2.5D marine CSEM modeling in the frequency-domain based on an improved interpolation scheme at receiver positions
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摘要:
在海洋可控源电磁法勘探中，接收站常置于海底.在进行海洋电磁场模拟时，由于海水和海底介质存在显著电性差异，这给海底接收点处场值的求取带来困难.本文提出一种新的接收点插值算法，该算法考虑到海底电场法向分量不连续性问题，用法向电流分量进行插值以准确求取海底任意接收点处电磁场值.本文利用交错网格有限差分法实现了二维介质中频率域海洋可控源法（CSEM）正演.对构造走向做傅里叶变换，将三维电磁模拟问题转换为波数域2.5维问题，即三维场源激励下针对二维地电模型的电磁模拟问题.使用交错网格有限差分法，基于一次场/二次场分离方法导出波数域二次电场离散形式，并进一步求得波数域电磁场.采用本文提出的改进的插值算法可求得海底任意接收点处波数域电磁场，采用傅里叶逆变换对波数域电磁场进行积分可得到接收点处空间域电磁场.模型算例表明，与常规的线性插值和严格插值算法相比，本文提出的改进的插值算法具有更高的精度.
Abstract:In the marine controlled-source electromagnetic (CSEM) survey, the receivers are usually placed at the seafloor. The resistivity contrast between the seawater and seafloor sediments is large, which can cause difficulties in numerical modeling of CSEM fields at receiver locations. In this paper, we present an improved interpolating method for calculating electric and magnetic fields at the seafloor with a resistivity contrast. This method is applied to the 2.5-dimensional (2.5D) frequency-domain CSEM modeling with towed transmitters and receivers located at the seafloor. Considering the discontinuity of the normal electric fields, we use the normal current electric density for interpolation. We simulate the 2.5D marine CSEM responses by the staggered finite-difference (SFD) method with Fourier transform to the strike direction. The final SFD equations are solved by the direct solver MUMPS (MUltifrontal Massively Parallel Sparse direct Solver). To avoid the source singularities, the secondary-field approach is used and the primary fields excited by the electric dipole source can be calculated quasi-analytically for the one-dimensional (1D) layered background model. We focus on interpolating of electric and magnetic fields in the wavenumber domain to the receiver locations at the seafloor interface between the conductive seawater and resistive seafloor formation. The secondary electric and magnetic fields are used for interpolation instead of the total fields for high numerical accuracy. After performing the inverse Fourier transform to the wavenumbers, the electric and magnetic fields in the space domain are obtained.To check the accuracy of our 2.5D marine CSEM SFD modeling algorithm with the improved receiver interpolating technique, we compare our results with both the 1D analytical results and the adaptive finite element results. The SFD numerical results are approved to be accurate.We also compare the numerical accuracy between our improved interpolation scheme and others, i.e., the conventional linear interpolation and the rigorous interpolation. The proposed interpolation only utilizes the nodes below/above the seafloor interface, and is proved to be much more accurate than the other two interpolating methods used.
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Key words:
- Marine CSEM /
- 2.5D /
- Numerical modeling /
- Interpolation scheme for receiver positions
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图 2
6×6网格剖分情况下系数矩阵K非零元素位置分布
Figure 2.
Illustration of the symmetric structure of the stiffness matrix for a 6×6 staggered grid.
图 4
网格剖分为168×88情况下插值结果对比
Figure 4.
Comparison of interpolating results for the 168×88 staggered-gridding
图 5
网格剖分为168×64情况下插值结果对比
Figure 5.
Comparison of interpolating results for the 168×64 staggered-gridding
图 6
网格剖分为112×88情况下插值结果对比
Figure 6.
Comparison of interpolating results for the 112×88 staggered-gridding
图 7
网格剖分为112×64情况下插值结果对比
Figure 7.
Comparison of interpolating results for the 112×64 staggered-gridding
图 9
海洋二维储层模型情况下三角网格剖分示意图
Figure 9.
Triangular gridding for 2D canonical reservoir model
图 10
网格剖分为168×90情况下插值结果对比
Figure 10.
Comparison of interpolating results for the 168×90 staggered-gridding
图 11
网格剖分为168×66情况下插值结果对比
Figure 11.
Comparison of interpolating results for the 168×66 staggered-gridding
图 12
网格剖分为112×90情况下插值结果对比
Figure 12.
Comparison of interpolating results for the 112×90 staggered-gridding
图 13
网格剖分为112×66情况下插值结果对比
Figure 13.
Comparison of interpolating results for the 112×66 staggered-gridding
表 1
一维模型情况下四种网格剖分对比
Table 1.
Four cases of staggered-gridding of the 1D canonical reservoir model
序号 网格总数 y方向网格
最小长度(m)z方向网格
最小长度(m)1 168×88 100 50 2 168×64 100 100 3 112×88 200 50 4 112×64 200 100 
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表 2
二维模型情况下四种网格剖分对比
Table 2.
Four cases of staggered-gridding of the 2D canonical reservoir model
序号 网格
总数y方向网格
最小长度(m)z方向网格
最小长度(m)1 168×90 100 50 2 168×66 100 100 3 112×90 200 50 4 112×66 200 100
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