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.

LAGUERRE-GAUSS FILTERS IN REVERSE TIME MIGRATION IMAGE RECONSTRUCTION

2017 ◽  
Vol 35 (1) ◽  
Author(s):  
Juan Guillermo Paniagua Castrillón ◽  
Olga Lucia Quintero Montoya ◽  
Daniel Sierra-Sosa
Keyword(s):  
Wave Equation ◽  
Cross Correlation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Elastic Wave Equation ◽  
Seismic 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...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...Palavras-chave: Transformação de Laguerre-Gauss, correlação cruzada atraso zero, migração sísmica, condição de imagem.

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.

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.

Reverse time migration of multiples: Reducing migration artifacts using the wavefield decomposition imaging condition

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. S307-S314 ◽  
Author(s):  
Yibo Wang ◽  
Yikang Zheng ◽  
Qingfeng Xue ◽  
Xu Chang ◽  
Tong W. Fei ◽  
...  
Keyword(s):  
Complex Function ◽  
Synthetic Data ◽  
Velocity Model ◽  
High Amplitude ◽  
Frequency Noise ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Time Migration ◽  
Wavefield Decomposition

In the implementation of migration of multiples, reverse time migration (RTM) is superior to other migration algorithms because it can handle steeply dipping structures and offer high-resolution images of the complex subsurface. However, the RTM results using two-way wave equation contain high-amplitude, low-frequency noise and false images generated by improper wave paths in migration velocity model with sharp velocity interfaces or strong velocity gradients. To improve the imaging quality in RTM of multiples, we separate the upgoing and downgoing waves in the propagation of source and receiver wavefields. A complex function involved with the Hilbert transform is used in wavefield decomposition. Our approach is cost effective and avoids the large storage of wavefield snapshots required by the conventional wavefield separation technique. We applied migration of multiples with wavefield decomposition on a simple two-layer model and the Sigsbee 2B synthetic data set. Our results demonstrate that the proposed approach can improve the image generated by migration of multiples significantly.

scholarly journals The Pseudo-Laplace Filter for Vector-Based Elastic Reverse Time Migration

2021 ◽  
Vol 9 ◽  
Author(s):  
Qizhen Du ◽  
Xiaoyu Zhang ◽  
Shukui Zhang ◽  
Fuyuan Zhang ◽  
Li-Yun Fu
Keyword(s):  
Cross Correlation ◽  
Second Order ◽  
Polarity Reversal ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
Partial Derivatives ◽  
Time Migration ◽  
Dot Product ◽  
Derivatives Of

The scalar images (PP and PS) can be effectively obtained in vector-based elastic reverse time migration by applying dot product–based scalar imaging conditions to the separated vector wavefields. However, the PP image suffers from polarity reversal issues when opening angles are greater than 90∘ and backscattering artifacts when opening angles are close to 180∘. To address these issues, we propose the pseudo-Laplace filter for the dot product–based scalar imaging condition. Based on the analysis of the Laplace filter in the scalar image of vector-based wavefields, the second-order parallel-oriented partial derivatives of Cartesian components cross-correlation results are selected to construct the pseudo-Laplace filter. In contrast, second-order normal-oriented partial derivatives of the Cartesian component’s cross-correlation results are omitted. The theoretical analysis with the plane wave assumption shows that the proposed pseudo-Laplace filter can solve the problems of backscattering artifacts and polarity reversal in PP images by the scalar imaging condition. Due to additional polarity correction and backscattering attenuation, numerical examples show excellent performance in PP images with a pseudo-Laplace filter. Furthermore, the application of the pseudo-Laplace filter requires trivial additional computation or storage.

Multi-Component Seismic Wave Field Prestack Reverse-Time Depth Migration

2013 ◽  
Vol 868 ◽  
pp. 11-14
Author(s):  
Jia Jia Yang ◽  
Bing Shou He ◽  
Jian Zhong Zhang
Keyword(s):  
Wave Equation ◽  
Elastic Wave ◽  
Cross Correlation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Elastic Wave Equation ◽  
Imaging Condition ◽  
Depth Migration ◽  
Time Migration ◽  
Excitation Time

Based on the elastic wave equation, high-order finite-difference schemes for reverse-time extrapolation in the space of staggered grid and the perfectly matched layer (PML) absorbing boundary condition for the equation are derived. Prestack reverse-time depth migration (RTM) of elastic wave equation using the excitation time imaging condition and normalized cross-correlation imaging condition is carried out. Numerical experiments show that reverse-time migration is not limited for the angle of incidence and dramatic changes in lateral velocity. The reverse-time migration results of normalized cross-correlation imaging condition give the better effect than that of excitation time imaging condition.

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