GRAVITY PROFILE INTERPRETATION USING THE FOURIER TRANSFORM

Geophysics ◽  
1974 ◽  
Vol 39 (6) ◽  
pp. 862-866 ◽  
Author(s):  
S. J. Collins ◽  
A. R. Dodds ◽  
B. D. Johnson
Keyword(s):  
Fourier Transform ◽  
Horizontal Cylinder ◽  
Direct Interpretation ◽  
Data Points ◽  
Lateral Extent ◽  
The Fourier Transform ◽  
Interpretation Method ◽  
Data Length ◽  
Gravity Profile

A number of attempts have been made to perform direct interpretation of gravity profiles using the Fourier transform of the profile. Of these, the methods of Odegard and Berg (1965) and Sharma et al. (1970) appear to be most applicable. The purpose of this study was to take one of the proposed models (Odegard and Berg’s horizontal cylinder) and determine the applicability of the interpretation method in terms of the number and lateral extent of the data points. The relative accuracies of the estimates of the depth and mass of a cylinder were determined as criteria for estimating the effects of data length and number of data points. In addition, the interpretation was extended to include the separation of two cylinders.

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.

scholarly journals Calculation of signal spectrum by means of stochastic inversion

2010 ◽  
Vol 28 (7) ◽  
pp. 1409-1418 ◽  
Author(s):  
T. Nygrén ◽  
Th. Ulich
Keyword(s):  
Fourier Transform ◽  
Sampling Rate ◽  
Digital Signal ◽  
Close Relation ◽  
Signal Spectrum ◽  
Inversion Method ◽  
Stochastic Inversion ◽  
Data Points ◽  
Sinusoidal Functions ◽  
The Fourier Transform

Abstract. The standard method of calculating the spectrum of a digital signal is based on the Fourier transform, which gives the amplitude and phase spectra at a set of equidistant frequencies from signal samples taken at equal intervals. In this paper a different method based on stochastic inversion is introduced. It does not imply a fixed sampling rate, and therefore it is useful in analysing geophysical signals which may be unequally sampled or may have missing data points. This could not be done by means of Fourier transform without preliminary interpolation. Another feature of the inversion method is that it allows unequal frequency steps in the spectrum, although this property is not needed in practice. The method has a close relation to methods based on least-squares fitting of sinusoidal functions to the signal. However, the number of frequency bins is not limited by the number of signal samples. In Fourier transform this can be achieved by means of additional zero-valued samples, but no such extra samples are used in this method. Finally, if the standard deviation of the samples is known, the method is also able to give error limits to the spectrum. This helps in recognising signal peaks in noisy spectra.

The application of Walsh transforms to interpret gravity anomalies due to some simple geometrically shaped causative sources: A feasibility study

Geophysics ◽  
1990 ◽  
Vol 55 (7) ◽  
pp. 843-850 ◽  
Author(s):  
R. K. Shaw ◽  
B. N. P. Agarwal
Keyword(s):  
Fourier Transform ◽  
Linear Time ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Horizontal Cylinder ◽  
Walsh Transform ◽  
Walsh Functions ◽  
The Fourier Transform ◽  
Depth Extent ◽  
Good Agreement

Walsh functions are a set of complete and orthonormal functions of nonsinusoidal waveform. In contrast to sinusoidal waveforms whose amplitudes may assume any value between −1 to +1, Walsh functions assume only discrete amplitudes of ±1 which form the kernel function of the Walsh transform. Because of this special nature of the kernel, computation of the Walsh transform of a given signal is simpler and faster than that of the Fourier transform. The properties of the Fourier transform in linear time are similar to those of the Walsh transform in dyadic time. The Fourier transform has been widely used in interpretation of geophysical problems. Considering various aspects of the Walsh transform, an attempt has been made to apply it to some gravity data. A procedure has been developed for automated interpretation of gravity anomalies due to simple geometrical causative sources, viz., a sphere, a horizontal cylinder, and a 2-D vertical prism of large depth extent. The technique has been applied to data from the published literature to evaluate its applicability, and the results are in good agreement with the more conventional ones.

scholarly journals Algorithm for B-scan Image Reconstruction in Optical Coherence Tomography

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
Kranti Patil ◽  
Anurag Mahajan ◽  
Balamurugan Subramani ◽  
Arulmozhivarman Pachiyappan ◽  
Roshan Makkar
Keyword(s):  
Optical Coherence Tomography ◽  
Fourier Transform ◽  
Optical Coherence ◽  
Cross Sectional ◽  
Image Construction ◽  
Data Points ◽  
Maximum Penetration ◽  
The Fourier Transform ◽  
Processing Techniques

Optical coherence tomography (OCT) is an evolving medical imaging technology that offers in vivo cross-sectional, sub-surface images in real-time. OCT has become popular in the medical as well as non-medical fields. The technique extensively uses for food industry, dentistry, dermatology, and ophthalmology. The technique is non-invasive and works on the Michelson interferometry principle, i.e., dependent on back reflections of the signal and its interference. The objective is to develop an algorithm for signal processing to construct an OCT image and then to enhance the quality of the image using image processing techniques like filtering. The image construction was primarily based on the Fourier transform (FT) of the dataset obtained by data acquisition. This FT could be performed rapidly with the extensively used algorithm of fast Fourier transform (FFT). The depth-wise information could be extracted from each A-scan, i.e., axial scan and also the B-scan was obtained from the A-scan to see the structure of sample. The maximum penetration depth achieved with proposed system was 2.82mm for 1024 data points. First and second layer of leaf were getting at thickness of 1mm and 1.6mm, respectively. A-scans for Human fingertip gave its first, second and third layer was at a thickness of 0.75mm, 0.9mm and 1.6mm, respectively. A-scans for foam sheet gave its first, second and third layer was at a thickness of 0.6mm, 0.75mm, and 0.85mm, respectively.

Comparison of Numerical and Experimental Strain Measurements of a Composite Panel Using Image Decomposition

2011 ◽  
Vol 70 ◽  
pp. 63-68 ◽  
Author(s):  
Christopher M Sebastian ◽  
Eann A Patterson ◽  
Donald Ostberg
Keyword(s):  
Fourier Transform ◽  
Image Decomposition ◽  
Image Correlation ◽  
Composite Panel ◽  
Data Sets ◽  
Full Field ◽  
Strain Measurements ◽  
Data Points ◽  
Optical Strain ◽  
The Fourier Transform

Image decomposition is used to address the problem of accurately and concisely describing the strain in an inhomogeneous composite panel that is bolted to a vehicle structure. In-service, the composite panel is subject to structural loads from the vehicle which can cause unintended damage to the panel. Finite element simulations have been performed with the plan to establish their fidelity using full-field optical strain measurements obtained using digital image correlation. A methodology is presented based on using orthogonal shape descriptors to decompose the data-rich maps of strain into information-preserved data sets of reduced dimensionality that facilitate a quantitative comparison of the computational and experimental results. The decomposition is achieved employing the Fourier transform followed by fitting Tchebichef moments to the maps of the magnitude of the Fourier transform. The results show that this approach is fast and reliably describes the strain fields using less than fifty moments as compared to the thousands of data points in each strain map.

Autoregressive analysis of aortic input impedance: comparison with Fourier transform

1991 ◽  
Vol 260 (3) ◽  
pp. H998-H1002 ◽  
Author(s):  
T. Kubota ◽  
R. Itaya ◽  
J. Alexander ◽  
K. Todaka ◽  
M. Sugimachi ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Input Impedance ◽  
Impedance Spectrum ◽  
Aortic Pressure ◽  
Accurate Estimate ◽  
Ar Model ◽  
Aortic Input Impedance ◽  
The Fourier Transform ◽  
Data Length ◽  
Autoregressive Analysis

We evaluated the advantages of the autoregressive (AR) model over the conventional Fourier transform in estimating aortic input impedance. In 10 anesthetized open-chest dogs, we digitized aortic pressure and flow at 200 Hz for 51.20 s under random ventricular pacing and subdivided them into five segments. We obtained aortic input impedance over the frequency range of 0.1-20 Hz both by AR model and by Fourier transform for various lengths of data, i.e., from one to four consecutive segments. For any given data length, the impedance spectrum estimated by the AR model was smoother than that obtained by the Fourier transform. To evaluate the accuracy of the estimated impedance, we predicted instantaneous aortic pressure of the fifth segment by convolving corresponding aortic flow with the impulse response of aortic input impedance. The prediction error was less with the AR model than that resulting from Fourier transform as long as the number of the segments was less than four. We conclude that the AR model provides a more accurate estimate of aortic input impedance than does the Fourier transform when data length is limited.

Investigation of the Fourier Transform for Analyzing Spectroscopic Data by Computerized Learning Machines

1971 ◽  
Vol 25 (2) ◽  
pp. 203-207 ◽  
Author(s):  
L. E. Wangen ◽  
N. M. Frew ◽  
T. L. Isenhour ◽  
P. C. Jurs
Keyword(s):  
Fourier Transform ◽  
Data Storage ◽  
Spectroscopic Data ◽  
Weighted Average ◽  
Learning Machines ◽  
Frequency Representation ◽  
Data Points ◽  
The Fourier Transform ◽  
Time Required

This paper investigates the use of the fast Fourier transform as an aid in the analysis and classification of spectroscopic data. The pattern obtained after transformation is viewed as a weighted average and/or as a frequency representation of the original spectroscopic data. In pattern recognition the Fourier transform allows a different (i.e., a frequency) representation of the data which may prove more amenable to linear separation according to various categories of the patterns. The averaging property means that the information in each dimension of the original pattern is distributed over all dimensions in the pattern resulting from the Fourier transformation. Hence the arbitrary omission or loss of data points in the Fourier spectrum has less effect on the original spectrum. This property is exploited for reducing the dimensionality of the Fourier data so as to minimize data storage requirements and the time required for development of pattern classifiers for categorization of the data. Examples of applications are drawn from low resolution mass spectrometry.

scholarly journals Strain Sensitivity Enhancement of Broadband Ultrasonic Signals in Plates Using Spectral Phase Filtering

2021 ◽  
Vol 11 (6) ◽  
pp. 2582
Author(s):  
Lucas M. Martinho ◽  
Alan C. Kubrusly ◽  
Nicolás Pérez ◽  
Jean Pierre von der Weid
Keyword(s):  
Fourier Transform ◽  
Guided Waves ◽  
Strain Level ◽  
Energy Concentration ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Frequency Representation ◽  
The Fourier Transform ◽  
Short Time ◽  
Sensitivity Gain

The focused signal obtained by the time-reversal or the cross-correlation techniques of ultrasonic guided waves in plates changes when the medium is subject to strain, which can be used to monitor the medium strain level. In this paper, the sensitivity to strain of cross-correlated signals is enhanced by a post-processing filtering procedure aiming to preserve only strain-sensitive spectrum components. Two different strategies were adopted, based on the phase of either the Fourier transform or the short-time Fourier transform. Both use prior knowledge of the system impulse response at some strain level. The technique was evaluated in an aluminum plate, effectively providing up to twice higher sensitivity to strain. The sensitivity increase depends on a phase threshold parameter used in the filtering process. Its performance was assessed based on the sensitivity gain, the loss of energy concentration capability, and the value of the foreknown strain. Signals synthesized with the time–frequency representation, through the short-time Fourier transform, provided a better tradeoff between sensitivity gain and loss of energy concentration.

Determination of starch crystallinity with the Fourier-transform terahertz spectrometer

2021 ◽  
Vol 262 ◽  
pp. 117928
Author(s):  
Shusaku Nakajima ◽  
Shuhei Horiuchi ◽  
Akifumi Ikehata ◽  
Yuichi Ogawa
Keyword(s):  
Fourier Transform ◽  
The Fourier Transform ◽  
Starch Crystallinity
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