Analysis of direction-decomposed and vector-based elastic reverse time migration using the Hilbert transform

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. S599-S617
Author(s):  
Ting Hu ◽  
Hong Liu ◽  
Xuebao Guo ◽  
Yuxin Yuan ◽  
Zhiyang Wang
Keyword(s):  
Hilbert Transform ◽  
Computational Cost ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Spatial Direction ◽  
Time Migration ◽  
Imaging Artifacts ◽  
Dip Angle ◽  
The Hilbert Transform ◽  
Poynting Vectors

Straightforward implementations of elastic reverse time migration (ERTM) often produce imaging artifacts associated with incorrectly imaged mode conversions, crosstalk, and back-scattered energies. To address these issues, we introduced three approaches: (1) vector-based normalized crosscorrelation imaging conditions (VBNICs), (2) directional separation of wavefields to remove low-wavenumber noise, and (3) postimaging filtering of the dip-angle gathers to eliminate the artifacts caused by nonphysical wave modes. These approaches are combined to create an effective ERTM workflow that can produce high-quality images. Numerical examples demonstrate that, first, VBNICs can produce correct polarities for PP/PS images and can compute migrated dip-angle gathers efficiently by using P/S decomposed Poynting vectors. Second, they achieve improved signal-to-noise and higher resolution when performing up/down decomposition before applying VBNICs, and left/right decomposition enhances steep dips imaging at the computational cost of adding the Hilbert transform to a spatial direction. Third, dip filtering using slope-consistency analysis attenuates the remaining artifacts effectively. An application of the SEG advanced modeling program (SEAM) model demonstrates that our ERTM workflow reduces noise and improves imaging ability for complex geologic areas.

A high efficiency wavefield decomposition method based on Hilbert transform

Geophysics ◽  
2021 ◽  
pp. 1-68
Author(s):  
Xue Guo ◽  
Ying Shi ◽  
Weihong Wang ◽  
Xuan Ke ◽  
Hong Liu ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Hilbert Transform ◽  
Decomposition Method ◽  
High Efficiency ◽  
Computational Cost ◽  
Difference Approximation ◽  
Reverse Time ◽  
Time Migration ◽  
The Hilbert Transform ◽  
Wavefield Decomposition

Wavefield decomposition can be used to extract effective information in reverse time migration (RTM) and full waveform inversion (FWI). The wavefield decomposition methods based on the Hilbert transform (HTWD) and the Poynting vector (PVWD) are the most commonly used. The HTWD needs to save the wavefields at all time steps or introduce additional numerical simulation, which increases the computational cost. The PVWD cannot handle multi-wave arrivals, and its performance is poor in complex situations. We propose an efficient wavefield decomposition method based on the Hilbert transform (EHTWD). The EHTWD constructs two wavefields to replace the original wavefield and the wavefield after Hilbert transform. The first wavefield is obtained by using the dispersion relation to modify the frequency components. The other wavefield is obtained by time difference approximation. Therefore, there is a 90° phase change between the two wavefields. In EHTWD, we only need two wavefields at different moments, which avoids the additional numerical simulation. The EHTWD is also suitable for wavefield decomposition in arbitrary directions. Compared with HTWD, the computational complexity can be greatly reduced with the decrease of the number of imaging time slices. The numerical examples of wavefield decomposition demonstrate that the proposed method can realize wavefield decomposition in any direction. The examples of imaging decomposition and real data also show that the EHTWD suppresses the imaging noise effectively.

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.

Surface-offset gathers from elastic reverse time migration and velocity analysis

Geophysics ◽  
2020 ◽  
Vol 85 (1) ◽  
pp. S47-S64
Author(s):  
Yang Zhao ◽  
Tao Liu ◽  
Xueyi Jia ◽  
Hongwei Liu ◽  
Zhiguang Xue ◽  
...  
Keyword(s):  
Velocity Ratio ◽  
Computational Cost ◽  
Cost Effective ◽  
Velocity Estimation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
The Common ◽  
Wave Decomposition

Angle-domain common-image gathers (ADCIGs) from elastic reverse time migration (ERTM) are valuable tools for seismic elastic velocity estimation. Traditional ADCIGs are based on the concept of common-offset domains, but common-shot domain implementations are often favored for computational cost considerations. Surface-offset gathers (SOGs) built from common-offset migration may serve as an alternative to the common-shot ADCIGs. We have developed a theoretical kinematic framework between these two domains, and we determined that the common SOG gives an alternative measurement of kinematic correctness in the presence of incorrect velocity. Specifically, we exploit analytical expressions for the image misposition between these two domains, with respect to the traveltime perturbation caused by velocity errors. Four formulations of the PP and PS residual moveout functions are derived and provide insightful information of the velocity error, angle, and PS velocity ratio contained in ERTM gathers. The analytical solutions are validated with homogeneous examples with a series of varied parameters. We found that the SOGs may perform in the way of simplicity and linearity as an alternative to the common-shot migration. To make a full comparison with ADCIGs, we have developed a cost-effective workflow of ERTM SOGs. A fast vector P- and S-wave decomposition can be obtained via spatial gradients at selected time steps. A selected ERTM imaging condition is then modified in which the migration is done by offset groups between each source and receiver pair for each P- and S-wave decomposition. Two synthetic (marine and land) examples are used to demonstrate the feasibility of our methods.

An angle-domain imaging condition for elastic reverse time migration and its application to angle gather extraction

Geophysics ◽  
2012 ◽  
Vol 77 (5) ◽  
pp. S105-S115 ◽  
Author(s):  
Rui Yan ◽  
Xiao-Bi Xie
Keyword(s):  
Plane Waves ◽  
Depth Image ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
S Waves ◽  
Time Migration ◽  
Dip Angle ◽  
And Migration ◽  
Local Image

An angle-domain imaging condition is recommended for multicomponent elastic reverse time migration. The local slant stack method is used to separate source and receiver waves into P- and S-waves and simultaneously decompose them into local plane waves along different propagation directions. We calculated the angle-domain partial images by crosscorrelating every possible combination of the incident and scattered plane P- and S-waves and then organized them into P-P and P-S local image matrices. Local image matrix preserves all the angle information related to the seismic events. Thus, by working in the image matrix, it is convenient to perform different angle-domain operations (e.g., filtering artifacts, correcting polarity, or conducting illumination and acquisition aperture compensations). Because local image matrix is localized in space, these operations can be designed to be highly flexible, e.g., target-oriented, dip-angle-dependent or reflection-angle-dependent. After performing angle-domain operations, we can stack the partial images in the local image matrix to generate the depth image, or partially sum them up to produce different angle-domain common image gathers, which can be used for amplitude versus angle and migration velocity analysis. We tested several numerical examples to demonstrate the applications of this angle-domain image condition.

Mini-batch Least-Squares Reverse Time Migration In A Deep Learning Framework

Geophysics ◽  
2020 ◽  
pp. 1-61
Author(s):  
Janaki Vamaraju ◽  
Jeremy Vila ◽  
Mauricio Araya-Polo ◽  
Debanjan Datta ◽  
Mohamed Sidahmed ◽  
...  
Keyword(s):  
Deep Learning ◽  
Least Squares ◽  
Spatial Resolution ◽  
Data Science ◽  
Computational Cost ◽  
Computation Time ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Learning Framework ◽  
Time Migration

Migration techniques are an integral part of seismic imaging workflows. Least-squares reverse time migration (LSRTM) overcomes some of the shortcomings of conventional migration algorithms by compensating for illumination and removing sampling artifacts to increase spatial resolution. However, the computational cost associated with iterative LSRTM is high and convergence can be slow in complex media. We implement pre-stack LSRTM in a deep learning framework and adopt strategies from the data science domain to accelerate convergence. The proposed hybrid framework leverages the existing physics-based models and machine learning optimizers to achieve better and cheaper solutions. Using a time-domain formulation, we show that mini-batch gradients can reduce the computation cost by using a subset of total shots for each iteration. Mini-batch approach does not only reduce source cross-talk but also is less memory intensive. Combining mini-batch gradients with deep learning optimizers and loss functions can improve the efficiency of LSRTM. Deep learning optimizers such as the adaptive moment estimation are generally well suited for noisy and sparse data. We compare different optimizers and demonstrate their efficacy in mitigating migration artifacts. To accelerate the inversion, we adopt the regularised Huber loss function in conjunction. We apply these techniques to 2D Marmousi and 3D SEG/EAGE salt models and show improvements over conventional LSRTM baselines. The proposed approach achieves higher spatial resolution in less computation time measured by various qualitative and quantitative evaluation metrics.

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