Transfer properties of the reduction of magnetic anomalies to the pole and to the equator

Reduction of magnetic anomalies to the magnetic pole and magnetic equator can be regarded as a linear transformation. The Hermitian transfer function characteristics of these transformations are discussed and improved using the Gaussian band‐pass window. This procedure is of use in one‐ and two‐dimensional cases. The application of the Gaussian band‐pass window eliminates the finite discontinuity of the transfer function of reductions at zero frequency in all cases. The frequency band passed by the Gaussian window can be controlled by its parameters. Reduction to the equator can be used at low magnetic latitudes where reduction of two‐dimensional anomalies to the pole has some instabilities caused by the infinite discontinuities of its transfer function. The windowed reductions are illustrated by their application to magnetic anomalies produced by two‐dimensional and three‐dimensional prisms.

Gaussian Band Shape Derived from Finite-Rate Oscillator Growth

The accepted classical model for derivation of the frequency spectrum from the time-dependence of oscillator activity is considered. The exponential decay function giving rise to a Lorentzian band is modified to allow for a finite rate of growth of the oscillator, the resulting frequency spectrum is obtained, and the form normalized to unit band half-width is compared to the equivalent Lorentzian and Gaussian bands. It is shown that as the rate of oscillator growth decreases from infinity to one approximating the rate of decay, the resulting band contour changes from Lorentzian to near-Gaussian. At sufficiently fast growth-rates the band closely approximates a linear combination of Lorentzian and Gaussian.