Samples recovered from Deep-Sea Drilling Project (DSDP) holes into the basaltic layer strongly suggest that a good model of the magnetization would be a spatially random one. To interpret future magnetometer observations made in the holes, we develop a theory relating the observed fields to the magnetizaion autocorrelation tensor, a function completely describing the second-order statistics of the medium. We examine special models with long- and short- range order and conclude that certain properties of the medium are highly desirable in making interpretation possible. Among these are that the autocorrelation tensor be independent of direction in a horizontal plane and that the direction of magnetization be uniform. Furthermore, useful interpretation is feasible only if three components of the magnetic field are measured, and it is preferable (but not essential) that the magnetometer is absolutely orientated about a vertical axis. We show that only in special circumstances (e.g., horizontal layering of the medium) does the magnetic field correlate directly with the average magnetization in a region surrounding the magnetometer. We analyze the natural remanent magnetization data from leg 37 of the DSDP to obtain partial information on the spatial statistics. There is no significant order vertically on scales longer than 10 m, but in two of the five holes there is correlation in the range 0.3-2 m. In three holes there is evidence of farily good uniformity of direction, a highly desirable property for interpretational purposes. Unfortunately, drill hole samples give us no information about the behavior of the autocorrelation tensor as a function of horizontal distance.