THE USE OF LINEAR FILTERING IN GRAVITY PROBLEMS

Geophysics ◽  
1971 ◽  
Vol 36 (6) ◽  
pp. 1174-1203 ◽  
Author(s):  
C. C. Ku ◽  
W. M. Telford ◽  
S. H. Lim
Keyword(s):  
Fourier Transform ◽  
Fourier Analysis ◽  
Frequency Domain ◽  
Gibbs Phenomenon ◽  
Downward Continuation ◽  
Main Lobe ◽  
Linear Filtering ◽  
Space Domain ◽  
Actual Field ◽  
High Pass

The technique of Fourier analysis is reviewed and the equivalence and relative advantages of convolution filtering in the space domain and multiplication filtering in the frequency domain are demonstrated with actual field examples. We discuss the design of ideal filters in terms of the relationships between the main lobe and the side lobes. Cut‐and‐try methods appear to favor the hanning window or the hamming window, since these windows minimize the Gibbs phenomenon associated with the downward continuation or high‐pass filtering operation. New sets of coefficients for convolution filtering, based upon Fourier transform theory and the sampling theory, are derived.

On: “The Use of Linear Filtering in Gravity Problems,” by C. C. Ku, W. M. Telford, and S. H. Lim (GEOPHYSICS, December 1971, p. 1174–1203)

Geophysics ◽  
1972 ◽  
Vol 37 (4) ◽  
pp. 704-705
Author(s):  
William D. Hibler
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Frequency Domain ◽  
Boundary Effects ◽  
Linear Filtering ◽  
Filter Function ◽  
Space Domain ◽  
Frequency Space ◽  
Finite Samples ◽  
Space Filter

In a subsection of their paper entitled “Convolution versus Multiplication,” the authors state that when using finite samples of equally spaced data, multiplication of the filter function in the frequency domain and the equivalent convolution in the space domain will yield different outputs. This is normally true but may be circumvented by using a carefully chosen frequency space‐filter function. Such a technique is normally referred to as the aperiodic fast Fourier transform convolution technique (Stockham, 1966), whereas normally multiplication in frequency space yields a periodic convolution with spurious boundary effects.

Synthesis and Simplification of Fractal Profile

2011 ◽  
Vol 279 ◽  
pp. 262-265
Author(s):  
Chao Zhou ◽  
Cheng Hui Gao ◽  
Jie Chen ◽  
Lian Feng Lai
Keyword(s):  
Finite Element ◽  
Fourier Transform ◽  
Frequency Domain ◽  
Discrete Fourier Transform ◽  
High Frequency ◽  
Space Domain ◽  
Finite Element Software ◽  
Redundant Data ◽  
Frequency Components

In order to import a synthesized fractal profile into finite element software, the profile synthesized by discrete Fourier transform was studied. The synthesized profile was filtered in frequency domain in order to filter its high frequency components and to make it smooth, and then the chord deviation algorithm was used to reduce its redundant data in space domain. It was found that: after filtering, the profile is smooth but with lots of redundant data; the chord deviation algorithm can simplify the profile which is redundant in space domain; the time needed in the process of importing a profile into finite element software can be reduced greatly after profile simplification.

JOINT INTERPRETATION OF AIRBORNE ELECTROMAGNETIC DATA IN THE TIME DOMAIN AND FREQUENCY DOMAIN

2018 ◽  
Vol 12 (7-8) ◽  
pp. 76-83
Author(s):  
E. V. KARSHAKOV ◽  
J. MOILANEN
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Frequency Interval ◽  
Single Spectrum ◽  
Simultaneous Inversion ◽  
Homogeneous Half Space ◽  
Time Domain Data ◽  
The Time Domain

Тhe advantage of combine processing of frequency domain and time domain data provided by the EQUATOR system is discussed. The heliborne complex has a towed transmitter, and, raised above it on the same cable a towed receiver. The excitation signal contains both pulsed and harmonic components. In fact, there are two independent transmitters operate in the system: one of them is a normal pulsed domain transmitter, with a half-sinusoidal pulse and a small "cut" on the falling edge, and the other one is a classical frequency domain transmitter at several specially selected frequencies. The received signal is first processed to a direct Fourier transform with high Q-factor detection at all significant frequencies. After that, in the spectral region, operations of converting the spectra of two sounding signals to a single spectrum of an ideal transmitter are performed. Than we do an inverse Fourier transform and return to the time domain. The detection of spectral components is done at a frequency band of several Hz, the receiver has the ability to perfectly suppress all sorts of extra-band noise. The detection bandwidth is several dozen times less the frequency interval between the harmonics, it turns out thatto achieve the same measurement quality of ground response without using out-of-band suppression you need several dozen times higher moment of airborne transmitting system. The data obtained from the model of a homogeneous half-space, a two-layered model, and a model of a horizontally layered medium is considered. A time-domain data makes it easier to detect a conductor in a relative insulator at greater depths. The data in the frequency domain gives more detailed information about subsurface. These conclusions are illustrated by the example of processing the survey data of the Republic of Rwanda in 2017. The simultaneous inversion of data in frequency domain and time domain can significantly improve the quality of interpretation.

Fourier analysis of the light changes of eclipsing variables in the frequency-domain

1989 ◽  
Vol 159 (2) ◽  
pp. 279-293 ◽  
Author(s):  
Hamid M. K. Al-Naimiy ◽  
Sabeeh R. Jabbar ◽  
Hasan A. Fleyen ◽  
Jinan M. Al-Razzaz
Keyword(s):  
Fourier Analysis ◽  
Frequency Domain

IDENTIFICATION OF INTERHARMONICS BASED ON WAVELET PACKET TRANSFORM

2021 ◽  
Vol 3 (1) ◽  
pp. 031-036
Author(s):  
S. A. GOROVOY ◽  
◽  
V. I. SKOROKHODOV ◽  
D. I. PLOTNIKOV ◽  
◽  
...  
Keyword(s):  
Fourier Transform ◽  
Simulation Model ◽  
Frequency Domain ◽  
Time Domain ◽  
Wavelet Packet ◽  
High Accuracy ◽  
Wavelet Packet Transform ◽  
Mathematical Apparatus ◽  
Nonlinear Load ◽  
The Time Domain

This paper deals with the analysis of interharmonics, which are due to the presence of a nonlinear load. The tool for the analysis was a mathematical apparatus - wavelet packet transform. Which has a number of advantages over the traditional Fourier transform. A simulation model was developed in Simulink to simulate a non-stationary non-sinusoidal mode. The use of the wavelet packet transform will allow to determine the mode parameters with high accuracy from the obtained wavelet coefficients. It also makes it possible to obtain information, both in the frequency domain of the signal and in the time domain.

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