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中国物理学会期刊

用改进的传输线算法计算水平层状横向同性地层中海洋可控源电磁响应

CSTR: 32037.14.aps.62.224101

Simulation of marine controlled-source electromagnetic response in horizontally layered transversely isotropic formation by using improved transmission line method

CSTR: 32037.14.aps.62.224101
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  • 利用二维Fourier变换与电磁场分解技术将层状横向同性地层中Maxwell方程转化成两个独立的关于横磁(TM)波和横电(TE)波的传输线方程; 借助传输线理论与叠加原理, 仅利用电流源传输线Green函数得到TM波和TE波的解, 改进传输线算法, 建立横向同性地层中频率-波数域电流源电场和磁场并矢Green函数的新算法与新的解析表达式, 提高海洋可控源电磁响应数值模拟效率. 在此基础上, 利用传输线Green函数的基本解以及边界条件, 推导出广义反射系数与振幅递推公式, 得到各个地层中传输线Green函数的解析解; 然后利用Fourier逆变换与Bessel公式将海洋可控源电磁响应表示为Sommerfeld形式的积分, 借助三次样条插值与Lommel积分公式快速计算其数值解. 通过数值模拟结果考察工作频率以及地层各向异性电阻率变化等对海洋电磁响应的影响.

     

    In this paper, the two-dimensional Fourier transform and wave decomposition technique are used to transform Maxwell’s equation in transversely isotropic (TI) formation into two independent sets of transmission line equations about transverse magnetic (TM) wave and transverse electric (TE) wave. According to both transmission line theory and superposition principle, an improved transmission line method is advanced to simplify the computational process of TM wave and TE wave only by introducing the transmission line Green’s functions of the current source. Thus, the new algorithm and the new expressions of current source electromagnetic (EM) dyadic Green’s functions in frequency-wavenumber domain are established for realizing the efficient simulation of marine controlled-source electromagnetic (MCSEM) responses in the horizontally layered TI formation. On this base, the basic solutions of the transmission line Green’s functions and EM boundary conditions are utilized to derive the recursive formula of the generalized reflections and amplitudes of the TE and TM waves, and the analytic solutions of the Green’s functions in each bed are obtained. Then, by using Fourier inverse transform and Bessel integral formula, the MCSEM responses in frequency-spatial domain are expressed in the Sommerfeld integral form. A combination of the cubic spline interpolation with the Lommel integral is used to efficiently compute the MCSEM responses. Finally, we validate the modeling algorithm and investigate the influences of changes in operation frequency and anisotropic coefficient on the MCSEM response in the TI formation.

     

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