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.

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.

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.

Vector elastic deconvolution migration with dual wavefield decomposition

Geophysics ◽  
2021 ◽  
pp. 1-81
Author(s):  
Benxin Chi ◽  
Kai Gao ◽  
Lianjie Huang
Keyword(s):  
New Method ◽  
Low Rank ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Wave Imaging ◽  
Migration Method ◽  
Anisotropic Elastic ◽  
The Hilbert Transform ◽  
Wavefield Decomposition

Elastic-wave imaging using multi-component data can provide more useful subsurface information than acoustic-wave imaging, but is usually algorithmically challenging. We develop a vector elastic deconvolution migration method for high-resolution imaging of subsurface structures in isotropic and anisotropic elastic media. Our new method employs a vector deconvolution imaging condition based on dual wavefield decomposition, including an explicit directional wavefield separation using the Hilbert transform, and a P/S vector wavefield decomposition using the low-rank decomposition method. Using three elastic models, we numerically demonstrate that our new method produces notably higher-resolution and more amplitude-balanced elastic images compared with a cross-correlation-based vector elastic reverse-time migration method.

scholarly journals VSP Imaging Using Free-Surface Multiples With Wavefield Decomposition: Synthetic and Field Data Examples

2021 ◽  
Vol 9 ◽  
Author(s):  
Yikang Zheng ◽  
Yibo Wang ◽  
Xu Chang
Keyword(s):  
Free Surface ◽  
Inverse Scattering ◽  
Hilbert Transform ◽  
Field Data ◽  
Data Migration ◽  
Reverse Time ◽  
Imaging Condition ◽  
Time Migration ◽  
Wavefield Decomposition

Vertical seismic profiling (VSP) is an effective technique to provide high-resolution seismic images of the reservoir area. However, the quality of the images is limited by the poor illumination of primary reflection wave. In conventional VSP imaging, only the upgoing primaries are used. Adding free-surface–related multiples into the imaging process can significantly improve the coverage of the illuminated area. Conventional migration methods using multiples need the complex process of multiple prediction. Data-to-data migration (DDM) is an effective imaging technique for multiples in which the recorded data is migrated directly. To improve the imaging quality of DDM in VSP imaging, we propose separating the wavefield into downgoing and upgoing components using Hilbert transform when reverse-time migration (RTM) is implemented in DDM, and the inverse-scattering imaging condition is further applied to the decomposed wavefields. The proposed method eliminates low-frequency noises and false images generated from the conventional cross-correlation imaging condition, and further enhance the illumination in the VSP imaging. Synthetic examples and application to a walkaway field data demonstrate that it can attenuate the noise and improve the imaging resolution effectively. By using DDM with inverse scattering imaging condition and wavefield decomposition based on Hilbert transform, VSP imaging using free-surface–related multiples becomes a practical complement for conventional VSP imaging.

3D forward modeling of upgoing and downgoing wavefields using Hilbert transform

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. F1-F8 ◽  
Author(s):  
Yikang Zheng ◽  
Yibo Wang ◽  
Xu Chang
Keyword(s):  
Fourier Transform ◽  
Hilbert Transform ◽  
Forward Modeling ◽  
Ocean Bottom ◽  
Reverse Time ◽  
Time Migration ◽  
Computation Efficiency ◽  
Wavefield Simulation ◽  
The Fourier Transform ◽  
The Hilbert Transform

The separation of upgoing and downgoing wavefields is an important technique in the processing of vertical seismic profiling data and ocean bottom cable data. It is also used in reverse time migration (RTM) based on the two-way wave equation to suppress low-frequency, high-amplitude noises and false images. Therefore, we model upgoing and downgoing wavefields directly in the wavefield propagation. There are several methods to obtain separated wavefields. The methods using the Fourier transform require storage of the wavefields, which is not practical due to the extremely high disk-space requirements. Methods using Poynting vectors have an ambiguity problem when crossing a peak or a trough of the wavefields. To improve the accuracy and stability of the modeled upgoing and downgoing wavefields in a complicated velocity model, we evaluate an efficient forward-modeling approach purely based on the Hilbert transform in 3D acoustic wavefield simulation. This method is implemented by the Hilbert transform along the time and depth axis, instead of the Fourier transform. We explicitly derive the formulas for upgoing and downgoing wavefield propagation and attach reproducible source codes. Applications to synthetic models indicate that this method can forward propagate upgoing and downgoing wavefields effectively and improve the imaging quality in migration. This method has various potential applications, e.g., 3D seismic imaging with high computation efficiency.

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