a 3-D magnetization distribution having a radially-averaged power spectrum proportional to some power of the spatial frequency. This simple model of the scale-invariant behaviour of crustal magnetization and the magnetic fields it produces can be exploited by several applications which require information on such spatial variation. A more realistic power spectrum, and equivalently, covariance model for continental crustal magnetization offers many advantages over the geologically incorrect assumption of a white power spectrum (equivalent to an uncorrelated distribution). Well log susceptibilities and natural remanent magnetization intensities measured for oceanic crust are shown here to exhibit scaling behaviour. Measurements from Ocean Drilling Program holes 504B, 735B, 801C and holes CY1, CY4 in the Troodos ophiolite sequence in Cyprus show overall values for the scaling exponent, between -1.36 and -0.68 for susceptibilities and between -1.52 and -0.54 for natural remanent magnetization intensities. Based on this small number of samples, scaling exponents determined for basalt, sheeted dyke and gabbro sequences within these logs show wide variation, indicating no apparent correlation between rock type and scaling behaviour.