Inversion velocity analysis in the subsurface-offset domain

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. R189-R200 ◽  
Author(s):  
Jie Hou ◽  
William W. Symes
Keyword(s):  
Objective Function ◽  
Inverse Operator ◽  
Real Data ◽  
Velocity Analysis ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Image Volume ◽  
Least Squares Migration ◽  
Data Frequency

Optimization-based migration velocity analysis updates long-wavelength velocity information by minimizing an objective function that measures the violation of a focusing criterion, applied to an image volume. Differential semblance optimization forms a smooth objective function in velocity and data, regardless of the data-frequency content. Depending on how the image volume is formed, however, the objective function may not be minimized at a kinematically correct velocity, a phenomenon characterized in the literature (somewhat inaccurately) as “gradient artifacts.” We find that the root of this pathology is imperfect image volume formation resulting from reverse time migration (RTM), and that the use of linearized inversion (least-squares migration) more or less eliminates it. A synthetic Marmousi example and a 2D real data example are used to demonstrate that an approximate inverse operator, a little more expensive than RTM, leads to recovery of a kinematically correct velocity.

An exact adjoint operation pair in time extrapolation and its application in least-squares reverse-time migration

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. H27-H33 ◽  
Author(s):  
Jun Ji
Keyword(s):  
Least Squares ◽  
Adjoint Operator ◽  
Synthetic Data ◽  
Forward Modeling ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Product Test ◽  
Least Squares Migration ◽  
Time Extrapolation

To reduce the migration artifacts arising from incomplete data or inaccurate operators instead of migrating data with the adjoint of the forward-modeling operator, a least-squares migration often is considered. Least-squares migration requires a forward-modeling operator and its adjoint. In a derivation of the mathematically correct adjoint operator to a given forward-time-extrapolation modeling operator, the exact adjoint of the derived operator is obtained by formulating an explicit matrix equation for the forward operation and transposing it. The programs that implement the exact adjoint operator pair are verified by the dot-product test. The derived exact adjoint operator turns out to differ from the conventional reverse-time-migration (RTM) operator, an implementation of wavefield extrapolation backward in time. Examples with synthetic data show that migration using the exact adjoint operator gives similar results for a conventional RTM operator and that least-squares RTM is quite successful in reducing most migration artifacts. The least-squares solution using the exact adjoint pair produces a model that fits the data better than one using a conventional RTM operator pair.

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.

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.

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.

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.

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.

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