Study On Three-dimensional Inversion Algorithm For CSAMT Data

Controlled Source Audio Frequency Magnetotelluric method (CSAMT) is an artificial source electromagnetic method to improve the weak signal of natural sources in audio frequency range and is widely used in oil and gas exploration because of its high signal-to noise ratio、high efficiency and low cost. But with the deepening of the oil and gas exploration, it is need to determine the reservoir parameters and spatial distribution more accurately to achieve the goal of the reservoir description. Then the controlled source electromagnetic data interpretation method is also put forward higher requirements. One dimensional or two-dimensional interpretation can also get better results when the condition of the stratum structure is relatively simple, but in the case of complex formation structure, the resistivity distribution of oil and gas trap structure would be shown a strong three-dimensional structure characteristics. It is impossible to reconstruct a three-dimensional resistivity of reservoir space distribution with a two-dimensional interpretation method based on a finite number of sounding point electromagnetic data on several online measurement, so the urgent task is to research a new three dimensional controlled source electromagnetic data interpretation method to adapt to the use of three dimensional volume to reconstruct the formation of the spatial distribution of the three dimensional resistivity and to reach the purpose of the fine study of underground oil and gas reservoir properties.With the unremitting efforts of geophysical workers, three dimensional inversion of MT technology is mature and has been satisfied the small or medium scale three dimensional data processing and interpretation. Forward of CSAMT is became complicated because of the launch source. The requirement of hardware is also became higher because of the large amount of observation data processing and higher precision interpretation. At the same time, the effect of 3D CSAMT data interpretation will directly affect the result of artificial source electromagnetic exploration and application level. The robust artificial source electromagnetic analysis method of 3D data can be effectively and accurately reconstruct 3D spatial distribution of the resistivity of formation, so the 3D inversion of CSAMT has been the research emphasis and difficulty of electromagnetic method in the world. With the improvement of the calculation method and ability of hardware, it is possible to make the 3D forward and inversion of controlled source electromagnetic method be practical.The main of this paper is to realize the 3D forward and inversion of CSAMT based on 3D forward and inversion of MT. the MAXWELL’equations were decomposed into background fields and anomaly fields in the 3D forward algorithm. The background fields can be calculated by analytical and numerical solution, and the anomalous fields can be realized by the finite difference algorithm, the 3D inversion algorithm in frequency domain can be calculated with the nonlinear conjugate gradient algorithm.Firstly, the total fields were decomposed based on MAXWELL’equations in frequency domain, and we got the background field equations and anomalous field equations respectively. Under the horizontal electric dipole source excitation, the potential function was introduced to calculate the electromagnetic response of homogeneous half space and layer space. To improve the calculation efficiency of finite difference algorithm, INK field integral and FOKKER integral were used to get the analytical solution of the electromagnetic response in surface and underground of homogeneous half space, then the calculation of air layer of the homogeneous half space and layer space were realized by numerical filtering algorithm calculating the Hankel transform to get the frequency response. In the paper, the background fields were firstly completed for the FD algorithm, then the difference format was discussed according to the characteristics of the FD algorithm. The secondary field expression of MAXWELL’ equations were dispersed based the difference format to form a large linear equations. Solving the large linear equations was the core issue of finite difference algorithm. To solve the problem of the large sparse matrix storage and computing, free matrix method was proposed to solve the linear system equations because each line of the matrix just contained thirteen nonzero elements. Considering the stability and convergence of the algorithm, the Krylov subspace iteration algorithm was studied based on preliminary conditions, that is, the minimum residual error iterative algorithm (QMR), which was mainly to solve the minimum value of the residual norm to eliminate the possibility of the oscillation in the iterative process and form a smooth monotone convergence of the iterative process. The model of CSAMT was subdivided with grids and then the air at the top of the boundary, the bottom boundary and the four sides of the border were produced. When the model space is big enough, the tangential component of electric fields on the border could be set to zero according to the Dirichlet conditions. But the transmission of electromagnetic wave was propagated in infinite space, it had to truncate the infinite space combined with the geophysical model in the numerical simulation analysis. If the truncated boundary was far from the source or abnormal body, the Dirichlet conditions were reasonable and could satisfy the requirement of numerical simulation. But it was necessary to consider the other boundary conditions for the stability of the numerical calculation. The perfectly matched layer boundary condition (PML) was analyzed in the next chapter. Then the message passing interface (MPI) was used to improve the calculated efficiency. In the last, homogeneous half space model、 layer space and 3D abnormal body model in homogeneous half space were designed respectively to verify the algorithm. Compared with the integral equation method, it was proved to be correct and stability.Nonlinear conjugate gradient (NLCG) is the most effective inversion method in 3D inversion method, which has been successfully applied in 3D inversion of MT. The core of NLCG is to calculate the gradient, in which the calculation of Jacobi matrix is the core, the model was update through the product of Jacobi and its transpose with the vector respectively. In fact, it was only needed to complete two forward and product of matrix and vector in four times to calculate the gradient. It was based on the impedance of electric and magnetic fields. It showed that the method was effective through the theoretical model inversion and the actual measured data calculation. But the inversion is slowly in the hardware and the influence of different sources、initial model and the multi-component joint inversion are still in the study.