scholarly journals Time-shift imaging condition in seismic migration

Geophysics ◽  
2006 ◽  
Vol 71 (6) ◽  
pp. S209-S217 ◽  
Author(s):  
Paul Sava ◽  
Sergey Fomel
Keyword(s):  
Time Lag ◽  
Synthetic Data ◽  
Complex Salt ◽  
Time Shift ◽  
Reverse Time ◽  
Data Set ◽  
Imaging Condition ◽  
Space And Time ◽  
Wavefield Extrapolation ◽  
Zero Time

Seismic imaging based on single-scattering approximation is in the analysis of the match between the source and receiver wavefields at every image location. Wavefields at depth are functions of space and time and are reconstructed from surface data either by integral methods (Kirchhoff migration) or by differential methods (reverse-time or wavefield extrapolation migration). Different methods can be used to analyze wavefield matching, of which crosscorrelation is a popular option. Implementation of a simple imaging condition requires time crosscorrelation of source and receiver wavefields, followed by extraction of the zero time lag. A generalized imaging condition operates by crosscorrelation in both space and time, followed by image extraction at zero time lag. Images at different spatial crosscorrelation lags are indicators of imaging accuracy and are also used for image-angle decomposition. In this paper, we introduce an alternative prestack imaging condition in which we preserve multiple lags of the time crosscorrelation. Prestack images are described as functions of time shifts as opposed to space shifts between source and receiver wavefields. This imaging condition is applicable to migration by Kirchhoff, wavefield extrapolation, or reverse-time techniques. The transformation allows construction of common-image gathers presented as functions of either time shift or reflection angle at every location in space. Inaccurate migration velocity is revealed by angle-domain common-image gathers with nonflat events. Computational experiments using a synthetic data set from a complex salt model demonstrate the main features of the method.

Noise removal by migration of time-shift images

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. S105-S111 ◽  
Author(s):  
Sheng Xu ◽  
Feng Chen ◽  
Bing Tang ◽  
Gilles Lambare
Keyword(s):  
Time Lag ◽  
Real Data ◽  
Velocity Model ◽  
Noise Removal ◽  
Time Shift ◽  
Reverse Time ◽  
Coherent Noise ◽  
Data Set ◽  
Depth Migration ◽  
Time Migration

When using seismic data to image complex structures, the reverse time migration (RTM) algorithm generally provides the best results when the velocity model is accurate. With an inexact model, moveouts appear in common image gathers (CIGs), which are either in the surface offset domain or in subsurface angle domain; thus, the stacked image is not well focused. In extended image gathers, the strongest energy of a seismic event may occur at non-zero-lag in time-shift or offset-shift gathers. Based on the operation of RTM images produced by the time-shift imaging condition, the non-zero-lag time-shift images exhibit a spatial shift; we propose an approach to correct them by a second pass of migration similar to zero-offset depth migration; the proposed approach is based on the local poststack depth migration assumption. After the proposed second-pass migration, the time-shift CIGs appear to be flat and can be stacked. The stack enhances the energy of seismic events that are defocused at zero time lag due to the inaccuracy of the model, even though the new focused events stay at the previous positions, which might deviate from the true positions of seismic reflection. With the stack, our proposed approach is also able to attenuate the long-wavelength RTM artifacts. In the case of tilted transverse isotropic migration, we propose a scheme to defocus the coherent noise, such as migration artifacts from residual multiples, by applying the original migration velocity model along the symmetry axis but with different anisotropic parameters in the second pass of migration. We demonstrate that our approach is effective to attenuate the coherent noise at subsalt area with two synthetic data sets and one real data set from the Gulf of Mexico.

Focusing analysis of seismic data with peg‐leg multiples

Geophysics ◽  
1997 ◽  
Vol 62 (1) ◽  
pp. 177-182
Author(s):  
Einar Maeland
Keyword(s):  
Seismic Data ◽  
Synthetic Data ◽  
Velocity Estimation ◽  
Time Shift ◽  
Data Set ◽  
Seismic Migration ◽  
Imaging Condition ◽  
Multilayered Medium ◽  
Velocity Information ◽  
Zero Offset

Seismic migration with an erroneous velocity field produces an “image” that must be interpreted to obtain reliable velocity information. Inclusion of multiples in common‐shot data makes velocity estimation more difficult. Zero‐offset migration, based on the exploding reflector model, can be used to identify peg‐leg multiples by application of an extra time shift in the imaging condition. The time and the corresponding position when reflected energy focuses must be detected by inspection of the migrated data set. Formulas are derived and the method is tested on synthetic data from a multilayered medium.

Simultaneous reverse time migration of primaries and free-surface related multiples without multiple prediction

Geophysics ◽  
2014 ◽  
Vol 79 (1) ◽  
pp. S1-S9 ◽  
Author(s):  
Yibo Wang ◽  
Xu Chang ◽  
Hao Hu
Keyword(s):  
Free Surface ◽  
Field Data ◽  
Synthetic Data ◽  
Velocity Model ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Imaging Condition ◽  
Time Migration ◽  
Multiple Prediction

Prestack reverse time migration (RTM) is usually regarded as an accurate imaging tool and has been widely used in exploration. Conventional RTM only uses primaries and treats free-surface related multiples as noise; however, free-surface related multiples can sometimes provide extra illumination of the subsurface, and this information could be used in migration procedures. There are many migration methods using free-surface related multiples, but most approaches need to predict multiples, which is time consuming and prone to error. We discovered a new RTM approach that uses the primaries and the free-surface related multiples simultaneously. Compared with migration methods that only use free-surface related multiples, the proposed approach can provide comparable migration results and does not need multiple predictions. In our approach, the source function in conventional RTM was replaced with recorded field data including primaries and free-surface related multiples, together with a synthetic wavelet; the back-propagated primaries in the conventional RTM were replaced with complete recorded field data. The imaging condition of the proposed approach was the same as the crosscorrelation imaging condition of conventional RTM. A three-layer velocity model with scatterers and the Sigsbee 2B synthetic data set were used for numerical experiments. The numerical results showed that the proposed approach can cover a wider range of the subsurface and provide better illumination compared with conventional RTM. The proposed approach was easy to implement and avoided tedious multiple prediction; it might be significant for general complex subsurface imaging.

An implicit stabilization strategy for Q-compensated reverse time migration

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. S169-S183
Author(s):  
Hanming Chen ◽  
Hui Zhou ◽  
Ying Rao
Keyword(s):  
Robust Stabilization ◽  
Synthetic Data ◽  
Frequency Noise ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Time Migration ◽  
Wavefield Extrapolation ◽  
Amplitude Compensation ◽  
Seismic Images

Reverse time migration with [Formula: see text] compensation ([Formula: see text]-RTM) is an effective approach to enhance the resolution of seismic images because it retrieves the amplitude loss and phase distortion induced by the viscosity of media. According to the crosscorrelation imaging condition, [Formula: see text]-RTM requires compensation for the amplitude loss in the propagation paths of source and receiver wavefields, which can be realized by solving an amplitude-boosted wave equation. However, the amplitude-boosted simulations suffer from numerical instability due to the amplification of high-frequency noise. We have developed a robust stabilization strategy for [Formula: see text]-RTM by incorporating a time-variant filter into the amplitude-boosted wavefield extrapolation step. We modify the Fourier spectrum of the operator that controls the amplitude compensation to be time variant, and we add to the spectrum a stabilization factor. Doing so, we integrate the time-variant filter into the viscoacoustic wave propagator implicitly, and we avoid any explicit filtering operation in [Formula: see text]-RTM. We verify the robustness of this stabilized [Formula: see text]-RTM with two synthetic data examples. We also apply this technique to a field data set to demonstrate the imaging improvements compared to an acoustic RTM and a more traditional [Formula: see text]-RTM method.

Regularization and datuming of seismic data by weighted, damped least squares

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. U67-U76 ◽  
Author(s):  
Robert J. Ferguson
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Synthetic Data ◽  
Real Data ◽  
Structural Data ◽  
Irregular Sampling ◽  
Data Set ◽  
Near Surface ◽  
Damped Least Squares ◽  
Wavefield Extrapolation

The possibility of improving regularization/datuming of seismic data is investigated by treating wavefield extrapolation as an inversion problem. Weighted, damped least squares is then used to produce the regularized/datumed wavefield. Regularization/datuming is extremely costly because of computing the Hessian, so an efficient approximation is introduced. Approximation is achieved by computing a limited number of diagonals in the operators involved. Real and synthetic data examples demonstrate the utility of this approach. For synthetic data, regularization/datuming is demonstrated for large extrapolation distances using a highly irregular recording array. Without approximation, regularization/datuming returns a regularized wavefield with reduced operator artifacts when compared to a nonregularizing method such as generalized phase shift plus interpolation (PSPI). Approximate regularization/datuming returns a regularized wavefield for approximately two orders of magnitude less in cost; but it is dip limited, though in a controllable way, compared to the full method. The Foothills structural data set, a freely available data set from the Rocky Mountains of Canada, demonstrates application to real data. The data have highly irregular sampling along the shot coordinate, and they suffer from significant near-surface effects. Approximate regularization/datuming returns common receiver data that are superior in appearance compared to conventional datuming.

3D plane-wave migration in tilted coordinates: A field data example

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCA199-WCA209 ◽  
Author(s):  
Guojian Shan ◽  
Robert Clapp ◽  
Biondo Biondi
Keyword(s):  
Plane Wave ◽  
Field Data ◽  
Synthetic Data ◽  
Data Set ◽  
Wave Source ◽  
Surface Data ◽  
The One ◽  
Wave Migration ◽  
Wavefield Extrapolation ◽  
Slant Stacking

We have extended isotropic plane-wave migration in tilted coordinates to 3D anisotropic media and applied it on a Gulf of Mexico data set. Recorded surface data are transformed to plane-wave data by slant-stack processing in inline and crossline directions. The source plane wave and its corresponding slant-stacked data are extrapolated into the subsurface within a tilted coordinate system whose direction depends on the propagation direction of the plane wave. Images are generated by crosscorrelating these two wavefields. The shot sampling is sparse in the crossline direction, and the source generated by slant stacking is not really a plane-wave source but a phase-encoded source. We have discovered that phase-encoded source migration in tilted coordinates can image steep reflectors, using 2D synthetic data set examples. The field data example shows that 3D plane-wave migration in tilted coordinates can image steeply dipping salt flanks and faults, even though the one-way wave-equation operator is used for wavefield extrapolation.

Acoustic and elastic numerical wave simulations by recursive spatial derivative operators

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. T167-T174 ◽  
Author(s):  
Dan Kosloff ◽  
Reynam C. Pestana ◽  
Hillel Tal-Ezer
Keyword(s):  
Synthetic Data ◽  
Analytic Solutions ◽  
Numerical Dispersion ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Lamb’S Problem ◽  
Dynamic Elasticity ◽  
Time Migration ◽  
Recursive Operators

A new scheme for the calculation of spatial derivatives has been developed. The technique is based on recursive derivative operators that are generated by an [Formula: see text] fit in the spectral domain. The use of recursive operators enables us to extend acoustic and elastic wave simulations to shorter wavelengths. The method is applied to the numerical solution of the 2D acoustic wave equation and to the solution of the equations of 2D dynamic elasticity in an isotropic medium. An example of reverse-time migration of a synthetic data set shows that the numerical dispersion can be significantly reduced with respect to schemes that are based on finite differences. The method is tested for the solutions of the equations of dynamic elasticity by comparing numerical and analytic solutions to Lamb’s problem.

scholarly journals Nonlinear scattering based imaging in elastic media: Theory, theorems, and imaging conditions

Geophysics ◽  
2013 ◽  
Vol 78 (3) ◽  
pp. S137-S155 ◽  
Author(s):  
Matteo Ravasi ◽  
Andrew Curtis
Keyword(s):  
Representation Theorem ◽  
Time Lag ◽  
Seismic Exploration ◽  
Elastic Media ◽  
Type Representation ◽  
Imaging Condition ◽  
Time Migration ◽  
Starting Point ◽  
Wavefield Extrapolation ◽  
Imaging Conditions

With the more widespread introduction of multicomponent recording devices in land and marine ocean-bottom seismic acquisition, elastic imaging may become mainstream in coming years. We have derived new, nonlinear, elastic imaging conditions. A correlation-type representation theorem for perturbed elastic media, commonly used in seismic interferometry to explain how a scattered wave response between two receivers/sources may be predicted given a boundary of sources/receivers, can be considered as a starting point for the derivation. Here, we use this theorem to derive and interpret imaging conditions for elastic migration by wavefield extrapolation (e.g., elastic reverse-time migration). Some approximations lead to a known, heuristically derived imaging condition that crosscorrelates P- and S-wave potentials that are separated in the subsurface after full-wavefield extrapolation. This formal connection reveals that the nonapproximated correlation-type representation theorem can be interpreted as a nonlinear imaging condition, that accounts also for multiply scattered and multiply converted waves, properly focusing such energy at each image point. We present a synthetic data example using either an ideal (acquisition on a full, closed boundary) or a real (partial boundary) seismic exploration survey, and we demonstrate the importance of nonlinearities in pure- and converted-mode imaging. In PP imaging, they result in better illumination and artifact reduction, whereas in PS imaging they show how zero time-lag and zero space-lag crosscorrelation imaging conditions are not ideal for imaging of converted-mode waves because no conversion arises from zero-offset experiments.

Acoustic modeling and migration of stacked cross‐hole data

Geophysics ◽  
1988 ◽  
Vol 53 (4) ◽  
pp. 492-500 ◽  
Author(s):  
Xianhuai Zhu ◽  
George A. McMechan
Keyword(s):  
Line Source ◽  
Synthetic Data ◽  
Point Sources ◽  
Scale Model ◽  
Model Data ◽  
Reverse Time ◽  
Imaging Condition ◽  
Surface Survey ◽  
Excitation Time ◽  
And Migration

Prestack computations for cross‐hole data are relatively expensive, as they are for prestack surface survey data. It is therefore of interest to develop methodologies for modeling and processing stacked cross‐hole data. In this context, stacking is over sources, not midpoints. Modeling with a line source produces data that are equivalent (by Huygen’s principle) to those obtained by stacking over a line of point sources. Reverse‐time finite‐difference migration may be applied to the resulting stacked section by generalizing the excitation‐ time imaging condition for a point source to a line source. Illustrations include successful applications to both synthetic data and scale‐model data.

scholarly journals LAGUERRE-GAUSS FILTERS IN REVERSE TIME MIGRATION IMAGE RECONSTRUCTION

2018 ◽  
Vol 35 (2) ◽  
Author(s):  
Juan Guillermo Paniagua Castrillón ◽  
Olga Lucia Quintero Montoya ◽  
Daniel Sierra-Sosa
Keyword(s):  
Cross Correlation ◽  
Synthetic Data ◽  
Low Frequency ◽  
Frequency Noise ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
Time Migration ◽  
Migration Imaging ◽  
Gauss Transform

ABSTRACT. Reverse time migration (RTM) solves the acoustic or elastic wave equation by means of the extrapolation from source and receiver wavefield in time. A migrated image is obtained by applying a criteria known as imaging condition. The cross-correlation between source and receiver wavefields is the commonly used imaging condition. However, this imaging condition produces spatial low-frequency noise, called artifacts, due to the unwanted correlation of the diving, head and backscattered waves. Several techniques have been proposed to reduce the artifacts occurrence. Derivative operators as Laplacian are the most frequently used. In this work, we propose a technique based on a spiral phase filter ranging from 0 to 2π, and a toroidal amplitude bandpass filter, known as Laguerre-Gauss transform. Through numerical experiments we present the application of this particular filter on three synthetic data sets. In addition, we present a comparative spectral study of images obtained by the zero-lag cross-correlation imaging condition, the Laplacian filtering and the Laguerre-Gauss filtering, showing their frequency features. We also present evidences not only with simulated noisy velocity fields but also by comparison with the model velocity field gradients that this method improves the RTM images by reducing the artifacts and notably enhance the reflective events. Keywords: Laguerre-Gauss transform, zero-lag cross-correlation, seismic migration, imaging condition. RESUMO. A migração reversa no tempo (RTM) resolve a equação de onda acústica ou elástica por meio da extrapolação a partir do campo de onda da fonte e do receptor no tempo. Uma imagem migrada é obtida aplicando um critério conhecido como condição de imagem. A correlação cruzada entre campos de onda de fonte e receptor é a condição de imagem comumente usada. No entanto, esta condição de imagem produz ruído espacial de baixa frequência, chamados artefatos, devido à correlação indesejada das ondas de mergulho, cabeça e retrodifusão. Várias técnicas têm sido propostas para reduzir a ocorrência de artefatos. Operadores derivados como Laplaciano são os mais utilizados. Neste trabalho, propomos uma técnica baseada em um filtro de fase espiral que varia de 0 a 2π, e um filtro passabanda de amplitude toroidal, conhecido como transformada de Laguerre-Gauss. Através de experimentos numéricos, apresentamos a aplicação deste filtro particular em três conjuntos de dados sintéticos. Além disso, apresentamos um estudo comparativo espectral de imagens obtidas pela condição de imagem de correlação cruzada atraso zero, a filtragem de Laplaciano e a filtragem Laguerre-Gauss, mostrando suas características de frequência. Apresentamos evidências não somente com campos simulados de velocidade ruidosa, mas também por comparação com os gradientes de campo de velocidade do modelo que este método melhora as imagens RTM, reduzindo os artefatos e aumentando notavelmente os eventos reflexivos. Palavras-chave: Transformação de Laguerre-Gauss, correlação cruzada atraso zero, migração sísmica, condição de imagem.

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