Effective Q-compensated reverse time migration using new decoupled fractional Laplacian viscoacoustic wave equation

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. S57-S69 ◽  
Author(s):  
Qingqing Li ◽  
Li-Yun Fu ◽  
Hui Zhou ◽  
Wei Wei ◽  
Wanting Hou
Keyword(s):  
Wave Equation ◽  
Fractional Laplacian ◽  
Seismic Waves ◽  
Laplacian Operator ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Phase Dispersion ◽  
Time Migration ◽  
Dispersion Effects ◽  
Amplitude Attenuation

Seismic waves are attenuated and distorted during propagation because of the conversion of acoustic energy to heat energy. We focus on intrinsic attenuation, which is caused by [Formula: see text], which is the portion of energy lost during each cycle or wavelength. Amplitude attenuation can decrease the energy of the wavefields, and dispersion effects distort the phase of seismic waves. Attenuation and dispersion effects can reduce the resolution of image, and they can especially distort the real position of interfaces. On the basis of the viscoacoustic wave equation consisting of a single standard linear solid, we have derived a new viscoacoustic wave equation with decoupled amplitude attenuation and phase dispersion. Subsequently, we adopt a theoretical framework of viscoacoustic reverse time migration that can compensate the amplitude loss and the phase dispersion. Compared with the other variable fractional Laplacian viscoacoustic wave equations with decoupled amplitude attenuation and phase dispersion terms, the order of the Laplacian operator in our equation is a constant. The amplitude attenuation term is solved by pseudospectral method, and only one fast Fourier transform is required in each time step. The phase dispersion term can be computed using a finite-difference method. Numerical examples prove that our equation can accurately simulate the attenuation effects very well. Simulation of the new viscoacoustic equation indicates high efficiency because only one constant fractional Laplacian operator exists in this new viscoacoustic wave equation, which can reduce the number of inverse Fourier transforms to improve the computation efficiency of forward modeling and [Formula: see text]-compensated reverse time migration ([Formula: see text]-RTM). We tested the [Formula: see text]-RTM by using Marmousi and BP gas models and compared the [Formula: see text]-RTM images with those without compensation and attenuation (the reference image). [Formula: see text]-RTM results match well with the reference images. We also compared the field data migration images with and without compensation. Results demonstrate the accuracy and efficiency of the presented new viscoacoustic wave equation.

An approach for attenuation-compensating multidimensional constant-Q viscoacoustic reverse time migration

Geophysics ◽  
2020 ◽  
Vol 85 (1) ◽  
pp. S33-S46
Author(s):  
Ali Fathalian ◽  
Daniel O. Trad ◽  
Kristopher A. Innanen
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Velocity Model ◽  
Seismic Wave Propagation ◽  
Image Resolution ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Phase Dispersion ◽  
Time Migration ◽  
Amplitude Attenuation

Simulation of wave propagation in a constant-[Formula: see text] viscoacoustic medium is an important problem, for instance, within [Formula: see text]-compensated reverse time migration (RTM). Processes of attenuation and dispersion influence all aspects of seismic wave propagation, degrading the resolution of migrated images. To improve the image resolution, we have developed a new approach for the numerical solution of the viscoacoustic wave equation in the time domain and we developed an associated viscoacoustic RTM ([Formula: see text]-RTM) method. The main feature of the [Formula: see text]-RTM approach is compensation of attenuation effects in seismic images during migration by separation of amplitude attenuation and phase dispersion terms. Because of this separation, we are able to compensate the amplitude loss effect in isolation, the phase dispersion effect in isolation, or both effects concurrently. In the [Formula: see text]-RTM implementation, an attenuation-compensated operator is constructed by reversing the sign of the amplitude attenuation and a regularized viscoacoustic wave equation is invoked to eliminate high-frequency instabilities. The scheme is tested on a layered model and a modified acoustic Marmousi velocity model. We validate and examine the response of this approach by using it within an RTM scheme adjusted to compensate for attenuation. The amplitude loss in the wavefield at the source and receivers due to attenuation can be recovered by applying compensation operators on the measured receiver wavefield. Our 2D and 3D numerical tests focus on the amplitude recovery and resolution of the [Formula: see text]-RTM images as well as the interface locations. Improvements in all three of these features beneath highly attenuative layers are evident.

Efficient reverse time migration based on fractional Laplacian viscoacoustic wave equation

2015 ◽  
Vol 204 (1) ◽  
pp. 488-504 ◽  
Author(s):  
Qingqing Li ◽  
Hui Zhou ◽  
Qingchen Zhang ◽  
Hanming Chen ◽  
Shanbo Sheng
Keyword(s):  
Wave Equation ◽  
Fractional Laplacian ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration

scholarly journals REVERSE TIME MIGRATION BY INTERPOLATION AND PSEUDO-ANALYTICAL METHODS

2014 ◽  
Vol 32 (4) ◽  
pp. 753 ◽  
Author(s):  
Rafael L. de Araújo ◽  
Reynam Da C. Pestana
Keyword(s):  
Wave Equation ◽  
Analytical Method ◽  
Time Derivative ◽  
Laplacian Operator ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Step ◽  
Seismic Migration ◽  
Time Migration ◽  
De Se

ABSTRACT. Within the seismic method, in order to obtain an accurate image, it is necessary to use some processing techniques, among them the seismic migration. The reverse time migration (RTM) uses the complete wave equation, which implicitly includes multiple arrivals, can image all dips and, therefore, makes it possible to image complex structures. However, its application on 3D pre-stack data is still restricted due to the enormous computational effort required. With recent technological advances and faster computers, 3D pre-stack RTM is being used to address the imaging challenges posed by sub-salt and other complex subsurface targets. Thus, in order to balance processing cost and with image’s quality and confiability, different numeric methods are used to compute the migration. This work presents two different ways of performing the reverse time migration using the complete wave equation: RTMby interpolation and by the pseudo-analytical method. The first migrates the data with different constant velocities and interpolate the results, while the second uses modifications in the computation of the Laplacian operator inorder to improve the finite difference scheme used to approximate the second-order time derivative, making it possible to propagate the wave field stably even using larger time steps. The method’s applicability was tested by the migration of two-dimensional pre- and pos-stack synthetic datasets, the SEG/EAGE salt model and the Marmousi model. A real pre-stack data from the Gulf of Mexico was migrated successfully and is also presented. Through the numerical examples the applicabilityand robustness of these methods were proved and it was also showed that they can extrapolate wavefields with a much larger time step than commonly used.Keywords: acoustic wave equation, seismic migration, reverse time migration, pseudo-spectral method, pseudo-analytical method, pseudo-Laplacian operator. RESUMO. No método sísmico, a fim de se obter uma imagem precisa, faz-se necessário o uso de técnicas de processamento, entre elas a migração sísmica.A migração reversa no tempo (RTM) empregada aqui não é um conceito novo. Ela usa a equação completa da onda, implicitamente inclui múltiplas chegadas, consegue imagear todos os mergulhos e, assim, possibilita o imageamento de estruturas complexas. Porém, sua aplicação em problemas 3D pré-empilhamento continua endo restrita por conta do grande esforço computacional requerido. Mas, recentemente, com o avanço tecnológico e computadores mais rápidos, a migração 3D pré-empilhamento tem sido aplicada, especialmente, em problemas de difícil imageamento, como o de estruturas complexas em regiões de pré-sal. Assim, com o intuito de equilibrar o custo de processamento com a qualidade e confiabilidade da imagem obtida, são utilizados diferentes métodos numéricos para computar a migração. Este trabalho apresenta duas diferentes maneiras de se realizar a migração reversa no tempo partindo da solução exata da equação completa da onda: RTM por interpolação e pelo método pseudo-analítico. No método de interpolação, a migração é aplicada utilizando-se várias velocidades constantes, seguido de um procedimento de interpolação para obter a imagem migrada através da composição das imagens computadas a partir dessas velocidades constantes. Já no método pseudo-analítico, introduz-se modificações no cálculo do operador Laplaciano visando melhorar a aproximação da derivada segunda no tempo, que são feitas por esquemas de diferenças finitas de segunda ordem, possibilitando assim propagar o campo de onda de forma estável usando-se passos maiores no tempo. A aplicabilidadedas metodologias foi testada por meio da migração de dados bidimensionais sintéticos pré e pós-empilhamento, o modelo de domo de sal da SEG/EAGE e o modelo Marmousi. Um dado real bidimensional, adquirido no Golfo do México não empilhado, também, foi usado e migrado com sucesso. Assim, através desses exemplos numéricos, mostra-se a aplicabilidade e a robustez desses novos métodos de migração reversa no tempo no imageamento de estruturas complexas com os campos de ondas propagados com passos maiores no tempo do que os usados comumente.Palavras-chave: equação da onda, migração sísmica, migração reversa no tempo, método pseudo-espectral, método pseudo-analítico, operador pseudo-Laplaciano.

Q-compensated reverse-time migration

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. S77-S87 ◽  
Author(s):  
Tieyuan Zhu ◽  
Jerry M. Harris ◽  
Biondo Biondi
Keyword(s):  
Image Resolution ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Pass Filter ◽  
Low Pass Filter ◽  
High Attenuation ◽  
Phase Dispersion ◽  
Time Migration ◽  
Amplitude Attenuation ◽  
Attenuation And Dispersion

Reduced amplitude and distorted dispersion of seismic waves caused by attenuation, especially strong attenuation, always degrades the resolution of migrated images. To improve image resolution, we evaluated a methodology of compensating for attenuation ([Formula: see text]) effects in reverse-time migration ([Formula: see text]-RTM). The [Formula: see text]-RTM approach worked by mitigating the amplitude attenuation and phase dispersion effects in source and receiver wavefields. Source and receiver wavefields were extrapolated using a previously published time-domain viscoacoustic wave equation that offered separated amplitude attenuation and phase dispersion operators. In our [Formula: see text]-RTM implementation, therefore, attenuation- and dispersion-compensated operators were constructed by reversing the sign of attenuation operator and leaving the sign of dispersion operator unchanged, respectively. Further, we designed a low-pass filter for attenuation and dispersion operators to stabilize the compensating procedure. Finally, we tested the [Formula: see text]-RTM approach on a simple layer model and the more realistic BP gas chimney model. Numerical results demonstrated that the [Formula: see text]-RTM approach produced higher resolution images with improved amplitude and phase compared to the noncompensated RTM, particularly beneath high-attenuation zones.

scholarly journals Depth-Extrapolation-Based True-Amplitude Full-Wave-Equation Migration from Topography

2021 ◽  
Vol 11 (7) ◽  
pp. 3010
Author(s):  
Hao Liu ◽  
Xuewei Liu
Keyword(s):  
Wave Equation ◽  
Partial Derivative ◽  
Model Experiment ◽  
Surface Velocity ◽  
Seismic Exploration ◽  
Initial Condition ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Full Wave ◽  
Time Migration

The lack of an initial condition is one of the major challenges in full-wave-equation depth extrapolation. This initial condition is the vertical partial derivative of the surface wavefield and cannot be provided by the conventional seismic acquisition system. The traditional solution is to use the wavefield value of the surface to calculate the vertical partial derivative by assuming that the surface velocity is constant. However, for seismic exploration on land, the surface velocity is often not uniform. To solve this problem, we propose a new method for calculating the vertical partial derivative from the surface wavefield without making any assumptions about the surface conditions. Based on the calculated derivative, we implemented a depth-extrapolation-based full-wave-equation migration from topography using the direct downward continuation. We tested the imaging performance of our proposed method with several experiments. The results of the Marmousi model experiment show that our proposed method is superior to the conventional reverse time migration (RTM) algorithm in terms of imaging accuracy and amplitude-preserving performance at medium and deep depths. In the Canadian Foothills model experiment, we proved that our method can still accurately image complex structures and maintain amplitude under topographic scenario.

Q least-squares reverse time migration based on the first-order viscoacoustic quasidifferential equations

Geophysics ◽  
2021 ◽  
pp. 1-65
Author(s):  
Yingming Qu ◽  
Yixin Wang ◽  
Zhenchun Li ◽  
Chang Liu
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Surface Topography ◽  
Density Perturbation ◽  
Second Order ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
First Order ◽  
Time Migration ◽  
Grid Scheme

Seismic wave attenuation caused by subsurface viscoelasticity reduces the quality of migration and the reliability of interpretation. A variety of Q-compensated migration methods have been developed based on the second-order viscoacoustic quasidifferential equations. However, these second-order wave-equation-based methods are difficult to handle with density perturbation and surface topography. In addition, the staggered grid scheme, which has an advantage over the collocated grid scheme because of its reduced numerical dispersion and enhanced stability, works in first-order wave-equation-based methods. We have developed a Q least-squares reverse time migration method based on the first-order viscoacoustic quasidifferential equations by deriving Q-compensated forward-propagated operators, Q-compensated adjoint operators, and Q-attenuated Born modeling operators. Besides, our method using curvilinear grids is available even when the attenuating medium has surface topography and can conduct Q-compensated migration with density perturbation. The results of numerical tests on two synthetic and a field data sets indicate that our method improves the imaging quality with iterations and produces better imaging results with clearer structures, higher signal-to-noise ratio, higher resolution, and more balanced amplitude by correcting the energy loss and phase distortion caused by Q attenuation. It also suppresses the scattering and diffracted noise caused by the surface topography.

Angle-Domain Gathers Computation Using Poynting Vector of Two-Way Acoustic Wave Equation

2014 ◽  
Vol 962-965 ◽  
pp. 2984-2987
Author(s):  
Jia Jia Yang ◽  
Bing Shou He ◽  
Ting Chen
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Real Data ◽  
Flow Density ◽  
Acoustic Wave Equation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Wave Fields ◽  
Time Migration ◽  
Source Wave

Based on two-way acoustic wave equation, we present a method for computing angle-domain common-image gathers for reverse time migration. The method calculates the propagation direction of source wave-fields and receiver wave-fields according to expression of energy flow density vectors (Poynting vectors) of acoustic wave equation in space-time domain to obtain the reflection angle, then apply the normalized cross-correlation imaging condition to achieve the angle-domain common-image gathers. The angle gathers obtained can be used for migration velocity analysis, AVA analysis and so on. Numerical examples and real data examples demonstrate the effectiveness of this method.

Implicit interpolation in reverse‐time migration

Geophysics ◽  
1997 ◽  
Vol 62 (3) ◽  
pp. 906-917 ◽  
Author(s):  
Jinming Zhu ◽  
Larry R. Lines
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Real Data ◽  
Seismic Sources ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Difference Wave ◽  
Time Migration ◽  
Seismic Acquisition ◽  
Recorded Data

Reverse‐time migration applies finite‐difference wave equation solutions by using unaliased time‐reversed recorded traces as seismic sources. Recorded data can be sparsely or irregularly sampled relative to a finely spaced finite‐difference mesh because of the nature of seismic acquisition. Fortunately, reliable interpolation of missing traces is implicitly included in the reverse‐time wave equation computations. This implicit interpolation is essentially based on the ability of the wavefield to “heal itself” during propagation. Both synthetic and real data examples demonstrate that reverse‐time migration can often be performed effectively without the need for explicit interpolation of missing traces.

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