Instantaneous frequency and amplitude at the envelope peak of a constant‐phase wavelet

Geophysics ◽  
1991 ◽  
Vol 56 (7) ◽  
pp. 1058-1060 ◽  
Author(s):  
A. E. Barnes
Keyword(s):  
Instantaneous Frequency ◽  
Seismic Data ◽  
Amplitude Spectrum ◽  
Propagation Time ◽  
Ricker Wavelet ◽  
Spectral Frequency ◽  
Zero Phase

Robertson and Nogami (1984) have shown that the instantaneous frequency at the peak of a zero‐phase Ricker wavelet is exactly equal to that wavelet’s average Fourier spectral frequency weighted by its amplitude spectrum. Bodine (1986) gave an example which shows this is also true for constant‐phase bandpass wavelets. Here I prove that this holds for any constant‐phase wavelet. I then develop an equation expressing this quantity as a function of propagation time through an attenuating medium. A corresponding equation is derived for the amplitude of the envelope peak. Taken together, these may aid in the analysis of seismic data as suggested by Robertson and Nogami (1984), Bodine (1986), and Robertson and Fisher (1988).

Estimation of quality factors from CMP records

Geophysics ◽  
2002 ◽  
Vol 67 (5) ◽  
pp. 1542-1547 ◽  
Author(s):  
Changjun Zhang ◽  
Tadeusz J. Ulrych
Keyword(s):  
Seismic Data ◽  
Amplitude Spectrum ◽  
Seismic Source ◽  
Peak Frequency ◽  
Analytical Relation ◽  
Frequency Variation ◽  
Q Factor ◽  
Quality Factors ◽  
Time Direction ◽  
Ricker Wavelet

Estimates of the quality, Q, factor are commonly obtained from vertical seismic data or stacked surface seismic data. This paper describes a method that allows Q‐factor to be estimated directly from common midpoint (CMP) gathers. Absorption of the wavefield is dependent on three parameters: frequency, traveltime in the medium, and medium Q‐factor. Assuming that the amplitude spectrum of the seismic source signature may be modeled by that of a Ricker wavelet, we derive an analytical relation between Q‐factor and seismic data peak frequency variation both along offset and vertical time direction. The Q‐factor is estimated from CMP gathers using a layer‐stripping approach.

Complex seismic trace analysis

Geophysics ◽  
1979 ◽  
Vol 44 (6) ◽  
pp. 1041-1063 ◽  
Author(s):  
M. T. Taner ◽  
F. Koehler ◽  
R. E. Sheriff
Keyword(s):  
Instantaneous Frequency ◽  
Seismic Data ◽  
Trace Analysis ◽  
Color Patterns ◽  
Phase Information ◽  
Real Component ◽  
The Real ◽  
Geological Interpretation ◽  
Envelope Amplitude ◽  
Spatial Changes

The conventional seismic trace can be viewed as the real component of a complex trace which can be uniquely calculated under usual conditions. The complex trace permits the unique separation of envelope amplitude and phase information and the calculation of instantaneous frequency. These and other quantities can be displayed in a color‐encoded manner which helps an interpreter see their interrelationship and spatial changes. The significance of color patterns and their geological interpretation is illustrated by examples of seismic data from three areas.

Determination of crustal thickness from spectral behavior of SH waves

1969 ◽  
Vol 59 (3) ◽  
pp. 1247-1258
Author(s):  
Abou-Bakr K. Ibrahim
Keyword(s):  
Amplitude Spectrum ◽  
Body Waves ◽  
Multiple Reflections ◽  
Matrix Formulation ◽  
Sh Waves ◽  
Crustal Model ◽  
Amplitude Spectra ◽  
Phase Spectra ◽  
Zero Phase

abstract The amplitude spectrum obtained from Haskell's matrix formulation for body waves travelling through a horizontally layered crustal model shows a sequence of minima and maxima. It is known that multiple reflections within the crustal layers produce constructive and destructive interferences, which are shown as maxima and minima in the amplitude spectrum. Analysis of the minima in the amplitude spectra, which correspond to zero phase in the phase spectra, enables us to determine the thickness of the crust, provided the ratio of wave velocity in the crust to velocity under the Moho is known.

scholarly journals Acoustic absorption measurement for the determination of the volume viscosity of pure fluids / Messverfahren für die akustischen Absorption zur Bestimmung der Volumenviskosität reiner Fluide

2019 ◽  
Vol 86 (s1) ◽  
pp. 2-6 ◽  
Author(s):  
Leander Claes ◽  
Lars Moritz Hülskämper ◽  
Elmar Baumhögger ◽  
Nadine Feldmann ◽  
René Spencer Chatwell ◽  
...  
Keyword(s):  
Amplitude Ratio ◽  
Amplitude Spectrum ◽  
Acoustic Energy ◽  
Propagation Time ◽  
Acoustic Absorption ◽  
Pure Fluids ◽  
Dissipative Effects ◽  
Volume Viscosity ◽  
Realistic Description ◽  
Pulse Echo

AbstractA realistic description of fluid mechanical and acoustic processes requires the volume viscosity of the medium to be known. This work describes how the volume viscosity of pure fluids can be determined by measuring acoustic absorption with the pulse-echo method. The challenge in realizing such a measurement method lies in the separation of the different dissipative effects that superimpose on absorption. Diffraction effects ultimately cause a dissipation of acoustic energy and acoustic reflector surfaces have a small, but finite transmission coefficient. Further, influences of the transducer (in particular its frequency response), as well as the system’s electrical components have to be taken into account. In contrast to the classical approach relying on the amplitude ratio, the absorption is determined by the moments of the amplitude spectrum. The measurement system applied is originally designed for precision measurements of the sound velocity by means of the propagation time difference of two acoustic signals.

scholarly journals Application of zero phase wavelet on synthetic seismic signals with noise

2018 ◽  
Vol 7 (2.7) ◽  
pp. 906
Author(s):  
Sai Srinivas Goli ◽  
Sireesha Papanaboyina ◽  
Satya Ramesh Kanchumarthi ◽  
Koteswara Rao Sanagapallea
Keyword(s):  
Event Detection ◽  
Seismic Data ◽  
Seismic Reflection ◽  
Seismic Signal ◽  
Accurate Information ◽  
Seismic Signals ◽  
Reflected Wave ◽  
Zero Phase

Detection of time of occurrences of different phases and frequencies is of highest importance in seismic reflected signals. Seismic reflection analysis gives us accurate information about the event detection, source acquisition of triggered seismic data and its mechanisms. In the present work an attempt is made to generate a synthetic seismic with noise generally present in the seismograph using. The synthetic seismic signal is extracted by zero phase wavelet. Crews software is used in this extraction. The zero phase wavelet could efficiently extract the seismic signal present in the reflected wave.  

Using instantaneous frequency and colored inversion attributes to distinguish and determine the sandstones facies of the Late Ordovician Mamuniyat reservoir, R-field in Murzuq Basin, Libya

2016 ◽  
Vol 4 (4) ◽  
pp. T507-T519 ◽  
Author(s):  
Yousf Abushalah ◽  
Laura Serpa
Keyword(s):  
Instantaneous Frequency ◽  
Seismic Data ◽  
Acoustic Impedance ◽  
Rock Physics ◽  
Side Lobe ◽  
Petroleum Reservoir ◽  
Seismic Reflection Data ◽  
Frequency Bands ◽  
Reflection Data ◽  
Sandstone Facies

The Mamuniyat petroleum reservoir in southwestern Libya is comprised of clean sandstones and intercalated shale and sand facies that are characterized by spatial porosity variations. Seismic reflection data from the field exhibit relatively low vertical seismic resolution, side lobes of reflection wavelets, reflection interference, and low acoustic impedance contrast between the reservoir and the units underneath the reservoir, which make mapping those facies a difficult task. In the absence of broadband seismic data, optimizing frequency bands of bandlimited data can be used to suppress pseudoreflectors resulting from side-lobe effects and help to separate the clean sandstone facies of the reservoir. We have optimized the data based on our investigation of seismic frequency bands and used instantaneous frequency analysis to reveal the reflection discontinuity that is mainly associated with the reservoir boundary of the sandstone facies of the clean Mamuniyat reservoir. We also preformed rock-physics diagnostic modeling and inverted the seismic data using spectral-based colored inversion into relative acoustic impedance. The inverted impedance matches the up-scaled impedance from the well data and the inversion of relative acoustic impedance confirms the conclusion that was drawn from the instantaneous frequency results. The interpretation of facies distributions based on the instantaneous frequency was supported by the inversion results and the rock-physics models.

Random denoising and signal nonlinearity approach by time-frequency peak filtering using weighted frequency reassignment

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. V229-V237 ◽  
Author(s):  
Hongbo Lin ◽  
Yue Li ◽  
Baojun Yang ◽  
Haitao Ma
Keyword(s):  
Weight Function ◽  
Instantaneous Frequency ◽  
Seismic Data ◽  
Signal To Noise Ratio ◽  
Random Noise ◽  
Signal To Noise ◽  
Transform Method ◽  
Time Frequency ◽  
Frequency Peak ◽  
Noise Ratio

Time-frequency peak filtering (TFPF) may efficiently suppress random noise and hence improve the signal-to-noise ratio. However, the errors are not always satisfactory when applying the TFPF to fast-varying seismic signals. We begin with an error analysis for the TFPF by using the spread factor of the phase and cumulants of noise. This analysis shows that the nonlinear signal component and non-Gaussian random noise lead to the deviation of the pseudo-Wigner-Ville distribution (PWVD) peaks from the instantaneous frequency. The deviation introduces the signal distortion and random oscillations in the result of the TFPF. We propose a weighted reassigned smoothed PWVD with less deviation than PWVD. The proposed method adopts a frequency window to smooth away the residual oscillations in the PWVD, and incorporates a weight function in the reassignment which sharpens the time-frequency distribution for reducing the deviation. Because the weight function is determined by the lateral coherence of seismic data, the smoothed PWVD is assigned to the accurate instantaneous frequency for desired signal components by weighted frequency reassignment. As a result, the TFPF based on the weighted reassigned PWVD (TFPF_WR) can be more effective in suppressing random noise and preserving signal as compared with the TFPF using the PWVD. We test the proposed method on synthetic and field seismic data, and compare it with a wavelet-transform method and [Formula: see text] prediction filter. The results show that the proposed method provides better performance over the other methods in signal preserving under low signal-to-noise ratio.

Time-frequency analysis of deep crustal reflection seismic data using Wigner-Ville distributions

2001 ◽  
Vol 38 (7) ◽  
pp. 1027-1035 ◽  
Author(s):  
Kris Vasudevan ◽  
Frederick A Cook
Keyword(s):  
Frequency Analysis ◽  
Instantaneous Frequency ◽  
Seismic Data ◽  
Drill Hole ◽  
Lateral Variation ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Reflection Seismic ◽  
Instantaneous Frequencies ◽  
Crustal Reflection

One important component of deep crustal reflection seismic data in the absence of drill-hole data and surface-outcrop constraints is classifying and quantifying reflectivity patterns. One approach to this component uses a recently developed data-decomposition technique, seismic skeletonization. Skeletonized coherent events and their attributes are identified and stored in a relational database, allowing easy visualization and parameterization of the reflected wavefield. Because one useful attribute, the instantaneous frequency, is difficult to derive within the current framework of skeletonization, time–frequency analysis and a new method, empirical mode skeletonization, are used to derive it. Other attributes related to time–frequency analysis that can be derived from the methods can be used for shallow and deep reflection seismic interpretation and can supplement the seismic attributes accrued from seismic skeletonization. Bright reflections observed from below the sedimentary basin in the Southern Alberta Lithosphere Transect have recently been interpreted to be caused by highly reflective sills. Time–frequency analysis of one of these reflections shows the lateral variation of energy with instantaneous frequency for any given time and the lateral variation of energy with time for any instantaneous frequency. Results from empirical mode skeletonization for the same segment of data illustrate the differences in the instantaneous frequencies among the intrinsic modes of the data. Thus, time–frequency distribution of amplitude or energy for any signal may be a good indicator of compositional differences that can vary from one location to another.

Energy distribution in wavelets and implications on resolving power

Geophysics ◽  
1993 ◽  
Vol 58 (1) ◽  
pp. 39-46 ◽  
Author(s):  
Ralph W. Knapp
Keyword(s):  
Phase Shift ◽  
Energy Distribution ◽  
Total Energy ◽  
Minimum Energy ◽  
Amplitude Spectrum ◽  
Resolving Power ◽  
Amplitude Envelope ◽  
Quadrature Phase ◽  
Partial Energy ◽  
Zero Phase

The suite of a wavelet is defined as being all wavelets that share a common amplitude spectrum and total energy but differ in phase spectra. Within a suite there are also classes of wavelets. A wavelet class has a common amplitude envelope and energy distribution. As such, it includes all wavelets that differ by only a constant‐angle phase shift. Of all wavelets within suite, the zero‐phase wavelet has the minimum energy envelope width; its energy is confined to minimum time dispersion. Therefore, the zero‐phase wavelet has maximum resolving power within the suite. Because a zero‐phase wavelet shares its amplitude envelope with a class of wavelets that differ by only a constant phase shift, all wavelets of the class also have maximum resolving power within the suite. The most familiar of these is the quadrature‐phase wavelet (90‐degree phase shift). Use of the complex trace results in an evaluation of the total energy, both potential and kinetic, of the wavelet signal. Assuming the wavelet signal is the output of a velocity geophone, partial energy represents only kinetic energy. Total energy better represents wavelet energy propagating through the earth. Use of partial energy (real signal only) applies a bias that favors the zero‐phase wavelets with respect to others of its class despite identical energy distribution. This bias is corrected when the wavelet envelope is used in the evaluation rather than wavelet trace amplitude. On a wiggle‐trace seismic section (amplitude display) a zero‐phase wavelet maintains a detectability advantage in the presence of noise because of a slightly greater amplitude; however, the advantage is lost in complex trace sections (energy displays) because both reflection strength and instantaneous frequency are independent of a constant phase shift in the wavelet. These sections are identical whether the wavelet is zero‐phase, quadrature‐phase or any other constant phase value, i.e., a wavelet within the zero‐phase class. (This does not imply that reflection strength sections should replace wiggle trace ones, only that they have advantages in the solution of some problems.)

Sign in / Sign up

Export Citation Format

Share Document