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.

A GENERAL EXPRESSION FOR THE FOURIER TRANSFORM OF THE GRAVITY ANOMALY DUE TO A FAULT

Geophysics ◽  
1977 ◽  
Vol 42 (7) ◽  
pp. 1458-1461 ◽  
Author(s):  
Bijon Sharma ◽  
T. K. Bose
Keyword(s):  
Fourier Transform ◽  
Gravity Anomaly ◽  
General Expression ◽  
Fault Plane ◽  
Gravity Anomalies ◽  
Arbitrary Angle ◽  
Vertical Fault ◽  
The Fourier Transform

The application of the method of the Fourier transform in interpreting gravity anomalies of faults has so far been based upon the Fourier transform of the gravity anomaly due to a single semi‐infinite block cut by a vertical fault. A general expression for the Fourier transform of the fault anomaly is here derived which is valid for an arbitrary angle of inclination of the fault plane. For deriving the general expression, the gravity anomaly of the fault is first separated into a constant and a variable term. The transforms of the two terms are calculated separately and then added to give the general expression for the Fourier transform of the fault anomaly.

scholarly journals ESTIMASI KETEBALAN SEDIMEN DENGAN ANALISIS POWER SPECTRAL PADA DATA ANOMALI GAYABERAT

GEOMATIKA ◽  
2018 ◽  
Vol 23 (2) ◽  
pp. 65 ◽  
Author(s):  
Mila Apriani ◽  
Admiral Musa Julius ◽  
Mahmud Yusuf ◽  
Damianus Tri Heryanto ◽  
Agus Marsono
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
Gravity Anomaly ◽  
Spectral Method ◽  
Gravity Data ◽  
Sediment Thickness ◽  
Transform Method ◽  
Fourier Transform Method ◽  
Power Spectral ◽  
The Fourier Transform

<p align="center"><strong>ABSTRAK</strong></p><p> </p><p>Penelitian dengan analisis <em>power spectral</em> data anomali gayaberat telah banyak dilakukan untuk estimasi ketebalan sedimen. Dalam studi ini penulis melakukan analisis spektral data anomali gayaberat wilayah DKI Jakarta untuk mengetahui kedalaman sumber anomali yang bersesuaian dengan ketebalan sedimen. Data yang digunakan berupa data gayaberat dari BMKG tahun 2014 dengan 197 lokasi titik pengukuran yang tersebar di koordinat 6,08º-6,36º LU dan 106,68º-106,97º BT. Studi ini menggunakan metode <em>power spectral</em>  dengan mentransformasikan data dari domain jarak ke dalam domain bilangan gelombang memanfaatkan transformasi <em>Fourier</em>. Hasil penelitian dengan menggunakan metode transformasi <em>Fourier  </em>menunjukkan bahwa ketebalan sedimen di Jakarta dari arah selatan ke utara semakin besar, di sekitar Babakan ketebalan diperkirakan 92 meter, sekitar Tongkol, Jakarta Utara diperkirakan 331 meter.</p><p><strong> </strong></p><p><strong>Kata kunci</strong>: <em>power spectral</em>, anomali gayaberat, ketebalan sedimen</p><p align="center"><strong><em> </em></strong></p><p align="center"><strong><em>ABSTRACT</em></strong></p><p><em> </em></p><p><em>Studies of spectral analysis of gravity anomaly data have been carried out to estimate the thickness of sediment. In this study the author did spectral analysis of gravity anomaly data of DKI Jakarta area to know the depth of anomaly source which corresponds to the thickness of sediment. The data used in the form of gravity data from BMKG 2014 with 197 locations of measurement points spread in coordinates 6.08º - 6.36º N and 106.68º - 106.97º E. This study used the power spectral method by transforming the data from the distance domain into the wavenumber domain utilizing the Fourier transform. The result of the research using Fourier transform method shows that the thickness of sediment in Jakarta from south to north is getting bigger, in Babakan the thickness of the sediment is around 92 meter, in Tongkol, North Jakarta is around 331 meter.</em></p><p><strong><em> </em></strong></p><p><strong><em>Keywords</em></strong><em>: </em><em>power spectral, gravity anomaly, sediment thickness</em><em></em></p>

Introduction

2009 ◽  
Author(s):  
Robert J Marks II
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Fourier Transform ◽  
Magnetic Resonance ◽  
Fourier Analysis ◽  
Fourier Integral ◽  
Sampling Theorem ◽  
Two Dimensional ◽  
The Fourier Transform ◽  
Array Imaging ◽  
Nuclear Magnetic

Jean Baptiste Joseph Fourier’s powerful idea of decomposition of a signal into sinusoidal components has found application in almost every engineering and science field. An incomplete list includes acoustics [1497], array imaging [1304], audio [1290], biology [826], biomedical engineering [1109], chemistry [438, 925], chromatography [1481], communications engineering [968], control theory [764], crystallography [316, 498, 499, 716], electromagnetics [250], imaging [151], image processing [1239] including segmentation [1448], nuclear magnetic resonance (NMR) [436, 1009], optics [492, 514, 517, 1344], polymer characterization [647], physics [262], radar [154, 1510], remote sensing [84], signal processing [41, 154], structural analysis [384], spectroscopy [84, 267, 724, 1220, 1293, 1481, 1496], time series [124], velocity measurement [1448], tomography [93, 1241, 1242, 1327, 1330, 1325, 1331], weather analysis [456], and X-ray diffraction [1378], Jean Baptiste Joseph Fourier’s last name has become an adjective in the terms like Fourier series [395], Fourier transform [41, 51, 149, 154, 160, 437, 447, 926, 968, 1009, 1496], Fourier analysis [151, 379, 606, 796, 1472, 1591], Fourier theory [1485], the Fourier integral [395, 187, 1399], Fourier inversion [1325], Fourier descriptors [826], Fourier coefficients [134], Fourier spectra [624, 625] Fourier reconstruction [1330], Fourier spectrometry [84, 355], Fourier spectroscopy [1220, 1293, 1438], Fourier array imaging [1304], Fourier transform nuclear magnetic resonance (NMR) [429, 1004], Fourier vision [1448], Fourier optics [419, 517, 1343], and Fourier acoustics [1496]. Applied Fourier analysis is ubiquitous simply because of the utility of its descriptive power. It is second only to the differential equation in the modelling of physical phenomena. In contrast with other linear transforms, the Fourier transform has a number of physical manifestations. Here is a short list of everyday occurrences as seen through the lens of the Fourier paradigm. • Diffracting coherent waves in sonar and optics in the far field are given by the two dimensional Fourier transform of the diffracting aperture. Remarkably, in free space, the physics of spreading light naturally forms a two dimensional Fourier transform. • The sampling theorem, born of Fourier analysis, tells us how fast to sample an audio waveform to make a discrete time CD or an image to make a DVD.

On: “Gravity Interpretation using the Fourier Integral” by J. W. Berg, Jr., and M. E. Odegard (GEOPHYSICS, vol. 30, no. 3, p. 424–438, June 1965)

Geophysics ◽  
1970 ◽  
Vol 35 (2) ◽  
pp. 358-358 ◽  
Author(s):  
H. A. Meinardus
Keyword(s):  
Fourier Transform ◽  
Gravity Anomalies ◽  
Fourier Integral ◽  
Hankel Transform ◽  
Cylindrical Symmetry ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dimensional Gravity ◽  
The One ◽  
Gravity Interpretation

The authors do not state explicitly that equations (1) and (12) express gravity anomalies of the two‐dimensional cylinder and fault respectively. These structures have an infinite extension along the strike, and all the gravity profiles perpendicular to the strike are identical. For this reason it is admissible to apply the one‐dimensional Fourier transform to obtain the one‐dimensional amplitude spectra shown in Figures (1) and (5). The situation, however, is different for the sphere, which does not have a one‐dimensional gravity profile in the above sense, but rather a two‐dimensional field with cylindrical symmetry. Instead of using the one‐dimensional Fourier transform as given by (6) along a straight line, we must apply the two‐dimensional Fourier transform over the whole area. Because of the circular symmetry, one radial variable will suffice in place of the two Cartesian coordinates x and y, and the two‐dimensional Fourier transform can be expressed as Hankel transform, so that equation (6) becomes [Formula: see text]

An analysis of the spectrum of a gravity anomaly over an inclined dike

Geophysics ◽  
1985 ◽  
Vol 50 (9) ◽  
pp. 1500-1501
Author(s):  
B. N. P. Agarwal ◽  
D. Sita Ramaiah
Keyword(s):  
Fourier Transform ◽  
Gravity Anomaly ◽  
Fourier Spectrum ◽  
Fourier Transforms ◽  
Weighted Average ◽  
Window Function ◽  
Average Spectrum ◽  
Amplitude Spectra ◽  
Distance Data ◽  
The Fourier Transform

Bhimasankaram et al. (1977) used Fourier spectrum analysis for a direct approach to the interpretation of gravity anomaly over a finite inclined dike. They derived several equations from the real and imaginary components and from the amplitude and phase spectra to relate various parameters of the dike. Because the width 2b of the dike (Figure 1) appears only in sin (ωb) term—ω being the angular frequency—they determined its value from the minima/zeroes of the amplitude spectra. The theoretical Fourier spectrum uses gravity field data over an infinite distance (length), whereas field observations are available only for a limited distance. Thus, a set of observational data is viewed as a product of infinite‐distance data with an appropriate window function. Usually, a rectangular window of appropriate distance (width) and of unit magnitude is chosen for this purpose. The Fourier transform of the finite‐distance and discrete data is thus represented by convolution operations between Fourier transforms of the infinite‐distance data, the window function, and the comb function. The combined effect gives a smooth, weighted average spectrum. Thus, the Fourier transform of actual observed data may differ substantially from theoretic data. The differences are apparent for low‐ and high‐frequency ranges. As a result, the minima of the amplitude spectra may change considerably, thereby rendering the estimate of the width of the dike unreliable from the roots of the equation sin (ωb) = 0.

scholarly journals Apparent Variation of v sin i and Rotational Modulation in Be Stars

2004 ◽  
Vol 215 ◽  
pp. 93-94
Author(s):  
C. Neiner ◽  
S. Jankov ◽  
M. Floquet ◽  
A. M. Hubert
Keyword(s):  
Fourier Transform ◽  
Magnetic Dipole ◽  
Be Stars ◽  
Line Profiles ◽  
Transform Method ◽  
Rotational Modulation ◽  
Be Star ◽  
Apparent Variation ◽  
The Fourier Transform ◽  
First Time

v sin i was determined by applying the Fourier transform method to the line profiles of two classical Be Stars. A variation is observed in the apparent v sin i which corresponds to the main frequencies associated to nrp modes. Rotational modulation is observed in wind sensitive UV lines of the Be star ω Ori and is associated with an oblique magnetic dipole which is discovered for the first time in a classical Be star.

Bleustein-Gulyaev Waves in an Inhomogeneous Layered Piezoelectric Half-Space

2006 ◽  
Vol 306-308 ◽  
pp. 1223-1228
Author(s):  
Fei Peng ◽  
Hua Rui Liu
Keyword(s):  
Fourier Transform ◽  
Phase Velocity ◽  
Half Space ◽  
Electric Potential ◽  
Piezoelectric Layer ◽  
Field Equations ◽  
Transform Method ◽  
Coupled Field ◽  
Coupled Field Equations ◽  
The Fourier Transform

The propagation of Bleustein-Gulyaev (BG) waves in an inhomogeneous layered piezoelectric half-space is investigated in this paper. Application of the Fourier transform method and by solving the electromechanically coupled field equations, solutions to the mechanical displacement and electric potential are obtained for the piezoelectric layer and substrate, respectively. The phase velocity equations for BG waves are obtained for the surface electrically shorted case. When the layer and the substrate are homogenous, the dispersion equations are in agreement with the corresponding results. Numerical calculations are performed for the case that the layer and the substrate are identical LiNbO3 except that they are polarized in opposite directions. Effects of the inhomogeneities induced by either the layer or substrate are discussed in detail.

Sign in / Sign up

Export Citation Format

Share Document