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| Forward modeling of the seismic wave field of pure qP waves in TTI media based on the pseudo-analytical method |
ZHANG Kui-Tao1( ), LIAO Jia-Rong1, GU Han-Ming2(), SUN Ying-Ying1, CHEN Yi-Yang1, WANG Kai1 |
1. Jiangxi Provincial Transportation Design and Research Institute Co.,Ltd.,Nanchang 330052,China
2. School of Geophysics and Geomatics,China University of Geosciences(Wuhan),Wuhan 430074,China |
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Abstract Forward modeling and reverse-time migration imaging techniques for pure quasi-P (qP) waves in anisotropic media have aroused extensive concern in recent years.However,conventional quasi-acoustic equations are subjected to the interference from quasi-shear waves,the limitation of model parameters (ε≥δ),propagation instability,and low calculation accuracy,thus significantly restricting their application.Hence,this study shifted the quasi-differential equation of qP waves to the space-wavenumber domain and derived the second-order pure qP wave equation of TTI media in the time domain through coordinate transformation.To improve the calculation accuracy,this study conducted the forward modeling of the seismic wave field of pure qP waves in TTI media based on the pseudo-analytical method (PAM).The numerical simulation results show that:(1)The method proposed in this study was free from the limitations of quasi-acoustic equations,the interference from quasi-shear waves,and model parameters,enabling stable propagation of the seismic wave field;(2)Compared to other methods,the PAM can effectively improve the numerical simulation accuracy;(3)The testing of simple and complex models verified the correctness and applicability of the proposed method.
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Received: 06 March 2023
Published: 26 February 2024
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Normalized pseudo-Laplace(NPL) operator
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A second derivative of space based on normalized pseudo-Laplace(NPL) operators
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Normalized pseudo-Laplace (NPL) operator under complex media model
a—Hess complex media model;b—NPL for the Hess model
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| 介质类型 | v0/(m·s-1) | ρ/(g·cm-3) | ε | δ | θ | | Ⅰ | 1700 | 2.5 | 0.20 | 0.10 | 0° | | Ⅱ | 1700 | 2.5 | 0.20 | 0.10 | 90° | | Ⅲ | 1700 | 2.5 | 0.20 | 0.10 | 45° | | Ⅳ | 1700 | 2.5 | 0.15 | 0.15 | 45° | | Ⅴ | 1700 | 2.5 | 0.10 | 0.20 | 45° |
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Homogeneous media model parameters
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Snapshot of the 400 ms moment wave field for uniform acoustic TTI medium pseudoacoustic wave equation (top) and pure qP wave equation (bottom)
a,d—corresponding media type III;b,e—corresponding media type IV;c,f—corresponding media type V
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Pure qP wave equation snapshot of the wave field at 400 ms in a homogeneous anisotropic medium
a—media type Ⅰ; b—media type Ⅱ; c—media type Ⅲ
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Snapshot of the 350 ms time wave of pure qP wave in uniform TTI medium
a—finite difference method(FDM); b—pseudo spectral method(PSM); c—pseudo analytical method(PAM)
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Two-dimensional BP2007 acoustic TTI media model parameters
a—P-wave velocity v0;b—P-wave anisotropy parameters ε;c—variation coefficient δ;d—polarization angle θ
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Two-dimensional BP2007 acoustic TTI medium 4 s time wave field snapshot(a) and seismic record(b)
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