Reflectivity blurring in subsurface extended image gathers

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. S521-S532
Author(s):  
Colin J. Thomson ◽  
Robin P. Fletcher ◽  
Philip W. Kitchenside ◽  
James Hobro
Keyword(s):  
Plane Wave ◽  
Reservoir Characterization ◽  
Wave Reflection ◽  
Computational Cost ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Reflection Coefficients ◽  
Reverse Time ◽  
Reflection Function ◽  
Time Migration

We explain how a reverse time migration (RTM) subsurface extended-image gather (EIG) relates to the reflection function for a finite-contrast interface via a blurring function. For a plane interface between locally homogeneous media, the reflection function contains the plane-wave reflection coefficients, and so we determine how the EIG relates to amplitude versus angle. The EIG and reflection function are multidimensional; hence, the blurring function in their linear relationship is higher dimensional. We explain how it may be computed and show that it describes spatial blurring and blurring over angle of the plane-wave reflection coefficients. We determine explicitly how a slant stack of the EIG at one slowness depends on the plane-wave coefficients at nearby slownesses. This angle blurring stems from the spatial nonstationarity of the blurring function, so it should be the most significant where the illumination changes most rapidly in space. To evaluate the theory, we use finite-difference modeling in the Sigsbee 2a model to generate synthetic survey data, RTM EIGs, blurring functions, and modeled gathers for a deep reflector. Two example image points are chosen. One has good illumination, with blurring over the angle less than 5°. The other point is just under the salt body, with poorer illumination and angle blurring of almost 10°. The description and examples are for two dimensions, but the extension to three dimensions is conceptually straightforward, as is an interface that dips relative to the EIG datum level. The computational cost of blurring functions implies their targeted use for the foreseeable future, for example, in reservoir characterization. The extension to elasticity and more-complicated scatterers is also foreseeable, and we emphasize the separation of the overburden and survey-geometry blurring effects from target properties.

Angle gathers from reverse time migration using analytic wavefield propagation and decomposition in the time domain

Geophysics ◽  
2016 ◽  
Vol 81 (1) ◽  
pp. S1-S9 ◽  
Author(s):  
Jiangtao Hu ◽  
Huazhong Wang ◽  
Xiongwen Wang
Keyword(s):  
Plane Wave ◽  
Time Domain ◽  
Computational Cost ◽  
Imaging Method ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
Time Migration ◽  
Local Plane ◽  
The Time Domain

Angle-domain common imaging gathers (ADCIGs) are important input data for migration velocity analysis and amplitude variation with angle analysis. Compared with Kirchhoff migration and one-way wave equation migration, reverse time migration (RTM) is the most accurate imaging method in complex areas, such as the subsalt area. We have developed a method to generate ADCIGs from RTM using analytic wavefield propagation and decomposition. To estimate the wave-propagation direction and angle by spatial Fourier transform during the time domain wave extrapolation, we have developed an analytic wavefield extrapolation method. Then, we decomposed the extrapolated source and receiver wavefields into their local angle components (i.e., local plane-wave components) and applied the angle-domain imaging condition to form ADCIGs. Because the angle-domain imaging condition is a convolution imaging condition about the source and receiver propagation angles, it is costly. To increase the efficiency of the angle-domain imaging condition, we have developed a local plane-wave decomposition method using matching pursuit. Numerical examples of synthetic and real data found that this method could generate high-quality ADCIGs. And these examples also found that the computational cost of this approach was related to the complexity of the source and receiver wavefields.

Efficient angle-domain common-image gathers using Cauchy-condition-based polarization vectors

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. S69-S77 ◽  
Author(s):  
Xiongwen Wang ◽  
Jianliang Qian ◽  
Huazhong Wang
Keyword(s):  
Plane Wave ◽  
Model Building ◽  
Computational Cost ◽  
Decomposition Algorithm ◽  
Reverse Time ◽  
Imaging Condition ◽  
Plane Wave Decomposition ◽  
Time Migration ◽  
Imaging Result ◽  
Wave Decomposition

Because angle-domain common-image gathers (ADCIGs) from reverse time migration (RTM) are capable of obtaining the correct illumination of a subsurface geologic structure, they provide more reliable information for velocity model building, amplitude-variation versus angle analysis, and attribute interpretation. The approaches for generating ADCIGs mainly consist of two types: (1) indirect approaches that convert extended image gathers into ADCIGs and (2) direct approaches that first obtain propagating angles of wavefronts and then map the imaging result to the angle domain. In practice, however, generation of ADCIGs usually incurs high computational cost, poor resolution, and other drawbacks. To generate efficient ADCIGs using RTM methods, we have introduced a novel approach to obtain polarization vectors — directions of particle motion — from the Cauchy wavefield (CWF) and an efficient localized plane-wave decomposition algorithm to implement the angle-domain imaging condition. The CWF is a wavefield constructed from the Cauchy condition of the wave equation at any given time, and it only contains negative frequencies of the original wavefield so that the polarization vector is obtained from the local CWF in the wavenumber domain. With polarization vectors at our disposal, we have further developed an efficient localized plane-wave decomposition algorithm to implement the angle-domain imaging condition. Numerical examples have indicated that the new approach is able to handle complex wave phenomenon and has advantages in illuminating subsurface structure.

First-order particle velocity equations of decoupled P- and S-wavefields and their application in elastic reverse time migration

Geophysics ◽  
2021 ◽  
pp. 1-78
Author(s):  
Zhiyuan Li ◽  
Youshan Liu ◽  
Guanghe Liang ◽  
Guoqiang Xue ◽  
Runjie Wang
Keyword(s):  
Particle Velocity ◽  
Computational Cost ◽  
Staggered Grid ◽  
Additional Stress ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Computational Accuracy ◽  
First Order ◽  
Time Migration ◽  
Stress Variable

The separation of P- and S-wavefields is considered to be an effective approach for eliminating wave-mode cross-talk in elastic reverse-time migration. At present, the Helmholtz decomposition method is widely used for isotropic media. However, it tends to change the amplitudes and phases of the separated wavefields compared with the original wavefields. Other methods used to obtain pure P- and S-wavefields include the application of the elastic wave equations of the decoupled wavefields. To achieve a high computational accuracy, staggered-grid finite-difference (FD) schemes are usually used to numerically solve the equations by introducing an additional stress variable. However, the computational cost of this method is high because a conventional hybrid wavefield (P- and S-wavefields are mixed together) simulation must be created before the P- and S-wavefields can be calculated. We developed the first-order particle velocity equations to reduce the computational cost. The equations can describe four types of particle velocity wavefields: the vector P-wavefield, the scalar P-wavefield, the vector S-wavefield, and the vector S-wavefield rotated in the direction of the curl factor. Without introducing the stress variable, only the four types of particle velocity variables are used to construct the staggered-grid FD schemes, so the computational cost is reduced. We also present an algorithm to calculate the P and S propagation vectors using the four particle velocities, which is simpler than the Poynting vector. Finally, we applied the velocity equations and propagation vectors to elastic reverse-time migration and angle-domain common-image gather computations. These numerical examples illustrate the efficiency of the proposed methods.

From acoustic to elastic inverse extended Born modeling: a first insight in the marine environment

Geophysics ◽  
2021 ◽  
pp. 1-73
Author(s):  
Milad Farshad ◽  
Hervé Chauris
Keyword(s):  
Least Squares ◽  
Marine Environment ◽  
Computational Cost ◽  
Physical Parameters ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
Physical Density ◽  
Acoustic Approximation

Elastic least-squares reverse time migration is the state-of-the-art linear imaging technique to retrieve high-resolution quantitative subsurface images. A successful application requires many migration/modeling cycles. To accelerate the convergence rate, various pseudoinverse Born operators have been proposed, providing quantitative results within a single iteration, while having roughly the same computational cost as reverse time migration. However, these are based on the acoustic approximation, leading to possible inaccurate amplitude predictions as well as the ignorance of S-wave effects. To solve this problem, we extend the pseudoinverse Born operator from acoustic to elastic media to account for the elastic amplitudes of PP reflections and provide an estimate of physical density, P- and S-wave impedance models. We restrict the extension to marine environment, with the recording of pressure waves at the receiver positions. Firstly, we replace the acoustic Green's functions by their elastic version, without modifying the structure of the original pseudoinverse Born operator. We then apply a Radon transform to the results of the first step to calculate the angle-dependent response. Finally, we simultaneously invert for the physical parameters using a weighted least-squares method. Through numerical experiments, we first illustrate the consequences of acoustic approximation on elastic data, leading to inaccurate parameter inversion as well as to artificial reflector inclusion. Then we demonstrate that our method can simultaneously invert for elastic parameters in the presence of complex uncorrelated structures, inaccurate background models, and Gaussian noisy data.

Plane-wave least-squares reverse time migration with a preconditioned stochastic conjugate gradient method

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. S33-S46 ◽  
Author(s):  
Chuang Li ◽  
Jianping Huang ◽  
Zhenchun Li ◽  
Rongrong Wang
Keyword(s):  
Plane Wave ◽  
Least Squares ◽  
Conjugate Gradient ◽  
Sampling Method ◽  
Singular Spectrum Analysis ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Numerical Tests ◽  
Time Migration

This study derives a preconditioned stochastic conjugate gradient (CG) method that combines stochastic optimization with singular spectrum analysis (SSA) denoising to improve the efficiency and image quality of plane-wave least-squares reverse time migration (PLSRTM). This method reduces the computational costs of PLSRTM by applying a controlled group-sampling method to a sufficiently large number of plane-wave sections and accelerates the convergence using a hybrid of stochastic descent (SD) iteration and CG iteration. However, the group sampling also produces aliasing artifacts in the migration results. We use SSA denoising as a preconditioner to remove the artifacts. Moreover, we implement the preconditioning on the take-off angle-domain common-image gathers (CIGs) for better results. We conduct numerical tests using the Marmousi model and Sigsbee2A salt model and compare the results of this method with those of the SD method and the CG method. The results demonstrate that our method efficiently eliminates the artifacts and produces high-quality images and CIGs.

Fast plane-wave reverse time migration

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. S549-S556 ◽  
Author(s):  
Xiongwen Wang ◽  
Xu Ji ◽  
Hongwei Liu ◽  
Yi Luo
Keyword(s):  
Time Delay ◽  
Plane Wave ◽  
Green’S Function ◽  
Green's Function ◽  
Time Domain ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Wave Source ◽  
Computation Cost ◽  
Time Migration

Plane-wave reverse time migration (RTM) could potentially provide quick subsurface images by migrating fewer plane-wave gathers than shot gathers. However, the time delay between the first and the last excitation sources in the plane-wave source largely increases the computation cost and decreases the practical value of this method. Although the time delay problem is easily overcome by periodical phase shifting in the frequency domain for one-way wave-equation migration, it remains a challenge for time-domain RTM. We have developed a novel method, referred as to fast plane-wave RTM (FP-RTM), to eliminate unnecessary computation burden and significantly reduce the computational cost. In the proposed FP-RTM, we assume that the Green’s function has finite-length support; thus, the plane-wave source function and its responding data can be wrapped periodically in the time domain. The wrapping length is the assumed total duration length of Green’s function. We also determine that only two period plane-wave source and data after the wrapping process are required for generating the outcome with adequate accuracy. Although the computation time for one plane-wave gather is twice as long as a normal shot gather migration, a large amount of computation cost is saved because the total number of plane-wave gathers to be migrated is usually much less than the total number of shot gathers. Our FP-RTM can be used to rapidly generate RTM images and plane-wave domain common-image gathers for velocity model building. The synthetic and field data examples are evaluated to validate the efficiency and accuracy of our method.

Angle-domain common-image gathers from plane-wave least-squares reverse time migration

Geophysics ◽  
2021 ◽  
pp. 1-60
Author(s):  
Chuang Li ◽  
Zhaoqi Gao ◽  
Jinghuai Gao ◽  
Feipeng Li ◽  
Tao Yang
Keyword(s):  
Inverse Problem ◽  
Plane Wave ◽  
Least Squares ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Migration Velocity Analysis ◽  
Amplitude Versus

Angle-domain common-image gathers (ADCIGs) that can be used for migration velocity analysis and amplitude versus angle analysis are important for seismic exploration. However, because of limited acquisition geometry and seismic frequency band, the ADCIGs extracted by reverse time migration (RTM) suffer from illumination gaps, migration artifacts, and low resolution. We have developed a reflection angle-domain pseudo-extended plane-wave least-squares RTM method for obtaining high-quality ADCIGs. We build the mapping relations between the ADCIGs and the plane-wave sections using an angle-domain pseudo-extended Born modeling operator and an adjoint operator, based on which we formulate the extraction of ADCIGs as an inverse problem. The inverse problem is iteratively solved by a preconditioned stochastic conjugate gradient method, allowing for reduction in computational cost by migrating only a subset instead of the whole dataset and improving image quality thanks to preconditioners. Numerical tests on synthetic and field data verify that the proposed method can compensate for illumination gaps, suppress migration artifacts, and improve resolution of the ADCIGs and the stacked images. Therefore, compared with RTM, the proposed method provides a more reliable input for migration velocity analysis and amplitude versus angle analysis. Moreover, it also provides much better stacked images for seismic interpretation.

Plane-wave least-squares reverse time migration in complex VTI media

2016 ◽  
Author(s):  
Jinqiang Huang ◽  
Daojun Si ◽  
Zhenchun Li ◽  
Jianping Huang
Keyword(s):  
Plane Wave ◽  
Least Squares ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Vti Media
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