Wavefield decomposition in arbitrary direction and an imaging condition based on stratigraphic dip

Geophysics ◽  
2020 ◽  
Vol 85 (5) ◽  
pp. S299-S312
Author(s):  
Xuebao Guo ◽  
Ying Shi ◽  
Weihong Wang ◽  
Hongliang Jing ◽  
Zhen Zhang
Keyword(s):  
Hilbert Transform ◽  
New Method ◽  
Frequency Noise ◽  
Arbitrary Direction ◽  
Vector Method ◽  
Imaging Condition ◽  
Dip Angle ◽  
The Hilbert Transform ◽  
Angle Gather ◽  
Wavefield Decomposition

In reverse time migration (RTM), wavefield decomposition can play an important role in addressing the issue of migration noise, especially low-frequency noise. The complete wavefield decomposition based on the Hilbert transform is a commonly used method in RTM, but it is accompanied by extra wavefield simulation and wavefield storage. We have developed three distinct methods. The first is a convenient method for wavefield decomposition, which is based on Poynting vectors. Only the unit vector in one direction is needed to realize the wavefield decomposition in an arbitrary direction by this method. It breaks through the limitation that the Hilbert transform-based method is applicable only to the up- and downgoing wave or left- and right-going wave decomposition, and the calculation cost is negligible compared with RTM. The second is a method based on the instantaneous wavenumber, which we developed for calculating the wave propagation direction. On the basis of wavefield decomposition, the imaging angle gather from the new method performs better than that of the Poynting vector method. Meanwhile, it also is used for generating the incident angle gather and dip angle gather. The latter expresses the dip angle of underground strata. More importantly, the above methods allow us to control the wavefield decomposition direction and three angles at any position underground. The third adopts a stratigraphic imaging condition method, and we briefly analyze the relationship between the new method and the inverse-scattering imaging condition. The stratigraphic imaging condition maps the results to the dip angle of the stratum through a spatial gradient wavefield, which can enhance the effective imaging information. The above three kinds of angle gathers also can be constructed by the stratigraphic imaging condition. Numerical experiments demonstrate that the imaging results and the angle gathers obtained by our proposed method have higher accuracy and resolution.

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.

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 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.

scholarly journals New approaches for automated data processing of annually laminated sediments

2004 ◽  
Vol 11 (5/6) ◽  
pp. 599-607 ◽  
Author(s):  
I. Rupf ◽  
G. Radons
Keyword(s):  
Data Processing ◽  
Hilbert Transform ◽  
Signal To Noise Ratio ◽  
Laminated Sediments ◽  
Frequency Noise ◽  
Detection And Counting ◽  
Actual Signal ◽  
Annually Laminated Sediments ◽  
The Hilbert Transform ◽  
Local Trend

Abstract. Laminated sediments, like evaporites and biogenic lake sediments, provide high-resolution paleo-climate records. Yet detection and counting of laminae causes still problems because sedimentary structures are often disturbed. In the past laminated rocks often were analysed manually - a tedious and subjective work. The present study describes four automated approaches for lamina detection based on 1d grey-scale vectors. Best results are obtained with a newly developed algorithm, called Adaptive Template Method (ATM) in combination with the Hilbert transform. ATM improves the signal to noise ratio of the grey-value signal. Its basic idea is to extract first a characteristic waveform, the template, which describes the typical grey-value variation transverse to the laminae. This is a kind of "template learning" process, which in practice is done by an appropriate averaging method. This template is in a second step used for processing the whole sample. One calculates the overlap of the template with the actual signal, the grey-value variation along the core, as function of position in core direction. This method generates a new signal with maxima at positions, where the template optimally matches the original signal. The new time-series is called AT-transform. It is smoother than the initial data sequence. High frequency noise and local trend effects are suppressed. Afterwards, the AT-transform can be analysed with the Hilbert transformation for extracting phase information. The data processing methods are tested both on artificial data sequences and on a seasonally laminated sedimentary record of the Oligocene Baruth Maar (Germany). Although ATM is no panacea for highly disturbed signals, our comparison with other approaches shows that it provides the best results. The combination of ATM and the Hilbert transform allows to detect clearly long-term oscillations in the sedimentation patterns and thus cycles in climatic variations.

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.

Up/down acoustic wavefield decomposition using a single propagation and its application in reverse time migration

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. S341-S353
Author(s):  
Daniel E. Revelo ◽  
Reynam C. Pestana
Keyword(s):  
Wave Equation ◽  
Rapid Expansion ◽  
Computational Time ◽  
Frequency Noise ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
First Order ◽  
Time Migration ◽  
Wavefield Decomposition

The separation of up- and downgoing wavefields is an important technique in the processing of multicomponent recorded data, propagating wavefields, and reverse time migration (RTM). Most of the previous methods for separating up/down propagating wavefields can be grouped according to their implementation strategy: a requirement to save time steps to perform Fourier transform over time or construction of the analytical wavefield through a solution of the wave equation twice (one for the source and another for the Hilbert-transformed source), in which both strategies have a high computational cost. For computing the analytical wavefield, we are proposing an alternative method based on the first-order partial equation in time and by just solving the wave equation once. Our strategy improves the computation of wavefield separation, and it can bring the causal imaging condition into practice. For time extrapolation, we are using the rapid expansion method to compute the wavefield and its first-order time derivative and then we can compute the analytical wavefield. By computing the analytical wavefield, we can, therefore, separate the wavefield into up- and downgoing components for each time step in an explicit way. Applications to synthetic models indicate that our method allows performing the wavefield decomposition similarly to the conventional method, as well as a potential application for the 3D case. For RTM applications, we can now use the causal imaging condition for several synthetic examples. Acoustic RTM up/down decomposition demonstrates that it can successfully remove the low-frequency noise, which is common in the typical crosscorrelation imaging condition, and it is usually removed by applying a Laplacian filter. Moreover, our method is efficient in terms of computational time when compared to RTM using an analytical wavefield computed by two propagations, and it is a little more costly than conventional RTM using the crosscorrelation imaging condition.

Model of multicomponent narrow-band periodical non-stationary random signal

2020 ◽  
Vol 2020 (48) ◽  
pp. 17-24
Author(s):  
I.M. Javorskyj ◽  
◽  
R.M. Yuzefovych ◽  
P.R. Kurapov ◽  
◽  
...  
Keyword(s):  
Time Series ◽  
Real Time ◽  
Hilbert Transform ◽  
Spectral Properties ◽  
Narrow Band ◽  
Analytic Signal ◽  
Random Signal ◽  
Hilbert Transformation ◽  
The Hilbert Transform

The correlation and spectral properties of a multicomponent narrowband periodical non-stationary random signal (PNRS) and its Hilbert transformation are considered. It is shown that multicomponent narrowband PNRS differ from the monocomponent signal. This difference is caused by correlation of the quadratures for the different carrier harmonics. Such features of the analytic signal must be taken into account when we use the Hilbert transform for the analysis of real time series.

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