The Cross-Hole Tomography Algorithm Study Based On The Bending Ray

Ground penetrating radar is a kind of efficiently technique for shallow layer geophysical explore. It sends high frequency electromagnetism impulse wave and makes use of the difference of the electrical property of underground medium to analyze and deduce the structure and character of the medium, based on kinematics and dynamics character of the wave, such as swing, wave form and frequency. GPR is applying on many fields such as engineering, hydrology and environment etc, and now it's application scale is enlarging . The detection scale of the GPR is limited because of effect of tectum and belt of weathering. Borehole antennas are value tools to probe the subsurface when the topmost soil show high conductivity and prevent penetration of EM energy from the surface ,or when the target is beyond the range at a given frequency. It has high resolution and large detection scale. It has two working modes: one is single-hole reflection mode, another is cross - hole tomography mode.This text mainly introduced the basic principle and the calculation method of cross -hole tomography mode (engineering CT technique), including the method of get the modulus matrix by contrast the point of radial and gridding, the course of synthesize time matrix with the slowness matrix given, the principle of inversion calculation with LSQR calculation method, and the course of conversion the form of the matrix and making picture.In this paper we study forward methods and inversion method from the principle of cross-hole tomography.This paper discusses the principles and implementation process of the linear traveltime interpolation method and the shortest paths raytracing method in the forward methods of tomography. The linear traveltime interpolation method is ray tracing method based on the traveltime by Asakawa. The method is based on the grid unit model, and applied to various non-uniform velocity mediator. It can track many kinds of raytracing include directive wave, refracted wave and transmission wave. It can be conclused that the method could calculate the traveltime and raytracing fast and exactily and it is more responsive to the complex conditions according to the calculation to the assumpted physical model. So it is a promising ray-tracing method.The shortest path ray-tracing method is implemmentated based on Fermat principle and the shortest path algorithm in network theory. The method originated in network theory, and it was applicated in seismic ray-tracing by Nakanishi and Yamaguchi firstly. Later, Moser and Klimes and Kvasnicha carried out a detailed study to the shortest path method. The shortest path method has been developed more mature, and the calculation procedure of basic algorithm is relatively fixed ralied to the continuous research of the scientific and technical personnel.In the inversion method of tomography, the paper mainly introduces Aigebraic Reconstruction Technique, Least Squares QR-factorization and Simultanous Iterative Reconstruction Techniques, derives the iterative formula, program on matlab and examine the algorithm using model.