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#### Instantaneous frequency

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Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2017 SEG International Exposition and Annual Meeting, September 24–29, 2017

Paper Number: SEG-2017-17672950

... ABSTRACT

**Instantaneous****frequency**is widely used for identifying specific seismic events, such as abnormal attenuation and thin bed tuning, based on its**frequency**content. It is one of the important seismic attributes related to the complex seismic trace. Although the definition itself is clear...
Abstract

ABSTRACT Instantaneous frequency is widely used for identifying specific seismic events, such as abnormal attenuation and thin bed tuning, based on its frequency content. It is one of the important seismic attributes related to the complex seismic trace. Although the definition itself is clear in theory, in practice the calculation can vary considerably, and deviate from the theoretical aim. Despite several decades since it occurred, there is still little consistency in the calculations of instantaneous frequency. We thus propose a robust and reliable scientific process to objectively compare various implementations of instantaneous frequency. To this end, through theory deduction and a physical model illustration, a complicated synthetic test dataset based on two oscillating function combinations, with varying frequencies and amplitudes, is generated. Correspondingly, its ‘ground truth’ instantaneous frequency is calculated by the analytic formula. In addition, several issues and weaknesses of current instantaneous frequency computations are pointed out and are considered in proposed quality metrics. Preliminary tests with quantitative and qualitative results show the effectiveness of the synthesized dataset and quality metrics for instantaneous frequency evaluations. Thereby, the benchmarking process may eventually improve the quality of instantaneous frequency algorithms throughout the industry. Presentation Date: Wednesday, September 27, 2017 Start Time: 2:15 PM Location: 340A Presentation Type: ORAL

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2015 SEG Annual Meeting, October 18–23, 2015

Paper Number: SEG-2015-5833787

... Summary

**Instantaneous****frequency**(IF) extracted by the Hilbert transform (HT) and continuous wavelet transform (CWT) is sensitive to noise and also suffers from meaningless values. We propose a robust method to extract**instantaneous****frequency**from seismic data based on timefrequency analysis...
Abstract

Summary Instantaneous frequency (IF) extracted by the Hilbert transform (HT) and continuous wavelet transform (CWT) is sensitive to noise and also suffers from meaningless values. We propose a robust method to extract instantaneous frequency from seismic data based on timefrequency analysis, which is called the synchrosqueezing three parameter wavelet transform (SSTPWT) using the three parameter wavelet (TPW). Compared with conventional instantaneous frequency extraction methods, the proposed method is proved to yield higher precision and better anti-noise performance. Experimental results on synthetic signals and real seismic data demonstrate the effectiveness of our method. Introduction Instantaneous attributes extracted from seismic data, especially the instantaneous frequency (IF), are generally used in seismic stratigraphic interpretation. For instance, seismic attributes always highlight some characteristics of seismic data and are very useful to assist interpreters to find structural anomalies and other geological phenomenon (Barnes, 1993; Chopra and Marfurt, 2005). Although IF has been introduced in seismic exploration for decades, improving the estimation precision and extending its applications are still active areas of research (Yang and Gao, 2010, Wang and Gao, 2013). The most common method to estimate instantaneous frequency is based on Hilbert transform presented by Taner et al. (1979). The analytic signal counterpart corresponding to the real-valued signal is found via the HT (Gabor, 1946). However this method is sensitive to noise, thus it brings difficulty for seismic attributes analysis, especially in a noisy environment. Gao et al. (1999) proved that the signal reconstruction after the continuous wavelet transform represents the corresponding analytic signal of the input real-valued signal in L 2 (R) . Based this, a wavelet-based method of computing IF is introduced and gets some positive results. In this paper, we present the synchrosqueezing three parameter wavelet transform to calculate the instantaneous frequency of the real signal. In the procedure, we combine the synchrosqueezing wavelet transform (Daubechies et al., 2011) and the three parameter wavelet (Gao et al., 2006) which substantially outperforms the popular morlet wavelet.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2015 SEG Annual Meeting, October 18–23, 2015

Paper Number: SEG-2015-5904996

... Summary This paper reports the application of

**instantaneous****frequency**in tight oil exploration, namely predicting the high-energy lacustrine shelly shoal of lower Jurassic Daanzhai Member in Central Sichuan Basin, China. The high-energy lacustrine shelly shoal Daanzhai Member is the target...
Abstract

Summary This paper reports the application of instantaneous frequency in tight oil exploration, namely predicting the high-energy lacustrine shelly shoal of lower Jurassic Daanzhai Member in Central Sichuan Basin, China. The high-energy lacustrine shelly shoal Daanzhai Member is the target of tight oil exploration in Jurassic strata. In this area it is hard to delineate the high-energy lacustrine shelly shoal from the low-energy ones using conventional approaches such as impedance inversion or amplitude attributes. But the author finds that instantaneous frequency could easily identify and predict the high-energy shelly shoal. Introduction The Sichuan Basin is an intracratonic basin of about 230,000 km 2 (Figure 1) and locates in the east of the Sichuan Province, southwestern China, with a complex tectonic and sedimentary history. It has experienced several important tectonic episodes (movements) since the Proterozoic. Subsidence and uplift are the main tectonic activities before the Yanshanian movement. Sichuan Basin since the Yanshanian movement has been intensively compressed laterally (Ma et al., 2007). The Daanzhai Member of lower Jurassic is the target of tight oil exploration in central Sichuan Basin. It mainly consists of shelly limestone and black shale/mudstone which are interbedded. The shelly limestone of Daanzhai Member covers about 6×10 4 km 2 and the total depth varies from 10 to 60 meters. The porosity falls between 0.13% and 3.18% and the permeability ranges from 0.0001mD to 0.3mD. All the evidence indicates the shelly limestone of Daanzhai Member is tight reservoir.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2015 SEG Annual Meeting, October 18–23, 2015

Paper Number: SEG-2015-5908239

... Summary As seismic data from field acquisition is a typical non-linear and non-stationary signal, the conventional method to extract the

**instantaneous****frequency**by the Hilbert transform which is proper for linear and stationary signal is limited in practice. A novel approach based...
Abstract

Summary As seismic data from field acquisition is a typical non-linear and non-stationary signal, the conventional method to extract the instantaneous frequency by the Hilbert transform which is proper for linear and stationary signal is limited in practice. A novel approach based on empirical mode decomposition (EMD) and the wavelet transform to extract seismic instantaneous frequency data is studied in this paper. In order to avoid artificial choice by experience, a method of choosing proper intrinsic mode function (IMF) decomposed from seismic traces is proposed by matching acoustic logging data and geological sequence. then, The selected IMF of seismic data is used to extract instantaneous frequency by the Morlet wavelet transform. By comparison of extracted instantaneous frequency in theoretical model and field data, it can be seen that result of the method in this paper is more effective than those from both of the Hilbert transform and the Hilbert-Huang transform. Introduction Extracting the instantaneous frequency of seismic data by different mathematical transform has become an important issue for recognizing reservoir geological characteristics and monitoring oil and gas reservoirs. In the process of seismic wave propagation, changes of seismic waveform are closely related to factors such as strata structure and petrophysical characteristic parameter. In order to analyze seismic signal, Taner (1979) presented a complex seismic trace technique and applied it firstly in the field of seismic exploration. Application of the Hilbert transform to extract seismic frequency in the oil exploration industry has been extensive and successful and become an important means of seismic data interpretation. Subsequently, Gao (1999) developed the method based on the wavelet transform which has strong anti-noise performance and high time resolution. Major shortcomings that lies in their methods are the theoretical basis on linear and stationary assumptions. Applications of the Hilbert transform are all limited to narrow-band signal and stationary signal. However, seismic data is nonlinear and non-stationary signal whose power spectral density is time-varying. For a non-stationary signal, the conventional method of using the Hilbert transform to extract instantaneous frequency is constrained. Norden E Huang (1998) proposed the Hilbert-Huang transform method, which adapted to not only stationary signal but also non-stationary signal, and played an important role in marine seismic research; Chen (2008) practiced application of extracting the instantaneous frequency by the Hilbert-Huang transform in the ocean data, which obtained good result. Nevertheless, for the method of extracting seismic instantaneous frequency by the Hilbert-Huang transform, the selection of multiple intrinsic mode functions (IMF) decomposed by empirical mode decomposition (EMD) of seismic data relied mostly on experience, without quantitative standard.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2013 SEG Annual Meeting, September 22–27, 2013

Paper Number: SEG-2013-0919

... (MEM) to WVD to obtain a robust and high resolution time-

**frequency**representation of seismic traces, and we also introduce a formula to estimate**instantaneous****frequency**(IF) in time domain. We apply our approach to the spectral decomposition and IF analysis of a seismic dataset from the Gulf of Mexico...
Abstract

SUMMARY Time-frequency (TF) analysis can reveal important details of seismic data and provide valuable information for reservoir characterization. Resolution in the TF plane is clearly critical for interpretation. Many methods applied to time-frequency representation introduce spurious or cross-terms, essentially when using bilinear functions such as the Wigner Ville Distribution (WVD). Most techniques proposed to overcome this shortcoming use a smoothed kernel which in turn can adversely affect the component’s concentration in the TF plane. We propose to apply the Maximum Entropy Method (MEM) to WVD to obtain a robust and high resolution time-frequency representation of seismic traces, and we also introduce a formula to estimate instantaneous frequency (IF) in time domain. We apply our approach to the spectral decomposition and IF analysis of a seismic dataset from the Gulf of Mexico. The analysis allows us to identify hydrates and a gas pocket.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2012 SEG Annual Meeting, November 4–9, 2012

Paper Number: SEG-2012-0396

... Summary Seismic

**instantaneous****frequency**(IF) is a useful attribute for characterizing depositional features from seismic data. However, commonly used IF estimations methods are sensitive to noise and also suffer from meaningless values. In this paper, we propose an IF regularization method...
Abstract

Summary Seismic instantaneous frequency (IF) is a useful attribute for characterizing depositional features from seismic data. However, commonly used IF estimations methods are sensitive to noise and also suffer from meaningless values. In this paper, we propose an IF regularization method based on time-frequency analysis. The Stockwell transform (ST), which has an advantage in providing multi-resolution time-frequency analysis while retaining the absolute phase of each frequency component, is used for IF regularization. We firstly decompose the estimated IF into the ST domain. By considering that most geologic changes are expressed only in certain local spectral ranges, we utilize an instantaneous amplitude parameterized low pass filter to identify the spectral ranges of IF from the multi-resolution results. After inverse ST is taken, noise and meaningless values are removed, and the regularized IF becomes more useful for describing geological features. The synthetic and real data examples demonstrate the effectiveness of our method.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2012 SEG Annual Meeting, November 4–9, 2012

Paper Number: SEG-2012-0902

... & gas energy distribution

**instantaneous****frequency**main menu test signal analytic counterpart estimation data quality extraction generalized morse wavelet reservoir characterization gmw noise olhede application seismic data The extraction of**instantaneous****frequency**from seismic data...
Abstract

Summary In this paper, a robust method for the extraction of instantaneous attributes is proposed in wavelet domain. A new class of analytic wavelets, the Generalized Morse Wavelets (GMWs), which have some desirable properties, are applied during the procedure of the proposed method. Compared to the conventional method based on Hilbert transform (HT), the new method is proved to yield higher precision and better anti-noise performance. Experimental results on synthetic signals and real seismic data show the validity of the method.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2011 SEG Annual Meeting, September 18–23, 2011

Paper Number: SEG-2011-1973

... ABSTRACT Study of synthetic models and field data shows that anomalous

**instantaneous****frequency**can aid thin-bed and stratigraphic interpretation. Time-**frequency**analysis of**instantaneous**-**frequency**spikes may improve continuity of**frequency**-spike “events” and presentation of**instantaneous**...
Abstract

ABSTRACT Study of synthetic models and field data shows that anomalous instantaneous frequency can aid thin-bed and stratigraphic interpretation. Time-frequency analysis of instantaneous-frequency spikes may improve continuity of frequency-spike “events” and presentation of instantaneous-frequency attributes for correlation of stratigraphic and reservoir features. Frequency-spike sections calculated in a proper frequency range highlight mostly seismically thin beds (type II, ). In the field-data example, frequency-spike sections assist in the interpretation of thick vs. thin beds, facies transition, and channels.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2010 SEG Annual Meeting, October 17–22, 2010

Paper Number: SEG-2010-1292

... Summary Synthetic models and field data show that anomalous

**instantaneous**-**frequency**(both**frequency**spikes and**frequency**“events”) are clearly linked to bed thickness.**Frequency**spikes are related to relative amplitude minima along a seismic trace that occur either at the merging point...
Abstract

Summary Synthetic models and field data show that anomalous instantaneous-frequency (both frequency spikes and frequency “events”) are clearly linked to bed thickness. Frequency spikes are related to relative amplitude minima along a seismic trace that occur either at the merging point of the top and base reflections of a wedge (type-I) or at the tip of the wedge (type-II). A type-II spike is indicative of a seismically thin bed (average 0.2? or thinner in this study; ? denotes wavelength). Abnormal frequency “events” related to type-II spikes tend to follow geologically defined thin reservoir units. As a result, type-II frequency anomalies are useful in recognizing thin reservoirs that are otherwise difficult to detect and correlate. Uncertainties caused by type-I spikes and inadequate lithologic and timestratigraphic information can be reduced by integrating well data, local geologic models, and lithology-indicative seismic attributes. Introduction Instantaneous frequency is one of the basic seismic attributes derived from a conventional seismic trace. Such a trace can be viewed as the real component of a complex trace, whose imaginary part (the quadrature trace) can be generated using the Hilbert transform. The complex trace permits unique separation of envelope amplitude and phase information and calculation of instantaneous frequency (Taner et al., 1979). One of the famous properties of instantaneous frequency is that it can go beyond the physically possible seismic frequency range acquired in field data. Anomalous frequency spikes can be above the high-frequency limit (even exceeding the Nyquist limit) or below the low-frequency limit (even being negative). Frequency anomalies largely correspond to waveform distortion caused by wavelet interference (Taner et al., 1979; Robertson and Fisher, 1988; Hardage et al., 1998). Anomalous instantaneous frequency is routinely considered a defect of complex seismic trace analysis. However, some authors have found the value of frequency anomalies in geologic interpretation. Robertson and Nogami (1984) tied the frequency spike to a halfwavelength (?/2) thickness in a wedge model. Rodovich and Oliveros (1998) compared frequency anomalies with discontinuities in a gas-reservoir succession. Hardage et al. (1998) utilized instantaneous frequency spikes as indicators of lower coherency, the flow-unit boundary, and stratigraphic terminations. Zeng (2010) explored geologic meanings of instantaneous-frequency anomalies and identified type-I and type-II frequency spikes. Type-II spikes are tied exclusively to seismically thin beds and have a certain geologic-interpretation meaning. In this study, synthetic models and field-data interpretation are extended to demonstrate that an anomalous frequency (even within a normal-frequency range of data) can be a useful attribute in assisting thin-bed detection and correlation. Type-I and type-II frequency spikes Figure 1 is a one-bed wedge model similar to that of Robertson and Nogami (1984) for the interpretive significance of the instantaneous-frequency attribute. A Ricker wavelet is convolved with the model to generate a seismic trough-peak couplet for the bed if thickness is less than ?/2, and separate trough and peak events for the top and base if it is otherwise (Figure 1A). Instantaneous frequency (Figure 1B) is related to wedge thickness in a nonlinear way (Figure 1C).

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2009 SEG Annual Meeting, October 25–30, 2009

Paper Number: SEG-2009-2457

... Summary We derive an approximate equation combining the quality factor Q , the traveltime of a wave, and the variation of the

**instantaneous****frequency**(IF) at the envelope peaks of two successive seismic wavelets, along the wave propagating direction, based on the theory of one-way wave...
Abstract

Summary We derive an approximate equation combining the quality factor Q , the traveltime of a wave, and the variation of the instantaneous frequency (IF) at the envelope peaks of two successive seismic wavelets, along the wave propagating direction, based on the theory of one-way wave propagation in a 1D viscoelastic medium. We then propose a method (called the WEPIF method) to estimate Q by measuring the variations of the wavelet envelope peak IF (WEPIF) with the traveltime of seismic wavelet. A test on synthetic VSP data shows that the WEPIF method is less sensitive to interference from the reflector than the logarithm spectral ratio and the centroid frequency shift methods. Applied to field VSP data, the WEPIF method gives a Q-curve with nearly the same distribution as the results from a known well. Applied to poststack seismic data, it produces a Q-profile that indicates an intense absorption zone corresponding to the excellent gas-bearing reservoir. This allows us to predict a potential high-productivity gas well. Drilling confirmed this prediction. The WEPIF method can be applied to poststack seismic data and zero-offset VSP data. Introduction Seismic waves propagating through the earth suffer attenuation and dispersion due to the viscosity of the media (Ricker, 1953; Futterman, 1962). Q is a diagnostic tool for reservoir characterization and hydrocarbon detection (Toksöz et al., 1979). Moreover, Q is very important when interpreting the effects of AVO, improving the resolution of seismic imaging, and advancing the study of material properties. In general, amplitude variations of seismic signals are used to estimate Q values (Tonn, 1991). Time-domain methods involve pulse amplitude decay (Brzostowski and McMechan, 1992), pulse rising time (Gladwin and Stacey, 1974; Kjartansson, 1979), and pulse broadening (Wright and Hoy, 1981), which all use pulse amplitude information. Nevertheless, amplitude information of seismic pulses is often influenced by scattering, geometric spreading, and other factors. In the Fourier-frequency domain, approaches for estimating Q include the logarithm spectral ratio (LSR) (Hauge, 1981; Stainsby and Worthington, 1985), centroid frequency shift (CFS) (Quan and Harris, 1997), and peak frequency shift (Zhang and Ulrych, 2002; Gao and Yang, 2007) methods, all of which require Fourier transforms to calculate the frequency spectra of seismic records sampled within a time window. In practice, it is difficult to properly select the window function and window length. Li et al. (2006) suggested using peak scale variations in the wavelet domain to estimate Q by assuming an idealized pulse as the seismic source wavelet. Its application is, however, restricted due to the fact that the difference between the real source wavelet and an idealized pulse may be substantial. Q can also be estimated by the variation of the instantaneous frequency (IF) of a seismic signal. Tonn (1991), Barnes (1991), and Engelhard (1996) obtained the relationship between the measured instantaneous spectra and seismic attenuation. Assuming that the source wavelet is an idealized band-pass wavelet, Barnes (1991) derived the relation between Q and IF variations of seismic waves, establishing a new approach for Q estimation.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2006 SEG Annual Meeting, October 1–6, 2006

Paper Number: SEG-2006-0968

... Summary Thin bed thickness can be predicted by peak

**instantaneous****frequency**when the thin bed response has small interference effects from other layers. Based on a simple wedge model, the peak**instantaneous****frequency**is inversely proportional to the layer thickness such that thinner layers...
Abstract

Summary Thin bed thickness can be predicted by peak instantaneous frequency when the thin bed response has small interference effects from other layers. Based on a simple wedge model, the peak instantaneous frequency is inversely proportional to the layer thickness such that thinner layers exhibit a higher peak instantaneous frequency. However, when the top and bottom reflection coefficients are different, this inverse trend becomes more complicated for layers less than one eighth wavelength thick. We use 3D seismic data from Fort Worth basin with 16 wells to calibrate this method to predict the thickness of the Pennsylvanian age Caddo limestone. We find the peak instantaneous frequency to be well-correlated with the layer thickness measured in the wells. We then use this simple inverse linear trend d to predict Caddo limestone thickness. Introduction Widess (1973) showed that we can estimate the thickness of thin layer (less than the tuning thickness) by exploiting the linear relation between thickness and reflection amplitude. In addition, the tuning thickness itself is inversely proportional to the peak spectral frequency of a broadband spectral response. Robertson and Nogami (1984) discussed the combination of envelope and instantaneous frequency to predict thin bed thickness. Chuang and Lawton (1995) studied four different wedge models to show that peak frequency slowly decreases as layer thickness increases. Based on instantaneous attributes (Taner et al., 1979), Partyka (2002) compared Widess’s amplitude method simple measurements of peak to trough travel time as well as discrete Fourier transform (spectral decomposition) components to predict thickness. Nissen (personal comm., 2002) demonstrated the relationship between instantaneous frequency and “D” sand thickness of Sooner unit in Colorado. Unfortunately, the instantaneous frequency obtained using complex trace analysis can become be unstable and unreliable when seismic data has a low signal to noise ratio. Instead, we propose using peak instantaneous frequency to predict thin bed thickness. Peak instantaneous frequency is calculated in a small window which is around the thin bed response. We assume that thin bed reservoir’s thickness is below or around tuning thickness. We constructed two simple wedge models to verify the relation between peak instantaneous frequency and thin bed thickness. The general trend is that thicker thin bed has lower peak instantaneous frequency, while thinner bed has higher peak instantaneous frequency. One limestone layer in Fort Worth basin is used to test this trend. Caddo limestone thickness came from 16 wells has good matches with computed peak instantaneous frequency from 3-D seismic data. A linear trend is used to approximately predict Caddo limestone thickness. Wedge model example We built two wedge models to test our method. The top and bottom reflection coefficients of the first wedge model have the same magnitude but opposite polarity (-0.01 and +0.01). The second wedge model has different magnitude top and bottom reflection coefficients (-0.01 and +0.009).The input wavelet is a zero-phase Ricker wavelet with peak frequency 35 Hz. Both wedge thicknesses increase from 0.3 m (first trace) to 25 m (last trace).

Proceedings Papers

Paper presented at the SPWLA 47th Annual Logging Symposium, June 4–7, 2006

Paper Number: SPWLA-2006-RR

... slowness curve borehole flexural wave Symposium well logging flexural wave

**instantaneous****frequency**-slowness method**instantaneous****frequency****frequency**slowness curve Signature mixed acoustic mode Upstream Oil & Gas acoustic mode dipole source spwla 47**instantaneous****frequency**curve wave...
Abstract

Dipole full waveform acoustic tools are used to estimate shear wave velocities, especially in soft and poorly consolidated formations. Under ideal conditions dipole source employed by those tools excites only borehole flexural wave that is propagating alo

Proceedings Papers

Paper presented at the The Ninth International Offshore and Polar Engineering Conference, May 30–June 4, 1999

Paper Number: ISOPE-I-99-322

... ABSTRACT: The quasi-steady hypothesis is widely used to describe the vortexinduced transverse force on a structural member in a time varying flow. The quasi-steady hypothesis depends upon the use of an

**instantaneous****frequency**. This paper discusses the concept of the**instantaneous****frequency**...
Abstract

ABSTRACT: The quasi-steady hypothesis is widely used to describe the vortexinduced transverse force on a structural member in a time varying flow. The quasi-steady hypothesis depends upon the use of an instantaneous frequency. This paper discusses the concept of the instantaneous frequency and develops a method for its calculation from a data set, based on the Hilbert transform and appropriate signal conditioning. Utilising data from an oscillating flow facility, the quasi-steady hypothesis is tested and shown to be well-founded for Kc ≈ 44 and 0.27 < steady current/oscillatory current < 1. INTRODUCTION 800 The instantaneous frequency of vortex-induced transverse force on a cylinder in an oscillatory flow is most frequently assumed to be given by the quasi-steady hypothesis. This hypothesis Bearman et al (1984), Obajasu et al (1988)) assumes that the Strouhal number is that which would be obtained in a steady flow of the given instantaneous velocity. Although Bearman et al have compared the results of force predictions made on this basis with measured forces they have not compared the predicted instantaneous frequency to the " measured instantaneous frequency. For the majority of each half wave cycle the instantaneous frequency of the cosine factor exceeds the frequency of the first factor, hence for this part of each half cycle the quasi-steady model may be viewed as a sinusoid with time varying amplitude and frequency. This hypothesis appears plausible on the basis of time-domain plots such as figure 1. This paper provides a basis for determination of the instantaneous frequency within a vortex burst from measured data and uses data obtained in an oscillatory/low facility to provide support for the quasi-steady hypothesis. Vortex Force Data Experimental data were obtained in the U-tube facility described by Reid and Hinwood (1987).

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 1997 SEG Annual Meeting, November 2–7, 1997

Paper Number: SEG-1997-1941

...SS 1.6

**Instantaneous****frequency**estimation using the reassignment method Jan E. Odegard,* Richard G. Baraniuk and Kurt L. Oehler Dept. of ECE, Rice University, Houston, Texas SUMMARY This paper explores the method of reassignment for ex- tracting**instantaneous****frequency**attributes from seismic data...
Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 1991 SEG Annual Meeting, November 10–14, 1991

Paper Number: SEG-1991-1335

... ABSTRACT No preview is available for this paper.

**instantaneous**phase**frequency**measure**instantaneous****frequency**equation low**frequency**shadow interpretation data processing taner gas sand data analysis anomaly lkole polytechnique seismic energy reservoir characterization...
Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 1987 SEG Annual Meeting, October 11–15, 1987

Paper Number: SEG-1987-0591

... ABSTRACT No preview is available for this paper. data processing 2 shekel reservoir characterization mean fourier

**frequency**envelope peak envelope interpretation**instantaneous****frequency**fourier mean**frequency**wavelet**frequency**upstream oil & gas fourier relation...
Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 1983 SEG Annual Meeting, September 11–15, 1983

Paper Number: SEG-1983-0613

...: Cambridge, Mass., M.I.T. Press Toksoz, N. M., Cheng, C. H., and Timur, A., 1976, Velocities of seismic waves in porous rocks: Geophysics, v. 41, p. 621-645. Sp Sand FIG 6. ERPRESSVRED Cycle-Octave Representation for

**Instantaneous****Frequency**Spectra S24.5 P. Goupillaud, Enpex; A. Grossmann, Centre de...Images

**Published:**16 March 2021

Images

**Published:**20 January 2010

Images

**Published:**20 January 2010

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