INTERPRETATION OF GRAVITY ANOMALIES DUE TO FINITE INCLINED DIKES USING FOURIER TRANSFORMATION

Geophysics ◽  
1977 ◽  
Vol 42 (1) ◽  
pp. 51-59 ◽  
Author(s):  
V. L. S. Bhimasankaram ◽  
R. Nagendra ◽  
S. V. Seshagiri Rao
Keyword(s):  
Fourier Transform ◽  
High Frequency ◽  
Fourier Transformation ◽  
Synthetic Data ◽  
Gravity Anomalies ◽  
Frequency Range ◽  
Unknown Parameters ◽  
Estimated Parameters ◽  
The Fourier Transform ◽  
Theoretical Considerations

The Fourier transform of the gravity field due to a finite dipping dike is derived and its real and imaginary components are separated. Analysis of these two functions in a certain high‐frequency range yields simple relations that can be used to estimate the unknown parameters of the dike. The theoretical considerations are tested on synthetic data after performing the discrete Fourier transform (DFT), and the validity of the method of interpretation is established from a comparison of the actual and estimated parameters.

Interpretation of gravity anomalies of dike-like bodies by Fourier transformation

1970 ◽  
Vol 7 (2) ◽  
pp. 512-516 ◽  
Author(s):  
Bijon Sharma ◽  
L. P. Geldart ◽  
D. E. Gill
Keyword(s):  
Fourier Transform ◽  
Detailed Analysis ◽  
Gravity Anomaly ◽  
Fourier Transformation ◽  
Amplitude Spectrum ◽  
Gravity Anomalies ◽  
Objective Method ◽  
The Fourier Transform

An objective method is presented for interpreting the gravity anomalies of a dike using the Fourier transform of the observed gravity anomaly function. The amplitude spectrum of the transformed function contains information about the depth, inclination, and the thickness of the dike. The usefulness of the Fourier transform technique is illustrated by a detailed analysis of the gravity anomaly of a dike.

FOURIER TRANSFORMS OF FINITE LENGTH THEORETICAL GRAVITY ANOMALIES

Geophysics ◽  
1977 ◽  
Vol 42 (7) ◽  
pp. 1450-1457 ◽  
Author(s):  
Robert D. Regan ◽  
William J. Hinze
Keyword(s):  
Fourier Transform ◽  
Analytical Solution ◽  
Finite Length ◽  
Fourier Transforms ◽  
Gravity Anomalies ◽  
Mathematical Structure ◽  
Practical Application ◽  
Convolution Integrals ◽  
The Fourier Transform ◽  
Interpretation Method

The mathematical structure of the Fourier transformations of theoretical gravity anomalies of several geometrically simple bodies appears to have distinct advantages in the interpretation of these anomalies. However, the practical application of this technique is dependent upon the transformation of an observed gravity anomaly of finite length. Ideally, interpretation methods similar to those for the transformations of the theoretical gravity anomalies should be developed for anomalies of a finite length. However, the mathematical complexity of the convolution integrals in the transform calculations of theoretical anomaly segments indicate that no general closed analytical solution useful for interpretation is available. Thus, in order to utilize the Fourier transform interpretation method, the data must be of sufficient length for the finite transform to closely approximate the theoretical transforms.

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.

THEORETICAL TRANSFORMS OF THE GRAVITY ANOMALIES OF TWO IDEALIZED BODIES

Geophysics ◽  
1978 ◽  
Vol 43 (3) ◽  
pp. 631-633 ◽  
Author(s):  
Robert D. Regan ◽  
William J. Hinze
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Three Dimensional ◽  
Gravity Anomalies ◽  
Vertical Line ◽  
The Fourier Transform ◽  
Line Elements ◽  
Distribution Of Magnetization

Odegard and Berg (1965) have shown that the interpretational process can be simplified for several idealized bodies by utilizing the Fourier transform of the resultant theoretical gravity anomalies. Additional studies relating similar conclusions for other idealized bodies have been reported by Gladkii (1963), Roy (1967), Sharma et al (1970), Davis (1971), Eby (1972), and Saha (1975), and a summary of the spatial and frequency domain equations is given in Regan and Hinze (1976, Table 1); however, the transforms of the three‐dimensional prism and vertical line elements, often utilized in interpretation, have not been previously examined in this manner. Although Bhattacharyya and Chen (1977) have developed and utilized the transform of the 3-D prism in their method for determining the distribution of magnetization in a localized region, it is still of value to present the interpretive advantages of the transform equation itself.

scholarly journals Extracting Features of Transient Electric Fields With Fourier And Wavelet Transform–A Case Study Of Lightning Positive Return Stroke

2021 ◽  
Vol 14 (14) ◽  
pp. 44-50
Author(s):  
Shriram Sharma
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Spectral Density ◽  
Frequency Spectrum ◽  
Electric Fields ◽  
Frequency Range ◽  
Return Stroke ◽  
The Fourier Transform ◽  
Positive Return ◽  
Domain Information

Frequency domain information were extracted from the time domain electric fields pertinent to the lightning positive return strokes applying Fourier transform and Wavelet transform. The electric field radiated by positive ground flashes striking the sea were recorded at 10 ns resolution at a coastal station to minimize the propagation effects. The frequency spectrum of the electric field of positive return strokes were computed applying the Fourier transform technique in the range of 10 kHz to 20 MHz owing to the fact that this range of frequency is of very much interest to the researchers and design engineers. The amplitude of the energy spectral density decreases nearly as ƒ-1 from 10 kHz to about 0.1 MHz and drops nearly as ƒ-2 up to 8 MHz.  Applying the wavelet transform technique, the same positive return strokes are found to radiate in the frequency range of 5.5 to 81 kHz with the average spread distribution of 13.6 kHz to about 30 kHz. From frequency spectrum obtained from the Fourier transform it is difficult to identify as which phase of the return stroke radiates in the higher frequency range and that in the lower frequency range, whereas, one can easily identify from the frequency spectrum obtained with the wavelet transform that ramp portion of the positive return stroke radiates in the larger spectral range as compared to that of initial peak of the return stroke.  Also, from the spectral density map obtained from wavelet transform one can easily observe the contribution of each phase in a range of frequency, which is not possible from the Fourier transform technique. Clearly, the wavelet transform is much more powerful tool to extract the frequency domain information of a non-stationary signal as compared to that of Fourier transform.

scholarly journals Pitfalls in the Evaluation of X-ray Diffraction Line Shape

1988 ◽  
Vol 41 (2) ◽  
pp. 237 ◽  
Author(s):  
Gerhard Zorn
Keyword(s):  
Fourier Transform ◽  
Computer Simulations ◽  
Line Shape ◽  
Fourier Transformation ◽  
Step Width ◽  
X Ray Diffraction ◽  
X Ray ◽  
Sampling Points ◽  
The Fourier Transform ◽  
Reliable Basis

The sources of errors in the analysis of X-ray diffraction profiles are described, and recipes are given to minimise or eliminate these errors. It is proposed that a sample at high temperatures is used as a standard. The influence of measurement statistics on the Fourier transform of deconvoluted functions is demonstrated through computer simulations. The necessity for smoothing procedures is stressed. It is shown how the parameter step width, number of sampling points, and position of origin for the Fourier transformation can be optimised, and thus a reliable basis can be created for the interpretation of the Fourier transform in terms of crystallite size, size distribution, and micros train.

Analysis of recurrent laryngeal inspiratory discharges in relation to fast rhythms

1994 ◽  
Vol 72 (3) ◽  
pp. 1304-1316 ◽  
Author(s):  
C. N. Christakos ◽  
M. I. Cohen ◽  
A. L. Sica ◽  
W. X. Huang ◽  
W. R. See ◽  
...  
Keyword(s):  
Spectral Analysis ◽  
High Frequency ◽  
Spectral Peak ◽  
Frequency Range ◽  
Medium Frequency ◽  
Firing Rates ◽  
High Frequency Oscillations ◽  
Rhythmic Discharge ◽  
Theoretical Considerations ◽  
Fast Rhythm

1. Inspiratory (I) activities of recurrent laryngeal (RL) motoneurons and efferent nerves were studied by autospectral, interval, and coherence analyses, with emphasis on fast rhythms of two types: medium-frequency oscillations (MFO, usual range 20-50 Hz for nerve autospectral peaks) and high-frequency oscillations (HFO, usual range 50-100 Hz). 2. In decerebrate, paralyzed, and artificially ventilated cats, recordings were taken from 27 isolated single RL fibers (14 cats) and 8 identified RL motoneurons in the medulla (6 cats), together with recordings of phrenic (PHR) and RL whole-nerve activities. In another 50 cats, RL and PHR nerve discharges were recorded simultaneously. 3. The autospectra of RL units showed prominent MFO peaks with frequencies close to that of the RL nerve MFO spectral peak, indicating presence of this type of fast rhythm in the units' discharges. Spectral analysis of RL unit activity in different segments of the I phase showed that the frequency of a unit's MFO was very close to the peak (maintained) firing rate of the unit during the portion of I analyzed. Thus a motoneuron's MFO spectral peak reflected its rhythmic discharge arising from the cell's refractoriness (and possibly with the rate changing in the course of I). 4. The coherences of motoneurons' MFOs to nerve MFOs were very low or 0, indicating that correlations between unitary MFOs of the RL population were rare and/or weak. 5. In those cats (19/20) that had discernible PHR nerve HFO autospectral peaks, about half of the recorded RL motoneurons (16/34) had HFO. For these motoneurons, the unit-nerve HFO coherences were substantial, indicating widespread correlations between unitary HFOs. 6. In a fraction of cats, coherence peaks in the MFO frequency range were observed between bilateral RL nerves, and between RL and PHR nerves, at frequencies that were subharmonics of the HFO frequency. 7. In light of theoretical considerations on the generation of aggregate rhythms from superposition of unitary rhythms, these observations indicate that, similarly, to the case of PHR motoneurons and nerves. 1) RL nerve MFO arises from superposition of uncorrelated, or at most partially correlated, MFOs of RL units, representing the rhythmic discharges of the cells. It is manifested therefore as a spectral deflection with a maximum in the band of peak firing rates of the units. 2) RL nerve HFO arises from correlated, common-frequency HFOs in a subpopulation of RL units, caused by HFO inputs from antecedent medullary I neurons.(ABSTRACT TRUNCATED AT 400 WORDS)

On: “Interpretation of Gravity Anomalies Due to Finite Inclined Dikes Using Fourier Transformation” by V. L. S. Bhimasankaram, R. Nagendra, and S. V. Seshagiri Rao (GEOPHYSICS, February 1977, p. 51–59)

Geophysics ◽  
1978 ◽  
Vol 43 (4) ◽  
pp. 823-824
Keyword(s):  
Fourier Transformation ◽  
Gravity Anomalies ◽  
Frequency Range ◽  
Straight Line ◽  
Elegant Solution

We feel that some of the results and conclusions in this paper need some comments. 1) The authors claim on p. 59 that their method clearly stands out as the first direct and elegant solution to the problem of the finite dipping dike in gravity prospecting. This is, in fact, not true, since Sharma et al (1970) arrived at exactly the same formulas. In our opinion their method of interpretation seems more realistic in many ways than the authors. For instance they find the depth to the dike from the slope of a straight line fitted to a spectral quantity, where the authors make use of selected points of the spectrum. The latter method seems to be more sensitive to noise than the former, where the straight line is fitted to the spectral quantity over some frequency range, thus some kind of averaging process is performed.

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 Magnetic storm free ULF analysis in relation with earthquakes in Taiwan

2012 ◽  
Vol 12 (5) ◽  
pp. 1747-1754 ◽  
Author(s):  
S. Wen ◽  
C.-H. Chen ◽  
H.-Y. Yen ◽  
T.-K. Yeh ◽  
J.-Y. Liu ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Cross Correlation ◽  
Low Frequency ◽  
Magnetic Anomalies ◽  
Magnetic Storms ◽  
Frequency Range ◽  
Geomagnetic Data ◽  
Before And After ◽  
The Cross ◽  
The Fourier Transform

Abstract. Despite early optimism, pre-earthquake anomalous phenomena can be determined by using enhanced amplitude at the ultra-low-frequency range from geomagnetic data via the Fourier transform. In reality, accuracy of the enhanced amplitude in relation to earthquakes (deduced from time-varied geomagnetic data) would be damaged by magnetic storms and/or other unwanted influences resulting from solar activity and/or variations in the ionosphere, respectively. We substitute values of the cross correlation between amplitudes, summarized from the earthquake-related (0.1–0.01 Hz) and the comparable (0.01–0.001 Hz) frequency bands, for isolated amplitude enhancements as indexes of determination associated with seismo-magnetic anomalies to mitigate disturbance caused by magnetic storms. A station located about 300 km away from the others is also taken into account to further examine whether changes of the cross correlation values are caused by seismo-magnetic anomalies limited within local regions or not. Analytical results show that the values suddenly decrease near epicenters a few days before and after 67% (= 6/9) of earthquakes (M > = 5) in Taiwan between September 2010 and March 2011. Seismo-magnetic signals determined by using the values of cross correlation methods partially improve results yielded from the Fourier transform alone and provide advantageous information of earthquake locations.

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