Wave‐equation datuming before stack

Geophysics ◽  
1984 ◽  
Vol 49 (11) ◽  
pp. 2064-2066 ◽  
Author(s):  
John R. Berryhill
Keyword(s):  
Wave Equation ◽  
Seismic Data ◽  
Arbitrary Shape ◽  
Forward Modeling ◽  
Common Source ◽  
Computationally Efficient ◽  
Seismic Line ◽  
Mathematical Algorithm ◽  
Zero Offset ◽  
Kirchhoff Integral

This note describes the extension to unstacked seismic data of a computationally efficient form of the Kirchhoff integral published several years ago. In the previous paper (Berryhill, 1979), a wave‐equation procedure was developed to change the datum of a collection of zero‐offset seismic traces from one surface of arbitrary shape to another, even when the velocity for wave propagation is not constant. This procedure was designated “wave‐equation datuming,” and its applications to zero‐offset data were shown to include velocity‐replacement datum corrections and multilayer forward modeling. Extending this procedure to unstacked data requires no change in the mathematical algorithm. It is necessary only to recognize that operating on a common‐source group of seismic traces has the effect of extrapolating the receivers from one datum to another, and that, because of reciprocity, operating on a common‐receiver group changes the datum of the sources. Two passes through the data, common‐source computations, then common‐receiver computations, are required to change the datum of an entire seismic line before stack from one surface to another. Common‐source and common‐receiver trace groups must take the form of symmetric split spreads if both directions of dip are to be treated equally; reciprocity allows split spreads to be constructed artificially if the data were not actually recorded in the required form.

Amplitude-variation-with-offset and prestack-waveform inversion: A direct comparison using a real data example from the Rock Springs Uplift, Wyoming, USA

Geophysics ◽  
2015 ◽  
Vol 80 (2) ◽  
pp. B45-B59 ◽  
Author(s):  
Subhashis Mallick ◽  
Samar Adhikari
Keyword(s):  
Wave Equation ◽  
Seismic Data ◽  
Quantitative Estimation ◽  
Waveform Inversion ◽  
Forward Modeling ◽  
Amplitude Variation ◽  
Data Set ◽  
Amplitude Variation With Offset ◽  
Rock Springs Uplift ◽  
Rock Springs

Recent advances in seismic data acquisition and processing allow routine extraction of offset-/angle-dependent reflection amplitudes from prestack seismic data for quantifying subsurface lithologic and fluid properties. Amplitude-variation-with-offset (AVO) inversion is the most commonly used practice for such quantification. Although quite successful, AVO has a few shortcomings primarily due to the simplicity in its inherent assumptions, and for any quantitative estimation of reservoir properties, they are generally interpreted in combination with other information. In recent years, waveform-based inversions have gained popularity in reservoir characterization and depth imaging. Going beyond the simple assumptions of AVO and using wave equation solutions, these methods have been effective in accurately predicting the subsurface properties. Developments of these waveform inversions have so far been along two lines: (1) the methods that use a locally 1D model of the subsurface for each common midpoint and use an analytical solution to the wave equation for forward modeling and (2) the methods that do not make any 1D assumption but use an approximate numerical solution to the wave equation in 2D or 3D for forward modeling. Routine applications of these inversions are, however, still computationally demanding. We described a multilevel parallelization of elastic-waveform inversion methodology under a 1D assumption that allowed its application in a reasonable time frame. Applying AVO and waveform inversion on a single data set from the Rock Springs Uplift, Wyoming, USA, and comparing them with one another, we also determined that the waveform-based method was capable of obtaining a much superior description of subsurface properties compared with AVO. We concluded that the waveform inversions should be the method of choice for reservoir property estimation as high-performance computers become commonly available.

Estimation of layer thickness and velocity changes using 4D prestack seismic data

Geophysics ◽  
2006 ◽  
Vol 71 (6) ◽  
pp. S219-S234 ◽  
Author(s):  
Thomas Røste ◽  
Alexey Stovas ◽  
Martin Landrø
Keyword(s):  
Layer Thickness ◽  
Seismic Data ◽  
Single Layer ◽  
Time Lapse ◽  
Seismic Velocities ◽  
Seismic Line ◽  
Velocity Increase ◽  
Reservoir Compaction ◽  
Velocity Changes ◽  
Zero Offset

In some hydrocarbon reservoirs, severe compaction of the reservoir rocks is observed. This compaction is caused by production and is often associated with stretching and arching of the overburden rocks. Time-lapse seismic data can be used to monitor these processes. Since compaction and stretching cause changes in layer thickness as well as seismic velocities, it is crucial to develop methods to distinguish between the two effects. We introduce a new method based on detailed analysis of time-lapse prestack seismic data. The equations are derived assuming that the entire model consists of only one single layer with no vertical velocity variations. The method incorporates lateral variations in (relative) velocity changes by utilizing zero-offset and offset-dependent time shifts. To test the method, we design a 2D synthetic model that undergoes severe reservoir compaction as well as stretching of the overburden rocks. Finally, we utilize the method to analyze a real 2D prestack time-lapse seismic line from the Valhall field, acquired in 1992 and 2002. For a horizon at a depth of around [Formula: see text], which is near the top reservoir horizon, a subsidence of [Formula: see text] and a velocity decrease of [Formula: see text] for the sequence from the sea surface to the top reservoir horizon are estimated. By assuming that the base of the reservoir remains constant in depth, a reservoir compaction of 3.6% (corresponding to a subsidence of the top reservoir horizon of [Formula: see text]) and a corresponding reservoir velocity increase of 6.7% (corresponding to a velocity increase of [Formula: see text]) are estimated.

Wave‐equation trace interpolation

Geophysics ◽  
1987 ◽  
Vol 52 (7) ◽  
pp. 973-984 ◽  
Author(s):  
Joshua Ronen
Keyword(s):  
Wave Equation ◽  
Conjugate Gradient ◽  
Seismic Data ◽  
Linear Relation ◽  
Field Data ◽  
Iterative Scheme ◽  
Partial Migration ◽  
Spatial Aliasing ◽  
Zero Offset ◽  
Multichannel Seismic Data

Spatial aliasing in multichannel seismic data can be overcome by solving an inversion in which the model is the section that would be recorded in a well sampled zero‐offset experiment, and the data are seismic data after normal moveout (NMO). The formulation of the (linear) relation between the data and the model is based on the wave equation and on Fourier analysis of aliasing. A processing sequence in which one treats missing data as zero data and performs partial migration before stacking is equivalent to application of the transpose of the operator that actually needs to be inverted. The inverse of that operator cannot be uniquely determined, but it can be estimated using spatial spectral balancing in a conjugate‐gradient iterative scheme. The first iteration is conventional processing (including prestack partial migration). As shown in a field data example in which severe spatial aliasing was simulated, a few more iterations are necessary to achieve significantly better results.

Three‐dimensional modeling and migration of seismic data using Fourier transforms

Geophysics ◽  
1988 ◽  
Vol 53 (9) ◽  
pp. 1194-1201 ◽  
Author(s):  
Jing Wen ◽  
George A. McMechan ◽  
Michael W. Booth
Keyword(s):  
Wave Equation ◽  
Seismic Data ◽  
Fourier Transforms ◽  
Three Dimensional ◽  
Scale Model ◽  
Model Data ◽  
Three Dimensional Modeling ◽  
Dimensional Modeling ◽  
Zero Offset ◽  
And Migration

Programs for 3-D modeling and migration, using 3-D Fourier transforms to solve the scalar wave equation in frequency‐wavenumber space, are developed, implemented, tested, and applied to synthetic and scale‐model data. With microtasking to fully use four CRAY processors in parallel, we can solve a complete [Formula: see text] modeling problem in about 2.5 minutes (elapsed time); of this time, the two 3-D Fourier transforms take 1 minute and the wave‐equation calculations take 1.5 minutes. The corresponding migration also takes 2.5 minutes. Thus, even iterative 3-D processing is now feasible. The two main assumptions in our algorithm are that the earth has a constant velocity and that the data are zero‐offset (or stacked). Tests with model data verify that the algorithm produces the correct results when these assumptions are satisfied. Tests with scale‐model data show that approximate images may still be obtained when the assumptions are not strictly met; but the images contain a variety of distortions, primarily related to undermigration and overmigration, so caution is required in interpretation.

APPLICATION OF THE EMPIRICAL MODE DECOMPOSITION METHOD TO GROUND-ROLL NOISE ATTENUATION IN SEISMIC DATA

2013 ◽  
Vol 31 (4) ◽  
pp. 619 ◽  
Author(s):  
Luiz Eduardo Soares Ferreira ◽  
Milton José Porsani ◽  
Michelângelo G. Da Silva ◽  
Giovani Lopes Vasconcelos
Keyword(s):  
Empirical Mode Decomposition ◽  
Seismic Data ◽  
Low Frequency ◽  
High Amplitude ◽  
Seismic Line ◽  
Seismic Processing ◽  
Mode Decomposition ◽  
Ground Roll ◽  
Fortran 90 ◽  
Emd Method

ABSTRACT. Seismic processing aims to provide an adequate image of the subsurface geology. During seismic processing, the filtering of signals considered noise is of utmost importance. Among these signals is the surface rolling noise, better known as ground-roll. Ground-roll occurs mainly in land seismic data, masking reflections, and this roll has the following main features: high amplitude, low frequency and low speed. The attenuation of this noise is generally performed through so-called conventional methods using 1-D or 2-D frequency filters in the fk domain. This study uses the empirical mode decomposition (EMD) method for ground-roll attenuation. The EMD method was implemented in the programming language FORTRAN 90 and applied in the time and frequency domains. The application of this method to the processing of land seismic line 204-RL-247 in Tacutu Basin resulted in stacked seismic sections that were of similar or sometimes better quality compared with those obtained using the fk and high-pass filtering methods.Keywords: seismic processing, empirical mode decomposition, seismic data filtering, ground-roll. RESUMO. O processamento sísmico tem como principal objetivo fornecer uma imagem adequada da geologia da subsuperfície. Nas etapas do processamento sísmico a filtragem de sinais considerados como ruídos é de fundamental importância. Dentre esses ruídos encontramos o ruído de rolamento superficial, mais conhecido como ground-roll . O ground-roll ocorre principalmente em dados sísmicos terrestres, mascarando as reflexões e possui como principais características: alta amplitude, baixa frequência e baixa velocidade. A atenuação desse ruído é geralmente realizada através de métodos de filtragem ditos convencionais, que utilizam filtros de frequência 1D ou filtro 2D no domínio fk. Este trabalho utiliza o método de Decomposição em Modos Empíricos (DME) para a atenuação do ground-roll. O método DME foi implementado em linguagem de programação FORTRAN 90, e foi aplicado no domínio do tempo e da frequência. Sua aplicação no processamento da linha sísmica terrestre 204-RL-247 da Bacia do Tacutu gerou como resultados, seções sísmicas empilhadas de qualidade semelhante e por vezes melhor, quando comparadas as obtidas com os métodos de filtragem fk e passa-alta.Palavras-chave: processamento sísmico, decomposição em modos empíricos, filtragem dados sísmicos, atenuação do ground-roll.

Extension of forward modeling phase-screen code in isotropic and anisotropic media up to critical angle

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. SM107-SM114 ◽  
Author(s):  
James C. White ◽  
Richard W. Hobbs
Keyword(s):  
Critical Angle ◽  
Model Space ◽  
Anisotropic Media ◽  
Forward Modeling ◽  
Phase Screen ◽  
Computationally Efficient ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Phase Corrections ◽  
Converted Phases

The computationally efficient phase-screen forward modeling technique is extended to allow investigation of nonnormal raypaths. The code is developed to accommodate all diffracted and converted phases up to critical angle, building on a geometric construction method. The new approach relies upon prescanning the model space to assess the complexity of each screen. The propagating wavefields are then divided as a function of horizontal wavenumber, and each subset is transformed to the spatial domain separately, carrying with it angular information. This allows both locally accurate 3D phase corrections and Zoeppritz reflection and transmission coefficients to be applied. The phase-screen code is further developed to handle simple anisotropic media. During phase-screen modeling, propagation is undertaken in the wavenumber domain where exact expressions for anisotropic phase velocities are available. Traveltimes and amplitude effects from a range of anisotropic shales are computed and compared with previous published results.

scholarly journals Wave Equation Datuming Applied to Seismic Data in Shallow Water Environment and Post-Critical Water Bottom Reflection

Energies ◽  
2017 ◽  
Vol 10 (9) ◽  
pp. 1414 ◽  
Author(s):  
Umberta Tinivella ◽  
Michela Giustiniani ◽  
Ivan Vargas-Cordero
Keyword(s):  
Wave Equation ◽  
Shallow Water ◽  
Seismic Data ◽  
Water Environment ◽  
Shallow Water Environment ◽  
Water Bottom

scholarly journals Musification of Seismic Data

2016 ◽  
Author(s):  
Ryan McGee ◽  
David Rogers
Keyword(s):  
Wave Equation ◽  
New Media ◽  
Seismic Data ◽  
Seismic Events ◽  
Digital Audio ◽  
The Public ◽  
General Wave ◽  
Musical Compositions ◽  
The Creation ◽  
Earth's Crust

Seismic events are physical vibrations induced in the earth’s crust which follow the general wave equation, making seismic data naturally conducive to audification. Simply increasing the playback rates of seismic recordings and rescaling the amplitude values to match those of digital audio samples (straight audification) can produce eerily realistic door slamming and explosion sounds. While others have produced a plethora of sucha udifications for international seismic events (i.e. earthquakes), the resulting sounds, while distinct to the trained auditory scientist, often lack enough variety to produce multiple instrumental timbres for the creation of engaging music for the public. This paper discusses approaches of sonification processing towards eventual musification of seismic data, beginning with straight audification and resulting in several musical compositions and new-media installations containing a variety of seismically derived timbres.

scholarly journals Study on the Velocity Analysis Method of Low SNR Seismic Data

2021 ◽  
Vol 11 (1) ◽  
pp. 78
Author(s):  
Jianbo He ◽  
Zhenyu Wang ◽  
Mingdong Zhang
Keyword(s):  
Seismic Data ◽  
Fresnel Zone ◽  
Signal To Noise Ratio ◽  
Normal Wave ◽  
Curvature Radius ◽  
Velocity Spectrum ◽  
Velocity Analysis ◽  
Signal To Noise ◽  
Noise Ratio ◽  
Zero Offset

When the signal to noise ratio of seismic data is very low, velocity spectrum focusing will be poor., the velocity model obtained by conventional velocity analysis methods is not accurate enough, which results in inaccurate migration. For the low signal noise ratio (SNR) data, this paper proposes to use partial Common Reflection Surface (CRS) stack to build CRS gathers, making full use of all of the reflection information of the first Fresnel zone, and improves the signal to noise ratio of pre-stack gathers by increasing the number of folds. In consideration of the CRS parameters of the zero-offset rays emitted angle and normal wave front curvature radius are searched on zero offset profile, we use ellipse evolving stacking to improve the zero offset section quality, in order to improve the reliability of CRS parameters. After CRS gathers are obtained, we use principal component analysis (PCA) approach to do velocity analysis, which improves the noise immunity of velocity analysis. Models and actual data results demonstrate the effectiveness of this method.

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