Directional spectral analysis and filtering of geophysical maps

Geophysics ◽  
1988 ◽  
Vol 53 (12) ◽  
pp. 1587-1591 ◽  
Author(s):  
Freyr Thorarinsson ◽  
Stefan G. Magnusson ◽  
Axel Bjornsson
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
Power Spectrum ◽  
Two Dimensional ◽  
Directional Filtering ◽  
Gravity And Magnetic ◽  
The Fourier Transform ◽  
Map Data ◽  
Tectonic Features

The detection of linear anomalies in map data is facilitated by studying the two‐dimensional power spectrum, because the directivity of the energy in the map is preserved in the Fourier transform. The lineaments associated with individual peaks in the spectrum are then separated from the map data by directional filtering and studied independently of other map features. Gravity and magnetic maps from an active rift area in southwestern Iceland are analyzed in this manner. The agreement between the filtered maps is good and they fit the observed tectonic features quite well.

Directional filtering for linear feature enhancement in geophysical maps

Geophysics ◽  
2000 ◽  
Vol 65 (6) ◽  
pp. 1758-1768 ◽  
Author(s):  
Michael P. Sykes ◽  
Umesh C. Das
Keyword(s):  
Fourier Transform ◽  
Radon Transform ◽  
Synthetic Data ◽  
Processing Technique ◽  
Petroleum Exploration ◽  
Transform Method ◽  
Linear Feature ◽  
Directional Filtering ◽  
The Fourier Transform ◽  
Tectonic Features

Geophysical maps of data acquired in ground and airborne surveys are extensively used for mineral, groundwater, and petroleum exploration. Lineaments in these maps are often indicative of contacts, basement faulting, and other tectonic features of interest. To aid the interpretation of these maps, a versatile processing technique of directional filtering, based on the 2-D “normal” Radon transform, is used to enhance or suppress specific lineaments. Synthetic data and field examples using electromagnetic and radiometric data are used to demonstrate the superiority of the Radon transform method over conventional Fourier transform filtering. The Radon transform technique is shown to be more versatile and less susceptible to processing artefacts than the Fourier transform methods.

scholarly journals Spectral Analysis of Traffic Functions in Urban Areas

2015 ◽  
Vol 27 (6) ◽  
pp. 477-484 ◽  
Author(s):  
Florin Nemtanu ◽  
Ilona Madalina Costea ◽  
Catalin Dumitrescu
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
Fourier Analysis ◽  
Traffic Flow ◽  
Traffic Control ◽  
Urban Areas ◽  
Urban Traffic ◽  
The Fourier Transform ◽  
The City ◽  
Different Time Scales

The paper is focused on the Fourier transform application in urban traffic analysis and the use of said transform in traffic decomposition. The traffic function is defined as traffic flow generated by different categories of traffic participants. A Fourier analysis was elaborated in terms of identifying the main traffic function components, called traffic sub-functions. This paper presents the results of the method being applied in a real case situation, that is, an intersection in the city of Bucharest where the effect of a bus line was analysed. The analysis was done using different time scales, while three different traffic functions were defined to demonstrate the theoretical effect of the proposed method of analysis. An extension of the method is proposed to be applied in urban areas, especially in the areas covered by predictive traffic control.

The Fourier transform and spectral analysis

1999 ◽  
pp. 240-277
Author(s):  
Bernard Mulgrew ◽  
Peter Grant ◽  
John Thompson
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
The Fourier Transform

scholarly journals Two-Dimensional Quaternion Linear Canonical Transform: Properties, Convolution, Correlation, and Uncertainty Principle

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Mawardi Bahri ◽  
Ryuichi Ashino
Keyword(s):  
Fourier Transform ◽  
Uncertainty Principle ◽  
Linear Canonical Transform ◽  
Two Dimensional ◽  
Quaternion Fourier Transform ◽  
Gaussian Functions ◽  
The Fourier Transform ◽  
Definition Of ◽  
Quaternion Linear Canonical Transform

A definition of the two-dimensional quaternion linear canonical transform (QLCT) is proposed. The transform is constructed by substituting the Fourier transform kernel with the quaternion Fourier transform (QFT) kernel in the definition of the classical linear canonical transform (LCT). Several useful properties of the QLCT are obtained from the properties of the QLCT kernel. Based on the convolutions and correlations of the LCT and QFT, convolution and correlation theorems associated with the QLCT are studied. An uncertainty principle for the QLCT is established. It is shown that the localization of a quaternion-valued function and the localization of the QLCT are inversely proportional and that only modulated and shifted two-dimensional Gaussian functions minimize the uncertainty.

scholarly journals Stokes flow singularities in a two-dimensional channel: a novel transform approach with application to microswimming

2013 ◽  
Vol 469 (2157) ◽  
pp. 20130198 ◽  
Author(s):  
Darren G. Crowdy ◽  
Anthony M. J. Davis
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
Boundary Value Problems ◽  
Stokes Flow ◽  
Evolution Equations ◽  
Two Dimensional ◽  
Third Order ◽  
Transform Method ◽  
Independent Variables ◽  
Simply Connected

A transform method for determining the flow generated by the singularities of Stokes flow in a two-dimensional channel is presented. The analysis is based on a general approach to biharmonic boundary value problems in a simply connected polygon formulated by Crowdy & Fokas in this journal. The method differs from a traditional Fourier transform approach in entailing a simultaneous spectral analysis in the independent variables both along and across the channel. As an example application, we find the evolution equations for a circular treadmilling microswimmer in the channel correct to third order in the swimmer radius. Significantly, the new transform method is extendible to the analysis of Stokes flows in more complicated polygonal microchannel geometries.

On: “Gravity Interpretation Using the Fourier Integral”, by M. E. Odegard and J. W. Berg, Jr. (GEOPHYSICS, June 1965, p. 127–138)

Geophysics ◽  
1975 ◽  
Vol 40 (2) ◽  
pp. 356-357
Author(s):  
Jay Gopal Saha
Keyword(s):  
Fourier Transform ◽  
Gravity Anomaly ◽  
Fourier Integral ◽  
Two Dimensional ◽  
Transform Method ◽  
Reverse Problem ◽  
Vertical Fault ◽  
Vertical Step ◽  
The Fourier Transform ◽  
Gravity Interpretation

In their paper, Odegard and Berg claim that from the gravity anomaly due to a two‐dimensional vertical fault the density, the throw, and the depth can be determined uniquely by a Fourier transform method. It is true that the solution of the reverse problem for a two‐dimensional vertical step is theoretically unique. The derivation of the Fourier transform by the authors, however, is erroneous.

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