The Principle of Complex Frequency Scaling ? Applicability in Inclined Continuation of Potential Fields

A remarkable property of Fourier transforms, especially applicable to inclined continuation of potential geophysical fields, is the principle of “complex frequency scaling”. Briefly stated, let f(x) be the (gravity/magnetic) field due to a two-dimensional structure along a principal profile and F(ω) be its Fourier transform. The field along a profile passing through the same reference origin and tilted by an angle δ in the counterclockwise direction (+X to −Z) is obtained by inverse Fourier transforming F[ω exp (−iδ)] for positive ω. The complex scaling property and proof of the resulting space-frequency domain relationship are presented, introducing the total field as the analytic signal of the horizontal component. The applicability of the complex scaling principle is illustrated by considering selected geometric models. This principle can be advantageously applied for continuation of two-dimensional potential fields onto inclined planes.