The concept of equivalent sources is described from first principles. Two types of sources that produce the same magnetic field are studied in detail: thin sheets and uniaxially magnetized half-spaces. Simple analytic solutions show that their magnetization variations are essentially given by the pseudogravity field and the magnetic field, respectively. While the former varies slowly to account for the slow variation in the vertically integrated magnetization, the latter varies rapidly to account for the spatial variation in rock magnetization close to the observation points. An extension of these simple distributions is the sandwich distribution. Using statistical arguments, we construct sandwich distributions. The depths and mean magnetizations of each layer are found from the decay of the azimuthally averaged power spectrum. The equivalent layer magnetizations closely resemble the magnetic field anomaly when upward-continued to a height equal to the mean depth of the layer.