Local Plane-wave Decomposition Research Articles

High-Resolution Anisotropic Prestack Kirchhoff Dynamic Focused Beam Migration

Kirchhoff beam migration is a kind of ray-based seismic imaging method boasting the advantages of both high efficiency and high accuracy. In this paper, anisotropic ray tracing will be applied to extend it to an anisotropic seismic imaging method. However, two problems exist in this method for imaging calculation: Firstly, the conventional local plane wave decomposition method has a low computational precision; secondly, the original beam propagator diverges quickly when the propagation distance increases. These two problems can both increase imaging noise, and finally reduce the resolution of the final imaging results. In this paper, the high-resolution anisotropic Kirchhoff dynamic focused beam migration is proposed to solve these two problems. Local plane wave decomposition method considered from the perspective of inversion is employed to obtain higher-quality slant stack data and dynamic focused beam propagator is adopted to control the divergence of beams. Both the anisotropic layer model and Hess model are adopted to test the imaging ability of the new method.

Application of Gaussian beam migration to VSP imaging

Vertical seismic profiling (VSP) technology plays an important role in oil and gas exploration. It can obtain data in the well with higher resolution than conventional surface seismic imaging methods, and effectively identify small faults along the well, thereby improving the description accuracy of the reservoir. Gaussian beam migration (GBM) has the ability to calculate the multi-arrival travel time, which has the advantages of both high efficiency and high imaging accuracy. In this paper, the observation system and the local plane wave decomposition step will be adjusted to expand the prestack GBM into a VSP imaging method. A layer model and a complex model will be employed to verify the imaging ability of VSP GBM. The correctness of VSP GBM will be proved by practical data test through comparing the results of VSP GBM with Kirchhoff migration in surface seismic.

A Topographic Kirchhoff Dynamic Focused Beam Migration Method Based on Compressed Sensing

Kirchhoff beam migration (KBM) is a ray-based seismic imaging method, which can handle multi-arrivals caused by model complexity. Apart from its high imaging precision, it also retains the merits of Kirchhoff migration, such as efficiency, stability, and flexibility. However, two issues should be taken into consideration when this method is expanded to the complicated surface conditions: first, the computational accuracy deficiency of the original local plane-wave decomposition method cannot suit for low signal-to-noise ratio seismic data; second, as the rays traveling, the beam width increases rapidly, which cannot guarantee the computational accuracy of the corresponding grid points’ attribute information. In addition, the insufficient coverage of the beam in the shallow part of the model might affect the imaging quality of this region. Kirchhoff dynamic focused beam migration based on compressed sensing is proposed to resolve these two problems. For the first problem, the local plane-wave decomposition method based on compressed sensing is introduced into KBM to enhance its computational accuracy. To solve the second problem, this paper adopts the dynamic focused beam to replace the original simplified Gaussian beam in the migration method, control the divergence of beam, and increase the coverage of beam in the shallow part of the model. Both Marmousi model and Canadian Foothills model are employed in this paper to test the new migration imaging method.

Reverse-time migration and amplitude correction in the angle-domain based on Poynting vector

We propose a method based on the Poynting vector that combines angle-domain imaging and image amplitude correction to overcome the shortcomings of reverse-time migration that cannot handle different angles during wave propagation. First, the local image matrix (LIM) and local illumination matrix are constructed, and the wavefield propagation directions are decomposed. The angle-domain imaging conditions are established in the local imaging matrix to remove low-wavenumber artifacts. Next, the angle-domain common image gathers are extracted and the dip angle is calculated, and the amplitude-corrected factors in the dip angle domain are calculated. The partial images are corrected by factors corresponding to the different angles and then are superimposed to perform the amplitude correction of the final image. Angle-domain imaging based on the Poynting vector improves the computation efficiency compared with local plane-wave decomposition. Finally, numerical simulations based on the SEG/EAGE velocity model are used to validate the proposed method.

Study of a full-wave equation-based seismic illumination analysis

Recently, the seismic illumination analysis has progressed considerably in methodology which has been developed not only from one-way wave equation-based illumination to full-wave equation-based illumination but also from conventional illumination analysis to directional illumination analysis with local plane-wave decomposition. Because of the inherent defects of the one-way wave equation, the full-wave equation-based seismic illumination methods have increasingly attracted more attention. However, full-wave equation-based wavefield includes both downgoing and upgoing waves, such as transmissive, turning, and reflected waves. This hybrid wavefield can mislead us in seismic illumination analysis. For the sake of a preferable seismic illumination analysis method, we separated upgoing and downgoing wavefields in the time domain using Poynting vector and defined the incident and reflected illumination analysis functions based on the separated wavefields. Furthermore, we applied these two new illumination functions in seismic illumination analysis with the Sigsbee2a model. Multiple-shot illumination results show that the full-wave illumination and incident illumination maps are consistent with the seismic migration image. Because of no interference caused by the interactions between upgoing and downgoing waves, the incident illumination is superior for illumination analysis. Successful application of the full-wave equation-based incident and reflected illumination functions in the actual acquisition direction design of marine seismic geometry verifies their applicability and reveals their excellent prospects.

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

Removing smearing-effect artifacts in angle-domain common-image gathers from reverse time migration

Local plane-wave decomposition (LPWD) and local shift imaging condition (LSIC) methods for extracting angle-domain common-image gathers (ADCIGs) from prestack reverse time migration are based on the local plane-wave assumption, and both suffer from a trade-off in choosing the local window size. Small windows produce clean ADCIGs, but with low angle resolution, whereas large windows produce noisy ADCIGs, which include smearing-effect artifacts, but with high angle resolution. The cause of the smearing-effect artifacts in LPWD is the crosscorrelation of plane waves obtained by decomposition of the source and receiver wavefronts, at points that do not lie on the source wavefront excitation time trajectory. The cause of the smearing-effect artifacts in LSIC is the decomposition of curved events of offset-domain common-image gathers (ODCIGs) at incorrect depth points at zero offset. These artifacts can occur even if the migration velocity model is correct. Two methods were proposed to remove the artifacts. In the LPWD method, the smearing-effect artifacts were removed by decomposing and crosscorrelating the resulting source and receiver plane waves only at image points and excitation (image) times. In the LSIC method, the artifacts were removed by decomposing curved events in ODCIGs into planar events only at zero-offset target image points. Numerical tests with synthetic data revealed the success of the proposed methods.

Leaky rays on optical fibres of arbitrary (circularly symmetric) index profiles

The local plane-wave decomposition approach used to analyse optical fibres of arbitrary refractive-index profiles has been extended to include the case of so called ‘leaky’ rays. The result thus obtained for acceptance angle represents a generalisation of results derived previously for simple forms of the profile by geometrical-optics methods.