海洋可控源电磁法三维时域有限差分数值模拟
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摘要
海洋可控源电磁法在海洋能源勘探、资源勘查、海洋目标探测中占有重要的地位，也是目前国际海洋勘探领域的研究热点。其中，海洋电磁三维时间域数值模拟是一项重要研究内容，也是具有挑战性的科学难题。本论文在国家863计划项目课题的资助下开展了海洋可控源电磁法三维时域有限差分（FDTDFinite-Difference Time-Domain）数值模拟。
论文在前人TEM勘探的FDTD模拟基本理论和关键技术的基础上，对海洋可控源电磁法FDTD开展了系统研究，主要研究内容和成果如下。
1.作为FDTD数值计算的检验标准，针对海洋电磁的特点，论文导出了源在导电空间激发的导电全空间、半空间中电偶极子的阶跃电流响应、截断电流响应、脉冲电流响应以及任意电流信号的时域响应解析式。并研究了导电全空间中阶跃电流响应与介质电阻率、传播时间、传播距离之间的关系，通过电偶极子场各个场分量在空间中的分布图分析，直观显示了海洋电磁响应的特征。
2.论文研究了层状导电空间中电偶极子场的数值计算，并将数值计算结果与全空间和半空间的解析结果进行对比，验证了程序的正确性。
3.论文重点研究了海洋环境下FDTD方法适用的控制方程，时空剖分方法，电磁场迭代差分公式，讨论了各类边界条件、稳定性、数值色散和源电流信号等关键技术，推导了扩散方程的三维Du Fort-Frankel格式，导出了“虚拟介电常数”的表达式。
4.论文研究中采用高斯脉冲作为发射信号，完成了电偶极子在全空间的场分布的计算，模拟结果表明：场在初期为椭球型，后期为球形，与解析结果给出的图样相似；同时，全空间高斯脉冲响应与脉冲响应的解析解的时序对应较好；其次，计算了海洋导电半空间的高斯脉冲响应，并与半空间脉冲响应的解析解做了比较；再者，计算了海洋三分空间的电磁场，在高阻异常和低阻异常层的情况下，电阻率异常界面清晰，结果符合先验知识。
5.针对浅海拖缆式海洋电磁勘探模式，应用FDTD方法分别对海洋油气等高阻储层和金属矿产等低阻储层做了一维构造、二维构造、三维构造的三维建模和数值模拟。通过正演数据的异常分析，说明了FDTD法在MCSEM数值模拟中的有效性。
6.提出了海空联合电磁勘探技术模式，开展了频率域一维和2.5维的数值模拟。同时，分别对海洋油气高阻异常和金属矿等低阻异常进行三维建模和FDTD数值模拟，对正演数据用各种方法进行异常分析，并与一维和2.5维频率域计算结果进行比对分析，说明了海空联合勘探模式的有效性，证明了FDTD法对海空联合勘探的可行性。
本文取得了以下性创新性成果：
1.导出了导电全空间、导电半空间中电偶极子任意电流的时域响应解析式。给出了层状导电空间中电偶极子任意电流时域响应的数值算法。
2.较为成功的将FDTD方法用于海洋可控源电磁勘探中，对其方程的建立、稳定性、数值色散、边界条件、虚拟介电常数、初始时刻等关键参数进行了讨论，使用高斯脉冲作为发射信号直接加到方程中，避免了前人使用解析结果作为初始条件加入迭代中的复杂性和局限性。将数值实验结果与解析结果进行对比，验证其有效性。
3.使用FDTD方法模拟了海洋中电磁波传播及与一维、二维、三维构造不同电阻率异常体相互作用的规律和特征，给出了全空间全时段海洋电磁场的时空分布，对海洋电磁研究和资料解释有一定的参考价值。
4.提出了海空联合电磁勘探技术模式，通过一维、2.5维频率域方法和三维FDTD方法时频域相结合验证了该模式的有效性。
本文的研究成果对海洋电磁勘探、设计、数值模拟及海洋目标探测都有参考价值。对CSEM和MCSEM的研究具有重要的理论意义和指导作用。
Recently, MCSEM (Marine Controlled Source Electromagnetic Method) hasbecome research focus in sea energy exploration, resource exploration, and marinetarget detection. Three-Dimensional Numerical Simulation of time domain is animportant branch of MCSEM and a challenging scientific problem. In this paper, FDTD(Finite-Difference Time-Domain) simulation for mcsem is carried out with the supportof a major national project.
On the basis of predecessors’ study of the basic theory and key technology to theland csem exploration with FDTD method, a comprehensive study of the applicationin MCSEM has been made in this article, including:
1. As a testing standard and basis of the validity of numerical simulation resultsof fdtd, for the characteristics of MCSEM, source inspired in conducting space, paperfirst exports analysis formulas of step current response, truncated current response,pulse current response and time-domain response of arbitrary current type of electricdipole in the whole space, half-space, studies the relationship of the step currentresponse of electric dipole, with the resistivity of the media, propagation time andrange in the entire space. Rather more, draws spatial distribution pattern of each fieldcomponent of electric dipole in Cartesian system.
2. Numerical solution of electric dipole field in the layered conductive space isgiven and compared with analytical solution in whole space and half space to verifythe correctness of the program.
3. The control equation of FDTD method suitable for marine CSEM, time andspace division method, electromagnetic iterative difference formula is studied, anddiscussed the key technology of various boundary conditions, stability, numericaldispersion and current source,3D Du Fort-Frankel derived format of diffusionequation,and expression of virtual dielectric constant are derived. Finally, the program is compiled and numerical experiments are carried out.
4. The validity and reliability of the marine FDTD method was conducted tovalidate and analyze. Field distribution of electric dipole in space is calculated withGauss pulse of transmission signal. The results show that the field is ellipsoid-shapedin the early stages, later is spherical, and the numerical results are similar to thepatterns of analytical ones; Gauss impulse responses in the whole space werecompared with analytical solution of pulse response, Timing is matched very well;Gauss pulse response of marine conductive half space was calculated and comparedwith analytical solution of impulse response in half space, Timing is matched verywell; Electromagnetic field of the ocean three space is calculated, for the situation ofcontaining high resistance layer and low resistance layer. Resistivity anomalyinterface is clear, and the results are consistent with prior knowledge. All these resultsindicated that parameters of FDTD is tunned appropriately, virtual velocity iscontrolled well, that verify the correctness and effectiveness of FDTD method inMCSEM.
5. According to the electromagnetic exploration model of towed MCSEM inshallow sea,3D numerical simulations have been done with the FDTD method for themarine high resistance body as oil and gas and other low resistivity reservoirs as metalmineral resources of one-dimensional, two-dimensional and three-dimensionalstructure. Anomaly analysis of forward data using a variety of methods, to illustratethe effectiveness of the FDTD method in the numerical simulation of MCSEM..
6. As for the electromagnetic exploration model of combination of air and sea,firstly, frequency domain numerical simulation of one dimensional and2.5dimensional is done to verify the effectiveness of the model. Then,3D modeling withFDTD is carried out respectively on high resistivity anomaly of the marine oil and gas,and low resistance anomaly of and metal ore. Last, abnormal analysis are done toforward data of3d modeling using various methods, and the results were comparedwith that of one-dimensional2.5dimensional frequency domain calculation. Twoconclusions can be maken, first of all, the joint exploration model of sea and air iseffective, and in addition, the numerical simulation method of FDTD is effective forthe joint exploration of sea and air.
This paper has obtained the following innovative results:
1. Export analytical formula of time-domain response of arbitrary electric currentof electric dipole in the whole conducting space and in a half space of conducting.Numerical algorithm of time-domain response of arbitrary electric current of electric dipole in layered conductive space is given.
2. The FDTD method is first applied in marine controlled source electromagneticexploration successfully. The key parameters such as equation, stability, numericaldispersion, boundary conditions, virtual dielectric constant, and the initial time arediscussed; much numerical experiments have been done, and the experimental resultshave a good agreement with analytical results, and verify its effectiveness. Fill a gapin the time domain numerical simulation of MCSEM. The paper use the Gauss pulseas transmission signal, and add it to the iterative equation directly, avoidingcomplexity and limitation of the previous method about source, in which analyticalresults are added to electromagnetic fields iterations as initial conditions. Unlike thelinear current signal, Gauss pulse has more important research value and practicalvalue. First of all, it is a pulse, with broadband characteristics; secondly, the risingedge of it can be used to simulate the step current, and falling edge of it can be used tosimulate the truncation current. While strong numerical dispersion can not be causedusing Gauss pulse rather than using step current and truncated current, which willgenerate high-frequency oscillations at early and late time; also, Low frequencyspectrum of the Gauss pulse is rich and easy to be controled and adjusted. Therefore,Gauss pulse is very suitable to be used as signal source of marine electromagneticnumerical simulation.
3. Using FDTD method, simulate the propagation of electromagnetic waves andthe interaction with different resistivity anomaly of one-dimensional, two-dimensional,three-dimensional structure in the ocean. Space-time distribution of the whole spacefull time marine electromagnetic field is given, which has a certain reference value forthe marine electromagnetic research and data interpretation.
4. One-dimensional,2.5dimensional frequency domain methods are combinedwith3D FDTD method to verify the validity of the air-sea electromagneticprospecting model.
The research results of this paper have reference value to the marineelectromagnetic exploration, design, numerical simulation and detection of marinetargets. More over, they have the theory significance and the important guiding role ofCSEM and MCSEM.
论文在前人TEM勘探的FDTD模拟基本理论和关键技术的基础上，对海洋可控源电磁法FDTD开展了系统研究，主要研究内容和成果如下。
1.作为FDTD数值计算的检验标准，针对海洋电磁的特点，论文导出了源在导电空间激发的导电全空间、半空间中电偶极子的阶跃电流响应、截断电流响应、脉冲电流响应以及任意电流信号的时域响应解析式。并研究了导电全空间中阶跃电流响应与介质电阻率、传播时间、传播距离之间的关系，通过电偶极子场各个场分量在空间中的分布图分析，直观显示了海洋电磁响应的特征。
2.论文研究了层状导电空间中电偶极子场的数值计算，并将数值计算结果与全空间和半空间的解析结果进行对比，验证了程序的正确性。
3.论文重点研究了海洋环境下FDTD方法适用的控制方程，时空剖分方法，电磁场迭代差分公式，讨论了各类边界条件、稳定性、数值色散和源电流信号等关键技术，推导了扩散方程的三维Du Fort-Frankel格式，导出了“虚拟介电常数”的表达式。
4.论文研究中采用高斯脉冲作为发射信号，完成了电偶极子在全空间的场分布的计算，模拟结果表明：场在初期为椭球型，后期为球形，与解析结果给出的图样相似；同时，全空间高斯脉冲响应与脉冲响应的解析解的时序对应较好；其次，计算了海洋导电半空间的高斯脉冲响应，并与半空间脉冲响应的解析解做了比较；再者，计算了海洋三分空间的电磁场，在高阻异常和低阻异常层的情况下，电阻率异常界面清晰，结果符合先验知识。
5.针对浅海拖缆式海洋电磁勘探模式，应用FDTD方法分别对海洋油气等高阻储层和金属矿产等低阻储层做了一维构造、二维构造、三维构造的三维建模和数值模拟。通过正演数据的异常分析，说明了FDTD法在MCSEM数值模拟中的有效性。
6.提出了海空联合电磁勘探技术模式，开展了频率域一维和2.5维的数值模拟。同时，分别对海洋油气高阻异常和金属矿等低阻异常进行三维建模和FDTD数值模拟，对正演数据用各种方法进行异常分析，并与一维和2.5维频率域计算结果进行比对分析，说明了海空联合勘探模式的有效性，证明了FDTD法对海空联合勘探的可行性。
本文取得了以下性创新性成果：
1.导出了导电全空间、导电半空间中电偶极子任意电流的时域响应解析式。给出了层状导电空间中电偶极子任意电流时域响应的数值算法。
2.较为成功的将FDTD方法用于海洋可控源电磁勘探中，对其方程的建立、稳定性、数值色散、边界条件、虚拟介电常数、初始时刻等关键参数进行了讨论，使用高斯脉冲作为发射信号直接加到方程中，避免了前人使用解析结果作为初始条件加入迭代中的复杂性和局限性。将数值实验结果与解析结果进行对比，验证其有效性。
3.使用FDTD方法模拟了海洋中电磁波传播及与一维、二维、三维构造不同电阻率异常体相互作用的规律和特征，给出了全空间全时段海洋电磁场的时空分布，对海洋电磁研究和资料解释有一定的参考价值。
4.提出了海空联合电磁勘探技术模式，通过一维、2.5维频率域方法和三维FDTD方法时频域相结合验证了该模式的有效性。
本文的研究成果对海洋电磁勘探、设计、数值模拟及海洋目标探测都有参考价值。对CSEM和MCSEM的研究具有重要的理论意义和指导作用。
Recently, MCSEM (Marine Controlled Source Electromagnetic Method) hasbecome research focus in sea energy exploration, resource exploration, and marinetarget detection. Three-Dimensional Numerical Simulation of time domain is animportant branch of MCSEM and a challenging scientific problem. In this paper, FDTD(Finite-Difference Time-Domain) simulation for mcsem is carried out with the supportof a major national project.
On the basis of predecessors’ study of the basic theory and key technology to theland csem exploration with FDTD method, a comprehensive study of the applicationin MCSEM has been made in this article, including:
1. As a testing standard and basis of the validity of numerical simulation resultsof fdtd, for the characteristics of MCSEM, source inspired in conducting space, paperfirst exports analysis formulas of step current response, truncated current response,pulse current response and time-domain response of arbitrary current type of electricdipole in the whole space, half-space, studies the relationship of the step currentresponse of electric dipole, with the resistivity of the media, propagation time andrange in the entire space. Rather more, draws spatial distribution pattern of each fieldcomponent of electric dipole in Cartesian system.
2. Numerical solution of electric dipole field in the layered conductive space isgiven and compared with analytical solution in whole space and half space to verifythe correctness of the program.
3. The control equation of FDTD method suitable for marine CSEM, time andspace division method, electromagnetic iterative difference formula is studied, anddiscussed the key technology of various boundary conditions, stability, numericaldispersion and current source,3D Du Fort-Frankel derived format of diffusionequation,and expression of virtual dielectric constant are derived. Finally, the program is compiled and numerical experiments are carried out.
4. The validity and reliability of the marine FDTD method was conducted tovalidate and analyze. Field distribution of electric dipole in space is calculated withGauss pulse of transmission signal. The results show that the field is ellipsoid-shapedin the early stages, later is spherical, and the numerical results are similar to thepatterns of analytical ones; Gauss impulse responses in the whole space werecompared with analytical solution of pulse response, Timing is matched very well;Gauss pulse response of marine conductive half space was calculated and comparedwith analytical solution of impulse response in half space, Timing is matched verywell; Electromagnetic field of the ocean three space is calculated, for the situation ofcontaining high resistance layer and low resistance layer. Resistivity anomalyinterface is clear, and the results are consistent with prior knowledge. All these resultsindicated that parameters of FDTD is tunned appropriately, virtual velocity iscontrolled well, that verify the correctness and effectiveness of FDTD method inMCSEM.
5. According to the electromagnetic exploration model of towed MCSEM inshallow sea,3D numerical simulations have been done with the FDTD method for themarine high resistance body as oil and gas and other low resistivity reservoirs as metalmineral resources of one-dimensional, two-dimensional and three-dimensionalstructure. Anomaly analysis of forward data using a variety of methods, to illustratethe effectiveness of the FDTD method in the numerical simulation of MCSEM..
6. As for the electromagnetic exploration model of combination of air and sea,firstly, frequency domain numerical simulation of one dimensional and2.5dimensional is done to verify the effectiveness of the model. Then,3D modeling withFDTD is carried out respectively on high resistivity anomaly of the marine oil and gas,and low resistance anomaly of and metal ore. Last, abnormal analysis are done toforward data of3d modeling using various methods, and the results were comparedwith that of one-dimensional2.5dimensional frequency domain calculation. Twoconclusions can be maken, first of all, the joint exploration model of sea and air iseffective, and in addition, the numerical simulation method of FDTD is effective forthe joint exploration of sea and air.
This paper has obtained the following innovative results:
1. Export analytical formula of time-domain response of arbitrary electric currentof electric dipole in the whole conducting space and in a half space of conducting.Numerical algorithm of time-domain response of arbitrary electric current of electric dipole in layered conductive space is given.
2. The FDTD method is first applied in marine controlled source electromagneticexploration successfully. The key parameters such as equation, stability, numericaldispersion, boundary conditions, virtual dielectric constant, and the initial time arediscussed; much numerical experiments have been done, and the experimental resultshave a good agreement with analytical results, and verify its effectiveness. Fill a gapin the time domain numerical simulation of MCSEM. The paper use the Gauss pulseas transmission signal, and add it to the iterative equation directly, avoidingcomplexity and limitation of the previous method about source, in which analyticalresults are added to electromagnetic fields iterations as initial conditions. Unlike thelinear current signal, Gauss pulse has more important research value and practicalvalue. First of all, it is a pulse, with broadband characteristics; secondly, the risingedge of it can be used to simulate the step current, and falling edge of it can be used tosimulate the truncation current. While strong numerical dispersion can not be causedusing Gauss pulse rather than using step current and truncated current, which willgenerate high-frequency oscillations at early and late time; also, Low frequencyspectrum of the Gauss pulse is rich and easy to be controled and adjusted. Therefore,Gauss pulse is very suitable to be used as signal source of marine electromagneticnumerical simulation.
3. Using FDTD method, simulate the propagation of electromagnetic waves andthe interaction with different resistivity anomaly of one-dimensional, two-dimensional,three-dimensional structure in the ocean. Space-time distribution of the whole spacefull time marine electromagnetic field is given, which has a certain reference value forthe marine electromagnetic research and data interpretation.
4. One-dimensional,2.5dimensional frequency domain methods are combinedwith3D FDTD method to verify the validity of the air-sea electromagneticprospecting model.
The research results of this paper have reference value to the marineelectromagnetic exploration, design, numerical simulation and detection of marinetargets. More over, they have the theory significance and the important guiding role ofCSEM and MCSEM.
引文
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