Fast algorithms for elastic-wave-mode separation and vector decomposition using low-rank approximation for anisotropic media

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. C97-C110 ◽  
Author(s):  
Jiubing Cheng ◽  
Sergey Fomel
Keyword(s):  
Elastic Wave ◽  
Fast Algorithms ◽  
Anisotropic Media ◽  
Wave Mode ◽  
Low Rank ◽  
Fourier Integral Operators ◽  
Reverse Time ◽  
Time Migration ◽  
Mode Separation ◽  
Vector Decomposition

Wave-mode separation and vector decomposition are significantly more expensive than wavefield extrapolation and are the computational bottleneck for elastic reverse time migration in heterogeneous anisotropic media. We have expressed elastic-wave-mode separation and vector decomposition for anisotropic media as space-wavenumber-domain operations in the form of Fourier integral operators and developed fast algorithms for their implementation using their low-rank approximations. Synthetic data generated from 2D and 3D models demonstrated that these methods are accurate and efficient.

Multidirectional-vector-based elastic reverse time migration and angle-domain common-image gathers with approximate wavefield decomposition of P- and S-waves

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. S57-S79 ◽  
Author(s):  
Chen Tang ◽  
George A. McMechan
Keyword(s):  
Wave Mode ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
S Waves ◽  
Time Migration ◽  
Mode Separation ◽  
Reflection Image ◽  
Wavefield Decomposition ◽  
Imaging Conditions

Elastic reverse time migration (E-RTM) has limitations when the migration velocities contain strong contrasts. First, the traditional scheme of P/S-wave mode separation is based on Helmholtz’s equations, which ignore the conversion between P- and S-waves at the current separation time. Thus, it contains an implicit assumption of the constant shear modulus and requires smoothing the heterogeneous model to approximately satisfy a locally constant condition. Second, the vector-based imaging condition needs to use the reflection-image normal, and it also cannot give the correct polarity of the PP image in all possible conditions. Third, the angle-domain common-image gathers (ADCIGs) calculated using the Poynting vectors (PVs) do not consider the wave interferences that happen at each reflector. Therefore, smooth models are often used for E-RTM. We relax this condition by proposing an improved data flow that involves three new contributions. The first contribution is an improved system of P/S-wave mode separation that considers the converted wave generated at the current time, and thus it does not require the constant-shear-modulus assumption. The second contribution is the new elastic imaging conditions based on multidirectional vectors; they can give the correct image polarity in all possible conditions without knowledge of the reflection-image normal. The third contribution is two methods to calculate multidirectional propagation vectors (PRVs) for RTM images and ADCIGs: One is the elastic multidirectional PV, and the other uses the sign of wavenumber-over-frequency ([Formula: see text]) ratio obtained from an amplitude-preserved approximate-propagation-angle-based wavefield decomposition to convert the particle velocities into multidirectional PRVs. The robustness of the improved data flow is determined by several 2D numerical examples. Extension of the schemes into 3D and amplitude-preserved imaging conditions is also possible.

Reverse Time Migration of Elastic Waves Using the Pseudospectral Time-Domain Method

2018 ◽  
Vol 26 (01) ◽  
pp. 1750033 ◽  
Author(s):  
Jiangang Xie ◽  
Mingwei Zhuang ◽  
Zichao Guo ◽  
Hai Liu ◽  
Qing Huo Liu
Keyword(s):  
Elastic Wave ◽  
Time Domain ◽  
Elastic Waves ◽  
Sampling Rate ◽  
Fdtd Method ◽  
Time Domain Method ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Domain Method

Reverse time migration (RTM), especially that for elastic waves, consumes massive computation resources which limit its wide applications in industry. We suggest to use the pseudospectral time-domain (PSTD) method in elastic wave RTM. RTM using PSTD can significantly reduce the computational requirements compared with RTM using the traditional finite difference time domain method (FDTD). In addition to the advantage of low sampling rate with high accuracy, the PSTD method also eliminates the periodicity (or wraparound) limitation caused by fast Fourier transform in the conventional pseudospectral method. To achieve accurate results, the PSTD method needs only about half the spatial sampling rate of the twelfth-order FDTD method. Thus, the PSTD method can save up to 87.5% storage memory and 90% computation time over the twelfth-order FDTD method. We implement RTM using PSTD for elastic wave equations and accelerate it by Open Multi-Processing technology. To keep the computational load balance in parallel computation, we design a new PML layout which merges the PML in both ends of an axis together. The efficiency and imaging quality of the proposed RTM is verified by imaging on 2D and 3D models.

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