Two Dimensional Short Time Hartley Transforms (original) (raw)
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Decomposition of seismic signals via time-frequency representations
Proceedings of the …, 1996
Decomposition of seismic signals via time-frequency representations Tom Tobback *, Philippe Steeghs, Guy G. Drijkoningen and Jacob T. Fokkema, Section ... packet transform and sliding win-dow Fourier transform are the most widely used see eg Chakraborty and Okaya 1995 . ...
Fourier–Hilbert versus Hartley–Hilbert transforms with some geophysical applications
Journal of Applied Geophysics, 2010
An intimate mathematical relation between Hartley and Hilbert transforms is given here in contrast with the well known Fourier and Hilbert transform relations. It is interesting to note that the Fourier-Hilbert and Hartley-Hilbert transforms while possessing the same magnitude differ in phase by 270°. The inverse Hartley-Hilbert transform returns the original function unlike the Fourier-Hilbert transform which results the negative of the original function. Further, it may be realized that the envelope defined here of the analytic signal in both Fourier-Hilbert and Hartley-Hilbert domains numerically remain the same while differing in polarity. The feasibility of Hartley-Hilbert transform for a straight forward interpretation, total magnetic anomaly due to a thin plate from Tejpur, India and self potential data of the Sulleymonkey anomaly in the Ergani Copper district, Turkey are illustrated in contrast with the Fourier-Hilbert transform. This pair of transforms have innumerable geophysical applications.
Hartley Transform: Basic Theory And Applications In Oceanographic Time Series Analysis
2002
The Hartley transform, a real valued alternative to the complex Fourier transform, is presented as an efficient tool for data analysis in physical oceanography. Basic theoretical properties of this real-valued transform are briefly reviewed. Similarities and differences between Fourier and Hartley integral transforms and their discrete versions, as well as computational benefits or disadvantages between numerical algorithms used to evaluate their discrete versions are presented. The Hartley transform is used to estimate the spectral density fhnction of ocean surface waves and coastal current time series.
Here we present a new mathematical tool, the localized (HL); Bracewell, 1990), that allows for the filtering of 1-D time series through the identification of the power at various spatial and temporal wavelengths. Its application to and the associated results are presented from its application to continuous Global Positioning System (GPS) data from southern California for the time period 1994 through 2006. The HL transform filter removes the high-frequency components of the data and effectively isolates the longer period signal. This long-period signal is modeled as time-dependent postseismic deformation using the viscoelastic-gravitational model of (2004) for six stations selected for their proximity to the Northridge earthquake. The x-, y-, and z-components of the postseismic deformation are compared to the filtered data. Results suggest that this long-period deformation is a result of postseismic relaxation and that the HL transform filter provides an important new technique for the filtering of geophysical data consisting of the superposition of the effects of numerous complex sources at a variety of spatial and temporal scales.
A novel interpretation of the two-dimensional discrete Hartley transform
1996
In this paper, a novel view of the two-dimensional discrete Hartley transform (2-D DHT) is proposed. We show that the 2-D DHT can be obtained by projecting the two-dimensional discrete Fourier transform (2-D DFT) from the extension field to the basefield. The conjugacy relation and the trace function are applied to perform the projection operator. It is quite different from the traditional treatment of the 2-D DHT, which is trigonometric decomposition based. Zusammenfassung In diesem Beitrag wird eine neue Sicht auf die zweidimensionale Hartley-Transformation (2-D DHT) vorgeschlagen. Wir zeigen, darj die 2-D DHT durch Projektion der zweidimensionalen diskreten Fourier-Transformation (2-D DFT) vom Erweiterungsfeld auf das Basisfeld erhalten werden kann. Die Konjugiert-Beziehung und die Spurfunktion werden angewendet, urn den Projektionsoperator darzustellen. Dies ist viillig verschieden von der traditionellen Behandlung der 2-D DHT. welche auf einer trigonometrischen Zerlegung basiert. R&sum& Nous proposons dans cet article une approche nouvelle de la transformation de Hartley discrete bi-dimensionnelle (2-D DHT). Nous montrons que la 2-D DHT peut etre obtenue en projetant la transformation de Fourier discrete bi-dimensionnelle (2-D DFT) du champ Btendu sur le champ de base. La relation de conjugaison et la fonction trace sont appliquees pour mettre en oeuvre I'operateur de projection. Ceci est completement different du traitement traditionnel de la 2-D DHT, qui est base sur une decomposition trigonometrique.
Hilbert-Huang Transform Analysis of Dynamic and Earthquake Motion Recordings
Journal of Engineering Mechanics, 2003
This study examines the rationale of Hilbert-Huang transform ͑HHT͒ for analyzing dynamic and earthquake motion recordings in studies of seismology and engineering. In particular, this paper first provides the fundamentals of the HHT method, which consist of the empirical mode decomposition ͑EMD͒ and the Hilbert spectral analysis. It then uses the HHT to analyze recordings of hypothetical and real wave motion, the results of which are compared with the results obtained by the Fourier data processing technique. The analysis of the two recordings indicates that the HHT method is able to extract some motion characteristics useful in studies of seismology and engineering, which might not be exposed effectively and efficiently by Fourier data processing technique. Specifically, the study indicates that the decomposed components in EMD of HHT, namely, the intrinsic mode function ͑IMF͒ components, contain observable, physical information inherent to the original data. It also shows that the grouped IMF components, namely, the EMD-based low-and highfrequency components, can faithfully capture low-frequency pulse-like as well as high-frequency wave signals. Finally, the study illustrates that the HHT-based Hilbert spectra are able to reveal the temporal-frequency energy distribution for motion recordings precisely and clearly.
Time–frequency localization with the Hartley S-transform
Signal Processing, 2004
The Hartley transform, like the Fourier transform, is used for determining the spectrum of a complete time series. However, problems arise if the time series has time-dependent spectral content, since the Hartley kernel has no time localization. To this end, a short-time Hartley transform has been proposed and defined in analogy with the short-time Fourier transform. The frequency invariance of the window used in the short-time Hartley transform, though, leads to problems similar to those encountered in the short-time Fourier transform; namely, poor time resolution at high frequencies, and artifacts at low frequencies. In the Fourier case, these problems can be addressed through use of the Stransform, whose window scales with frequency to accommodate the scaling of the Fourier sinusoid. We apply the same principles to define the Hartley S-transform, using a scalable window. r
Use of time-scale representations for the analysis of seismic signals
The presented study, based on the continuous wavelet transform and time-frequency representations, introduce new algorithms which perform different kinds of separation processing depending on the nature of the seismic data. When dealing with a one dimensional recorded signal (one sensor), we propose a segmentation of its time-scale representation. This leads to the automatic detection and separation of the different waves. This algorithm can be applied to a whole seismic profile containing several sensors, by tracking the segmentation features in the time-scale image sequence. The resulting separation algorithm is efficient as long as the patterns of the different waves do not overlap in the time-scale plane. Afterwards, the purpose is to take into account the redundancy of information in more dimensional data to increase the separation possibilities in presence of interference. In the case of vectorial sensors, we use the polarization information to separate the different waves usi...
2012 IEEE Symposium on Industrial Electronics and Applications, 2012
Seismic electric signal (SES) is one of features for predicting earthquakes (EQs) because of its significant changes in the amplitude of the signal prior to the earthquake. This paper presents detailed analysis of SES recorded prior to earthquake that occurred in Greece in the period from January 1, 2008 to June 30, 2008. During this period of time 5 earthquakes were recorded with magnitudes greater than 6R. In this analysis STFT involving adaptively sliding window technique is used, in which Hamming and rectangular window functions are applied and compared. The comparison shows that Hamming window gives better results in analyzing the first significantly changes of SES prior to the EQ. The application of Hamming window resulted in less rippled spectrum shape which is more suitable to be used in characterizing the SES.
2013
This paper presents a review of spectral decomposition of seismic data, since it's inception nearly in 1997. It discusses various techniques and applications of spectral decomposition in seismic data processing and interpretation. It is also known as timefrequency analysis consists of transforming non stationary signal in time/space from time/space domain to time/space vs frequency domain. The frequency domain representation illustrates many important features that are not apparent in time domain representation. Spectral decomposition is a non-unique process for which various techniques exists and newer modified techniques are being discovered. Over the years, spectral decomposition of seismic data has progressed from tool for stratigraphy analysis to direct hydrocarbon indicator (DHI) technique. This technique is mostly used by seismic interpreters and being DHI, it is a potential weapon for minimizing dry well drilling. In coming time, spectral decomposition may can play a sig...