SPECTRUM OF THE POTENTIAL FIELD DUE TO RANDOMLY DISTRIBUTED SOURCES

Covariance and spectral density functions of all three components of random potential fields are mutually related. The spectra of any one component on two different levels are related through an exponential function of the separation of the levels. If, starting from the earth’s surface, we continue the observed random field downward, we find that at a certain level the field becomes unstable. Such a limiting depth can be estimated from the spectrum of the observed field. The spectrum of the random field is related to the spectrum of random density or intensity of magnetization. The random sources are assumed to be confined to a thin sheet or a thick, infinite sheet, or to a semi‐infinite medium. In all these cases, a relation connecting the spectrum of the random density or the intensity of magnetization and the spectrum of the random field has been established.