地球物理学报  2011, Vol. 54 Issue (9): 2357-2367 PDF

1. 中国科学院地质与地球物理研究所,北京 100029;
2. 中国科学院研究生院,北京 100049

Boundary-volume integral equation numerical modeling for complex near surface
GUAN Xi-Zhu1,2, FU Li-Yun1, TAO Yi1, YU Geng-Xin1
1. Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China;
Abstract: Complex near surface causes the anomalous variation of the amplitude and phase of seismic reflection signal from deep structures, and it is the most important factor to degrade the quality of seismic data. In this paper, we use the boundary-volume integral equation technique to simulate the seismic wave propagation in the complex near surface structure by solving the wave propagation equation with complex near surface condition. In the boundary-volume integral equation technique, the boundary element method can simulate irregular surface and geological structure for seismic wave propagation, and the volume element method can simulate the effect of the heterogeneous medium in low subweathered zone for the seismic wave propagation. Compared with other numerical simulation methods, the main advantage of the boundary-volume integral equation technique is its accurate geometric description of irregular surface and interface to simulate the boundary scattering waves by the free surface; it explicitly applies the continuous boundary conditions of the complex near surface to implement the semi-analytical numerical simulation; it can deal with the complex near surface structure piecewise and effectively simulate the scattering body wave field caused by the inhomogeneous medium under the complex near surface. Numerical results show that the method is practical and effective.
Key words: Complex near surface      Seismic wave propagation      Wave propagation equation numerical simulation      Boundary-volume integral equation technique      Scattering noise from near surface
1 引言

2 方法原理与基本方程

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 图 1 起伏地形及其下非均质低降速层构成的散射介质模型 Fig. 1 Geometry of a scattering medium in the homogeneous free space

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 图 2 角点P(r)及对应的张角 Fig. 2 Angular point P(r) and its angle

3 积分方程的数值离散

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F0 为利用公式(4)计算得到的点源激发入射到边界Γ0 上的各个离散点作用而产生的震源项向量，即

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(1) 针对具体模型，建立包含震源项的边界-体积分方程.

(2) 选用不同的离散单元与形函数，对边界积分方程进行边界元离散，用配置法对体积分方程进行离散.

(3) 对由(2)式得到的单元系数矩阵组装成总体系数矩阵.

(4) 求解总体系数矩阵并回代入对应的边界-体积分方程，得到频率域的波场值.

(5) 对不同频率的波场值进行逆FFT，变换到时间域，得到接收点处的合成地震记录.

4 数值解与解析解的对比分析

 图 3 半圆峡谷模型(a)和均匀沉积谷模型(b)及SH 波入射示意图 Fig. 3 Geometry of semicircular canyon topography model (a) and semicircular valley with homogeneous medium model (b) with incident SH waves

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 图 4 半圆峡谷模型的地震响应 (a)SH 波45°入射地表各点对不同η 值的振幅响应(实线为解析解，虚线为数值解)；(b)SH-波垂直入射地表各点的地震合成记录. Fig. 4 The seismic responses of the semicircular canyon topography model (a) The amplitude response for various n with 45° incident harmonic plane wave(solid lines denote the exact solutions and the dots denote numeric results) ； (b) Synthetic seismograms with 0° incident harmonic plane wave.

 图 5 SH-波垂直入射均匀沉积谷模型的地震响应 (a)地表各点对不同η 值的振幅响应(实线为解析解，虚线为数值解)；(b)地表各点的地震合成记录. Fig. 5 The seismic responses of the semicircular valley model with 0° incident harmonic plane wave (a) The amplitude response for various n (solid lines denote the exact solutions and the dots denote numeric results) ； (b)Synthetic seismograms.

 图 6 SH-波入射沉积谷模型(垂直入射(a)，60°入射(b))对不同离散单元长度进行数值模拟得到的η =1时地表各点的地震振幅响应(实线为解析解，虚线为数值解) Fig. 6 The seismic responses of the semicircular valley model (0° incident SH wave (a) and 60° incident SH wave(b) with the dimensionless frequencies η=1 for various sampling rates (the solid lines denote the exact solutions and the dots denote numeric results)

 图 7 半空间随机非均质沉积谷模型 Fig. 7 The semicircular valley with random heterogeneous medium model in the half-space with incident SH wave

 图 8 SH-波入射随机非均质沉积谷模型地表各点的地震振幅响应曲线 固定η =1对谷内速度扰动量δ 取不同值时的数值模拟结果(a)和固定δ=10%对不同η 值的数值模拟结果(b). Fig. 8 The seismic responses of the semicircular valley with random heterogeneous medium model (a) The amplitude response with η=1 for various velocity perturbation 8；(b) The amplitude response with 8=10% for various velocity perturbation η

5 数值算例

 图 9 不同复杂程度近地表模型及其对应的地表合成地震炮集记录 (a)平地表匀均介质近地表模型及其地表合成地震炮集记录；(b)起伏地表模型及其地表合成地震炮集记录；(c)起伏地表弱非均质(δ=5%)近地表层模型及其地表合成地震炮集记录；(d)起伏地表强非均质(δ=15%)近地表层模型及其地表合成地震炮集记录. Fig. 9 The models of different complex near surface and the synthetic seismograms for these model (a) The homogeneous near-surface mdoel with flat topography and its synthetic seismograms； (b) The homogeneous near-surface model with rough topography and its synthetic seismograms； (c) The weak heterogeneous near-surface model (δ=5%) with rough topography and its synthetic seismograms； (d) The strong heterogeneous near-surface model(δ= 15%) with rough topography and its synthetic seismograms.

 图 10 复杂地表与平地表盐丘模型地震模拟比较 (a)复杂地表盐丘模型；(b)起伏自由表面接收合成的反射地震记录；(c)平地表合成的反射地震记录. Fig. 10 Synthetic seismograms for rugged free surface (a) Satt model with rough topography；(b) The reflection synthetic seismograms with rough topography；(c) The reflection synthetic seismograms with flat topography.

 图 11 崎岖地表低降速带复杂近地表模型地震模拟 (a)复杂近地表模型；(b)左边放炮地表接收合成炮集；(c)中间放炮地表接收合成炮集；(d)右边放炮地表接收合成炮集. Fig. 11 Synthetic seismograms for complex near surface model with rugged free surface and low subweathered zone (a) The complex near surface model；(b) The synthetic seismograms with the source on the left；(c) The synthetic seismograms with the source at the center；(d) The synthetic seismograms with the source on the right.
6 结论

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