An effective imaging condition for reverse-time migration using wavefield decomposition

Geophysics ◽  
2011 ◽  
Vol 76 (1) ◽  
pp. S29-S39 ◽  
Author(s):  
Faqi Liu ◽  
Guanquan Zhang ◽  
Scott A. Morton ◽  
Jacques P. Leveille
Keyword(s):  
Low Frequency ◽  
Real Data ◽  
Cost Effective ◽  
High Amplitude ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
Velocity Models ◽  
Time Migration ◽  
Computationally Intensive

Reverse-time migration (RTM) exhibits great superiority over other imaging algorithms in handling steeply dipping structures and complicated velocity models. However, low-frequency, high-amplitude noises commonly seen in a typical RTM image have been one of the major concerns because they can seriously contaminate the signals in the image if they are not handled properly. We propose a new imaging condition to effectively and efficiently eliminate these specific noises from the image. The method works by first decomposing the source and receiver wavefields to their one-way propagation components, followed by applying a correlation-based imaging condition to the appropriate combinations of the decomposed wavefields. We first give the physical explanation of the principle of such noises in the conventional RTM image. Then we provide the detailed mathematical theory for the new imaging condition. Finally, we propose an efficient scheme for its numerical implementation. It replaces the computationally intensive decomposition with the cost-effective Hilbert transform, which significantly improves the efficiency of the imaging condition. Applications to various synthetic and real data sets demonstrate that this new imaging condition can effectively remove the undesired low-frequency noises in the image.

Reducing artifacts of elastic reverse time migration by the deprimary technique

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. S569-S577 ◽  
Author(s):  
Yang Zhao ◽  
Houzhu Zhang ◽  
Jidong Yang ◽  
Tong Fei
Keyword(s):  
Complex Function ◽  
Noise Removal ◽  
Pure Mode ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Imaging Condition ◽  
Velocity Models ◽  
Time Migration ◽  
Wavefield Decomposition

Using the two-way elastic-wave equation, elastic reverse time migration (ERTM) is superior to acoustic RTM because ERTM can handle mode conversions and S-wave propagations in complex realistic subsurface. However, ERTM results may not only contain classical backscattering noises, but they may also suffer from false images associated with primary P- and S-wave reflections along their nonphysical paths. These false images are produced by specific wave paths in migration velocity models in the presence of sharp interfaces or strong velocity contrasts. We have addressed these issues explicitly by introducing a primary noise removal strategy into ERTM, in which the up- and downgoing waves are efficiently separated from the pure-mode vector P- and S-wavefields during source- and receiver-side wavefield extrapolation. Specifically, we investigate a new method of vector wavefield decomposition, which allows us to produce the same phases and amplitudes for the separated P- and S-wavefields as those of the input elastic wavefields. A complex function involved with the Hilbert transform is used in up- and downgoing wavefield decomposition. Our approach is cost effective and avoids the large storage of wavefield snapshots that is required by the conventional wavefield separation technique. A modified dot-product imaging condition is proposed to produce multicomponent PP-, PS-, SP-, and SS-images. We apply our imaging condition to two synthetic models, and we demonstrate the improvement on the image quality of ERTM.

scholarly journals Application of the continuous wavelet transform in the extraction of directional data on RTM imaging condition wavefields

2018 ◽  
Vol 8 (2) ◽  
Author(s):  
Juan Guillermo Paniagua Castrillón ◽  
Olga Lucía Quintero- Montoya
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Low Frequency ◽  
Continuous Wavelet ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Model Quality ◽  
Directional Information ◽  
Imaging Condition ◽  
Time Migration

Low-frequency artifacts in reverse time migration result from unwanted cross-correlation of the source and receiver wavefields at non-reflecting points along ray-paths. These artifacts can hide important details in migrated models and increase poor interpretation risk. Some methods have been proposed to avoid or reduce the number of these artifacts, preserving reflections, and improving model quality, implementing other strategies such as modification of the wave equation, proposing other imaging conditions, and using image filtering techniques. One of these methods uses wavefield decomposition, correlating components of the wavefields that propagate in opposite directions. We propose a method for extracting directional information from the RTM imaging condition wavefields to obtain characteristics allowing for better, more refined imaging. The method works by separating directional information about the wavefields based on the continuous wavelet transform (CWT), and the analysis of the main changes on the frequency content revealed within the scalogram obtained by a Gaussian wavelet family. Through numerical applications, we demonstrate that this method can effectively remove undesired artifacts in migrated images. In addition, we use the Laguerre-Gauss filtering to improve the results obtained with the proposed method.

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.

scholarly journals A causal imaging condition for reverse time migration using the Discrete Hilbert transform and its efficient implementation on GPU

2019 ◽  
Vol 16 (5) ◽  
pp. 894-912
Author(s):  
Feipeng Li ◽  
Jinghuai Gao ◽  
Zhaoqi Gao ◽  
Xiudi Jiang ◽  
Wenbo Sun
Keyword(s):  
Image Quality ◽  
Hilbert Transform ◽  
Real Data ◽  
Processing Unit ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Discrete Hilbert Transform ◽  
Imaging Condition ◽  
Time Migration ◽  
Wavefield Decomposition

Abstract Reverse time migration (RTM) has shown a significant advantage over other imaging algorithms for imaging complex subsurface structures. However, low-wavenumber noise severely contaminates the image, which is one of the main issues in the RTM algorithm. To attenuate the undesired low-wavenumber noise, the causal imaging condition based on wavefield decomposition has been proposed. First, wavefield decompositions are performed to separate the wavefields as up-going and down-going wave components, respectively. Then, to preserve causality, it constructs images by correlating wave components that propagate in different directions. We build a causal imaging condition in this paper. Not only does it consider the up/down wavefield decomposition, but it also applies the decomposition on the horizontal direction to enhance the image quality especially for steeply dipping structures. The wavefield decomposition is conventionally achieved by the frequency-wavenumber (F-K) transform that is very computationally intensive compared with the wave propagation process of the RTM algorithm. To improve the efficiency of the algorithm, we propose a fast implementation to perform wavefield separation using the discrete Hilbert transform via the Graphics Processing Unit. Numerical tests on both the synthetic models and a real data example demonstrate the effectiveness of the proposed method and the efficiency of the optimized implementation scheme. This new imaging condition shows its ability to produce high image quality when applied to both the RTM stack image and also the angle domain common image gathers. The comparison of the total elapsed time for different methods verifies the efficiency of the optimized algorithm.

An improvement in wavefield extrapolation and imaging condition to suppress reverse time migration artifacts

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. S403-S409 ◽  
Author(s):  
Farzad Moradpouri ◽  
Ali Moradzadeh ◽  
Reynam Pestana ◽  
Reza Ghaedrahmati ◽  
Mehrdad Soleimani Monfared
Keyword(s):  
Weighting Function ◽  
Real Data ◽  
Expansion Method ◽  
Rapid Expansion ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Imaging Condition ◽  
Time Migration ◽  
Poynting Vectors

Reverse time migration (RTM) as a full wave equation method can image steeply dipping structures incorporating all waves without dip limitation. It causes a set of low-frequency artifacts that start to appear for reflection angles larger than 60°. These artifacts are known as the major concern in RTM method. We are first to attempt to formulate a scheme called the leapfrog-rapid expansion method to extrapolate the wavefields and their first derivatives. We have evaluated a new imaging condition, based on the Poynting vectors, to suppress the RTM artifacts. The Poynting vectors information is used to separate the wavefields to their downgoing and upgoing components that form the first part of our imaging condition. The Poynting vector information is also used to calculate the reflection angles as a basis for our weighting function as the second part of the aforementioned imaging condition. Actually, the weighting function is applied to have the most likely desired information and to suppress the artifacts for the angle range of 61°–90°. This is achieved by dividing the angle range to a triplet domain from 61° to 70°, 71° to 80°, and 81° to 90°, where each part has the weight of [Formula: see text], [Formula: see text], and [Formula: see text], respectively. It is interesting to note that, besides suppressing the artifacts, the weighting function also has the capability to preserve crosscorrelation from the real reflecting points in the angle range of 61°–90°. Finally, we tested the new RTM procedure by the BP synthetic model and a real data set for the North Sea. The obtained results indicate the efficiency of the procedure to suppress the RTM artifacts in producing high-quality, highly illuminated depth-migrated image including all steeply dipping geologic structures.

Excitation amplitude imaging condition for prestack reverse-time migration

Geophysics ◽  
2013 ◽  
Vol 78 (1) ◽  
pp. S37-S46 ◽  
Author(s):  
Bao D. Nguyen ◽  
George A. McMechan
Keyword(s):  
Signal To Noise Ratio ◽  
Grid Point ◽  
Synthetic Data ◽  
Cost Effective ◽  
Excitation Amplitude ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Step ◽  
Imaging Condition ◽  
Time Migration

An implicitly stable ratio imaging condition for prestack reverse-time migration (RTM) was defined using excitation criteria. Amplitude maxima and their corresponding occurrence times were saved at each grid point during forward source wavefield extrapolation. Application of the imaging condition involves dividing the amplitudes of the back-propagated receiver wavefield by the precomputed maximum source wavefield amplitude only at the grid points that satisfy the image time at each time step. The division normalizes by the source amplitude, so only the highest signal-to-noise ratio portion of the data is used. Provided that the source and receiver wavefield amplitudes are accurate at the reflection points, the peak wavelet amplitudes in the migrated image are the angle-dependent reflection coefficients and low wavenumber artifacts are significantly reduced compared to those in images calculated by crosscorrelation. Using excitation information and time-binning for the imaging condition improves computational and storage efficiency by three or more orders of magnitude when compared to crosscorrelation with the full source wavefield. Numerical tests with synthetic data for the Marmousi2 model have shown this method to be a cost-effective and practical imaging condition for use in prestack RTM.

Vector-based elastic reverse time migration based on scalar imaging condition

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. S111-S127 ◽  
Author(s):  
Qizhen Du ◽  
ChengFeng Guo ◽  
Qiang Zhao ◽  
Xufei Gong ◽  
Chengxiang Wang ◽  
...  
Keyword(s):  
Alternative Methods ◽  
Polarity Reversal ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Converted Wave ◽  
Imaging Condition ◽  
Time Migration ◽  
Wavefield Separation ◽  
Wave Modes

The scalar images (PP, PS, SP, and SS) of elastic reverse time migration (ERTM) can be generated by applying an imaging condition as crosscorrelation of pure wave modes. In conventional ERTM, Helmholtz decomposition is commonly applied in wavefield separation, which leads to a polarity reversal problem in converted-wave images because of the opposite polarity distributions of the S-wavefields. Polarity reversal of the converted-wave image will cause destructive interference when stacking over multiple shots. Besides, in the 3D case, the curl calculation generates a vector S-wave, which makes it impossible to produce scalar PS, SP, and SS images with the crosscorrelation imaging condition. We evaluate a vector-based ERTM (VB-ERTM) method to address these problems. In VB-ERTM, an amplitude-preserved wavefield separation method based on decoupled elastic wave equation is exploited to obtain the pure wave modes. The output separated wavefields are both vectorial. To obtain the scalar images, the scalar imaging condition in which the scalar product of two vector wavefields with source-normalized illumination is exploited to produce scalar images instead of correlating Cartesian components or magnitude of the vector P- and S-wave modes. Compared with alternative methods for correcting the polarity reversal of PS and SP images, our ERTM solution is more stable and simple. Besides these four scalar images, the VB-ERTM method generates another PP-mode image by using the auxiliary stress wavefields. Several 2D and 3D numerical examples are evaluated to demonstrate the potential of our ERTM method.

Imaging conditions for elastic reverse time migration

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. S95-S111 ◽  
Author(s):  
Wei Zhang ◽  
Ying Shi
Keyword(s):  
Decomposition Method ◽  
Inner Product ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Imaging Condition ◽  
Subsurface Structures ◽  
Time Migration ◽  
Imaging Conditions ◽  
Wave Modes

Elastic reverse time migration (RTM) has the ability to retrieve accurately migrated images of complex subsurface structures by imaging the multicomponent seismic data. However, the imaging condition applied in elastic RTM significantly influences the quality of the migrated images. We evaluated three kinds of imaging conditions in elastic RTM. The first kind of imaging condition involves the crosscorrelation between the Cartesian components of the particle-velocity wavefields to yield migrated images of subsurface structures. An alternative crosscorrelation imaging condition between the separated pure wave modes obtained by a Helmholtz-like decomposition method could produce reflectivity images with explicit physical meaning and fewer crosstalk artifacts. A drawback of this approach, though, was that the polarity reversal of the separated S-wave could cause destructive interference in the converted-wave image after stacking over multiple shots. Unlike the conventional decomposition method, the elastic wavefields can also be decomposed in the vector domain using the decoupled elastic wave equation, which preserves the amplitude and phase information of the original elastic wavefields. We have developed an inner-product imaging condition to match the vector-separated P- and S-wave modes to obtain scalar reflectivity images of the subsurface. Moreover, an auxiliary P-wave stress image can supplement the elastic imaging. Using synthetic examples with a layered model, the Marmousi 2 model, and a fault model, we determined that the inner-product imaging condition has prominent advantages over the other two imaging conditions and generates images with preserved amplitude and phase attributes.

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