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

1984 ◽  
Vol 15 (4) ◽  
pp. 266-266
Author(s):  
R. Nagendra ◽  
N. Laxminarayana
Keyword(s):  
Potential Fields ◽  
Complex Frequency ◽  
Frequency Scaling

The principle of complex frequency scaling—Applicability in inclined continuation of potential fields

Geophysics ◽  
1984 ◽  
Vol 49 (11) ◽  
pp. 2019-2023 ◽  
Author(s):  
R. Nagendra ◽  
N. Laxminarayana
Keyword(s):  
Fourier Transforms ◽  
Potential Fields ◽  
Dimensional Structure ◽  
Complex Frequency ◽  
Two Dimensional ◽  
Complex Scaling ◽  
Frequency Scaling ◽  
Space Frequency ◽  
Scaling Principle ◽  
Inclined Planes

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 [Formula: see text] 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 ϕ in the counter‐clockwise direction (+X to −Z) is obtained by inverse Fourier transforming F[ωexp(−iϕ)] 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.

Bistatic SAR Data Focusing Using a Frequency Scaling Algorithm Based on an Analytical Spectrum in Tandem Configuration

2011 ◽  
Vol 33 (6) ◽  
pp. 1447-1452
Author(s):  
Shi-chao Chen ◽  
Qi-song Wu ◽  
Ming Liu ◽  
Meng-dao Xing ◽  
Zheng Bao
Keyword(s):  
Frequency Scaling ◽  
Tandem Configuration ◽  
Bistatic Sar ◽  
Sar Data
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