基于域分解的CSAMT三维正反演研究

发布时间：2018-05-31 11:58

本文选题：CSAMT + 域分解　；参考：《中国地质大学(北京)》2017年硕士论文

【摘要】：可控源音频大地电磁法(CSAMT)是一种人为建立场源并观测电磁反射信号,同时能够加强抗干扰、增强信噪比的电磁勘探方法。通过不同频率对地下不同深度信息的灵敏度不同,且具有较好的垂向分辨能力,因此该方法被广泛应用于矿产资源、水文地质和油气资源等领域,还在地质普查、地热勘查和环境工程等领域上发挥了重要作用。CSAMT在数值模拟与反演中,有限元法在计算精度上较高,但是有限元法正演求解过程中对于边界条件应用性较高;积分方程法仅对异常体剖分,但在计算并矢格林函数积分上效率低下;有限差分法计算效率较高,但对于网格的剖分要求严格,并且还要进行散度校正。随着社会的发展,计算效率和计算精度深受重视,因此要基于各种数值模拟方法的优缺点,本文将研究区域剖分为由积分方程法计算的边界区域和利用有限元法计算的内部区域。利用整体积分方程法和局部微分方程法的联用方法(GILD)来进行CSAMT三维正演,由于积分方程法进行三维正演无需边界条件的优点,让该方法应用在边界区域,继而为有限元法提供边界条件;由于有限元法在刚度矩阵和荷载矩阵合成高效的特点替换内部区域应用积分方程法的并矢格林函数积分的大量计算,这样减少了正演计算时间,降低了硬件内存需求,同时提高了计算精度。利用内部区域各自互不关联的独立性大大提高了 GILD算法的可并行性,本文采用OpenMP并行加速,在计算并矢格林函数积分和刚度矩阵大幅度提高了三维正演计算效率。三维反演采用传统的阻尼最小二乘法,针对观测点范围内区域进行三维反演,在反演过程中不断改进阻尼因子,最终在同时满足拟合差和模型的光滑度上,达到较好的反演结果;反演低阻体的效果比反演高阻体的要好。本文通过对同一观测数据,进行不同大小区域进行反演,结果表明,反演区域的大小对反演本身毫无影响,剖分的越多,仅在计算系数矩阵的耗时上越长。
[Abstract]:The controllable source audio magnetotelluric method (CSAMT) is a kind of electromagnetic exploration method, which can establish the field source and observe the electromagnetic reflection signal, at the same time, it can strengthen the anti-interference and enhance the signal-to-noise ratio (SNR). The sensitivity of different frequencies to different depth of underground information is different, and the method has good vertical resolution. Therefore, this method is widely used in mineral resources, hydrogeology and oil and gas resources, and is also in geological survey. CSAMT has played an important role in the fields of geothermal exploration and environmental engineering. In the numerical simulation and inversion, the finite element method has a higher accuracy, but the application of the finite element method to the boundary conditions is higher in the forward modeling process. The integral equation method is not efficient in the computation of dyadic Green's function, but the integral equation method is efficient only for abnormal bodies, but the finite difference method is more efficient, but it is strict for mesh generation, and the divergence correction should be carried out. With the development of society, the efficiency and precision of calculation are paid more attention to, so we should base on the merits and demerits of various numerical simulation methods. In this paper, the study area is divided into the boundary region calculated by the integral equation method and the internal region calculated by the finite element method. The global integral equation method and the local differential equation method are used to carry out the three-dimensional forward modeling of CSAMT. Because the integral equation method has the advantage of no boundary condition, the method is applied in the boundary region. Then the boundary conditions are provided for the finite element method, because the finite element method is efficient in the combination of stiffness matrix and load matrix, it replaces a large number of calculations of the dyadic Green's function integral by the integral equation method in the internal region, thus reducing the forward calculation time. The requirement of hardware memory is reduced and the calculation precision is improved. The parallelism of the GILD algorithm is greatly improved by using the independence of the internal regions. In this paper, the parallelism of the GILD algorithm is improved by using the OpenMP parallel acceleration, and the efficiency of 3D forward modeling is greatly improved in the computation of dyadic Green's function integral and stiffness matrix. The traditional damped least square method is used in the 3D inversion, and the damping factor is improved continuously in the inversion process for the region within the range of the observation point. Finally, the fitting error and the smoothness of the model are satisfied at the same time. The result of inversion is better than that of high resistivity. In this paper, the inversion of the same observed data is carried out in different regions. The results show that the size of the inversion region has no effect on the inversion itself. The more the division is, the longer the computation time of the coefficient matrix is.
【学位授予单位】：中国地质大学(北京)
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P631.325

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