Numerical methods for the migration of constant‐offset sections in homogeneous and horizontally layered media

Geophysics ◽  
1983 ◽  
Vol 48 (9) ◽  
pp. 1195-1203 ◽  
Author(s):  
Augustin A. Dubrulle
Keyword(s):  
Plane Wave ◽  
Frequency Domain ◽  
Plane Waves ◽  
Synthetic Data ◽  
Computer Experiments ◽  
Layered Media ◽  
Time Shift ◽  
Seismic Section ◽  
Diffraction Curve ◽  
The Time Domain

This paper describes schemes for the frequency‐domain migration of constant‐offset sections in homogeneous and horizontally layered media. Their main advantage is that individual constant‐offset sections can be processed in isolation. The basis for these schemes is a generalization of the following plane‐wave analysis of migration for the zero‐offset case. Migration can be viewed in the time domain as a process whereby the plane waves echoed from a source to a geophone by a reflecting point are shifted in time to a common intersection. The shift applicable to each plane wave can be derived from the knowledge of the diffraction curve for the reflecting point in a neighborhood of the geophone abscissa. This time shift in turn determines the phase shift applicable in the frequency domain to the associated Fourier component of the seismic section. The central part of our methods is the construction of those elements of the diffraction curve pertinent to the shifts from the velocity map of the time section. The result is a table of shifts for an appropriate sample of plane‐wave directions, to be used for interpolation in the migration process. The effectiveness of the method is illustrated by computer experiments with synthetic data.

Estimating interannual variability arising from weather events

2001 ◽  
Vol 38 (A) ◽  
pp. 274-288 ◽  
Author(s):  
Xiaogu Zheng ◽  
James Renwick
Keyword(s):  
Frequency Domain ◽  
Interannual Variability ◽  
Time Domain ◽  
Synthetic Data ◽  
Estimation Procedure ◽  
Frequency Domain Method ◽  
Domain Method ◽  
Weather Events ◽  
Long Time ◽  
The Time Domain

The advantages and limitations of frequency domain and time domain methods for estimating the interannual variability arising from day-to-day weather events are summarized. A modification of the time domain method is developed and its application in examining a precondition for the frequency domain method is demonstrated. A combined estimation procedure is proposed: it takes advantage of the strengths of both methods. The estimation procedures are tested with sets of synthetic data and are applied to long time series of three meteorological parameters. The impacts of the different methods on tests of potential long-range predictability for seasonal means are also discussed.

Beam stacking: A generalized preprocessing technique

Geophysics ◽  
1987 ◽  
Vol 52 (9) ◽  
pp. 1199-1210 ◽  
Author(s):  
Shalom Raz
Keyword(s):  
Frequency Domain ◽  
Plane Waves ◽  
Intrinsic Property ◽  
Beam Width ◽  
Propagation Path ◽  
Gaussian Beams ◽  
Starting Point ◽  
The Time Domain ◽  
Preprocessing Technique ◽  
Spatial Support

Gaussian beams are well understood frequency‐ domain entities combining the directional properties of plane waves with an effectively finite region of support. These outstanding properties are retained not only on a prescribed observation plane, but throughout the propagation path. A preprocessing sequence aimed at transforming raw seismic data into beam stacks is proposed. That is, time‐harmonic Gaussian beams are synthesized, replacing the plane waves generated by conventional slant‐stacking procedures. The suggested scheme is characterized by an open parameter, essentially the beam width, whose selection is critical to ultimate success. Specific criteria for choosing this parameter can be given. In the limits of zero and infinite beam widths, beam stacks degenerate to the original raw data and to the conventional slant stacks, respectively. Although beam stacking is basically a frequency‐domain procedure, a transformation into the time domain, using frequency constituents within selected bands, may be accomplished without losing finite spatial support. Advantages of choosing beam‐stacked data as a starting point for subsequent inversion may be cited on two levels. The intrinsic property of finite spatial support overcomes edge effects. In addition, the degree of localization achieved by beam stacking may point the way to new approaches to seismic imaging.

3D prestack plane-wave, full-waveform inversion

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE135-VE144 ◽  
Author(s):  
Denes Vigh ◽  
E. William Starr
Keyword(s):  
Plane Wave ◽  
Data Acquisition ◽  
Time Domain ◽  
Waveform Inversion ◽  
Back Propagation ◽  
Synthetic Data ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Full Waveform ◽  
The Time Domain

Prestack depth migration has been used for decades to derive velocity distributions in depth. Numerous tools and methodologies have been developed to reach this goal. Exploration in geologically more complex areas exceeds the abilities of existing methods. New data-acquisition and data-processing methods are required to answer these new challenges effectively. The recently introduced wide-azimuth data acquisition method offers better illumination and noise attenuation as well as an opportunity to more accurately determine velocities for imaging. One of the most advanced tools for depth imaging is full-waveform inversion. Prestack seismic full-waveform inversion is very challenging because of the nonlinearity and nonuniqueness of the solution. Combined with multiple iterations of forward modeling and residual wavefield back propagation, the method is computer intensive, especially for 3D projects. We studied a time-domain, plane-wave implementation of 3D waveform inversion. We found that plane-wave gathers are an attractive input to waveform inversion with dramatically reduced computer run times compared to traditional shot-gather approaches. The study was conducted on two synthetic data sets — Marmousi2 and SMAART Pluto 1.5 — and a field data set. The results showed that a velocity field can be reconstructed well using a multiscale time-domain implementation of waveform inversion. Although the time-domain solution does not take advantage of wavenumber redundancy, the method is feasible on current computer architectures for 3D surveys. The inverted velocity volume produces a quality image for exploration geologists by using numerous iterations of waveform inversion.

Circuit Models of Lossy Multic onductor Transmission Lines: Incident Plane Wave Effect

2016 ◽  
Vol 6 (5) ◽  
pp. 2369
Author(s):  
Saih Mohamed ◽  
Rouijaa Hicham ◽  
Ghammaz Abdelilah
Keyword(s):  
Plane Wave ◽  
Frequency Domain ◽  
Transmission Lines ◽  
Time Domain ◽  
Method Of Characteristics ◽  
Incident Plane Wave ◽  
Wave Effect ◽  
Incident Plane ◽  
Simulation Results ◽  
The Time Domain

<p>In this paper, we concentrate on the variety impacts of incident plane wave on multiconductor transmission lines, utilizing Branin’s method, which is alluded to as the method of characteristics. The model can be directly used for the time-domain and frequency-domain analyses, Moreover,  it had the advantage of being used without the need of setting the  preconditions of  the  charges  applied  to  its  ends; this permits it to be effortlessly embedded in circuit simulators, for example Spice, Saber, and Esacap. This model validity is affirmed by contrasting our simulation results under ESACAP and different results, and we will talk about variety impacts of incident plane wave.</p>

Transient analytic point‐source response of a layered acoustic medium: Part I

Geophysics ◽  
1985 ◽  
Vol 50 (9) ◽  
pp. 1466-1477 ◽  
Author(s):  
Martin Tygel ◽  
Peter Hubral
Keyword(s):  
Wave Propagation ◽  
Plane Wave ◽  
Point Source ◽  
Time Domain ◽  
Plane Waves ◽  
Natural Extension ◽  
Acoustic Medium ◽  
Angle Of Incidence ◽  
The Time Domain ◽  
Plane Wave Propagation

The exact transient responses (e.g., reflection or transmission responses) of a transient point source above a stack of parallel acoustic homogeneous layers between two half‐spaces can be analytically obtained in the form of a finite integral strictly in the time domain. (The theory is presented in part II of this paper, this issue.) The transient acoustic potential of the point source is decomposed into transient plane waves, which are propagated through the layers at any angle of incidence as well in the time domain; finally, they are superposed to obtain the total point‐source response. The theory dealing with transient analytic plane wave propagation is described here. It constitutes an essential part of computing the synthetic seismogram by the new transient method proposed in part II. The plane‐wave propagation is achieved by an exact discrete recursion that automatically handles the conversion of homogeneous waves into inhomogeneous transient plane waves at layer boundaries. A particularly efficient algorithm is presented, that can be viewed as a natural extension of the popular normal‐incidence Goupillaud (1961)-type algorithm to the nonnormal incidence case.

An Application of the Frequency-Domain Experience Mode Decomposition to Enhance Deconvolution Results

2013 ◽  
Vol 397-400 ◽  
pp. 2120-2123
Author(s):  
Ya Nan Zhang ◽  
Yong Shou Dai ◽  
Jin Jie Ding ◽  
Man Man Zhang ◽  
Rong Rong Wang
Keyword(s):  
Reflection Coefficient ◽  
Frequency Domain ◽  
Empirical Mode Decomposition ◽  
Amplitude Spectrum ◽  
Seismic Section ◽  
Mode Decomposition ◽  
The Time Domain ◽  
Non Stationary Signal ◽  
Different Characteristics ◽  
Emd Method

To improve the resolution of the seismic section after deconvolution, a method based on frequency-domain experience mode decomposition was proposed. Empirical mode decomposition (EMD) method is usually used to analyze the time domain non-stationary signal, in order to better recover original reflection coefficient sequence, empirical mode decomposition was implemented for frequency-domain amplitude spectrum. Through the different characteristics between the equivalent filter amplitude after deconvolution and reflection coefficient sequence amplitude in frequency-domain, the real reflection coefficient sequence was recovered. Simulation results indicate that the method is effective and feasible.

scholarly journals Circuit Models of Lossy Multic onductor Transmission Lines: Incident Plane Wave Effect

2016 ◽  
Vol 6 (5) ◽  
pp. 2369
Author(s):  
Saih Mohamed ◽  
Rouijaa Hicham ◽  
Ghammaz Abdelilah
Keyword(s):  
Plane Wave ◽  
Frequency Domain ◽  
Transmission Lines ◽  
Time Domain ◽  
Method Of Characteristics ◽  
Incident Plane Wave ◽  
Wave Effect ◽  
Incident Plane ◽  
Simulation Results ◽  
The Time Domain

<p>In this paper, we concentrate on the variety impacts of incident plane wave on multiconductor transmission lines, utilizing Branin’s method, which is alluded to as the method of characteristics. The model can be directly used for the time-domain and frequency-domain analyses, Moreover,  it had the advantage of being used without the need of setting the  preconditions of  the  charges  applied  to  its  ends; this permits it to be effortlessly embedded in circuit simulators, for example Spice, Saber, and Esacap. This model validity is affirmed by contrasting our simulation results under ESACAP and different results, and we will talk about variety impacts of incident plane wave.</p>

Estimating interannual variability arising from weather events

2001 ◽  
Vol 38 (A) ◽  
pp. 274-288
Author(s):  
Xiaogu Zheng ◽  
James Renwick
Keyword(s):  
Frequency Domain ◽  
Interannual Variability ◽  
Time Domain ◽  
Synthetic Data ◽  
Estimation Procedure ◽  
Frequency Domain Method ◽  
Domain Method ◽  
Weather Events ◽  
Long Time ◽  
The Time Domain

The advantages and limitations of frequency domain and time domain methods for estimating the interannual variability arising from day-to-day weather events are summarized. A modification of the time domain method is developed and its application in examining a precondition for the frequency domain method is demonstrated. A combined estimation procedure is proposed: it takes advantage of the strengths of both methods. The estimation procedures are tested with sets of synthetic data and are applied to long time series of three meteorological parameters. The impacts of the different methods on tests of potential long-range predictability for seasonal means are also discussed.

Double-plane-wave reverse time migration in the frequency domain

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. S367-S382 ◽  
Author(s):  
Zeyu Zhao ◽  
Mrinal K. Sen ◽  
Paul L. Stoffa
Keyword(s):  
Plane Wave ◽  
Frequency Domain ◽  
Green's Functions ◽  
Green’S Functions ◽  
Plane Waves ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Time Migration ◽  
Double Plane

We have developed an efficient, accurate, and flexible plane-wave migration algorithm in the frequency domain by using a compressed and coupled-plane-wave data set, known as the double-plane-wave (DPW) data set. The DPW data set obtained by slant stacking of seismic shot profiles over source and receiver/offset represents seismic data in a fully decomposed plane-wave domain, which is called the DPW domain. A new DPW migration algorithm is derived under the Born approximation in the frequency domain, and it is referred to as the frequency-domain DPW reverse time migration (RTM). Frequency plane-wave Green’s functions need to be constructed and used during the migration. Time dips in shot profiles help to estimate the range of plane-wave decomposition. Therefore, the number of frequency plane-wave Green’s functions required for migration is limited. Furthermore, frequency plane-wave Green’s functions can be used for imaging each set of plane waves — either source or receiver/offset plane waves. As a result, the computational burden of computing Green’s function is substantially reduced; this results in increasing the migration efficiency. A selected range of plane-wave components can be migrated independently to image specific targets. Ray-parameter common-image gathers can be generated after migration without extra effort. The algorithm was tested on several synthetic data sets to show its feasibility and usefulness. The frequency-domain DPW RTM can also include anisotropy by constructing plane-wave Green’s function in anisotropic media.

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