中文摘要：

阐述了矩阵多分辨分析理论中的标准形式与非标准形式，并以Hilbert算子为例，说明了算子多分辨表示的压缩效果，为小波域偏移算法奠定了理论基础．从三维雷达波动方程出发，利用爆炸反射原理和浮动坐标变换，推导出三维探地雷达波动方程差分格式，并通过方程分裂算法及小波多分辨算法，在小波域求解波场外推矩阵，进而得到探地雷达小波域三维波动方程偏移算法，在此基础上，开发了探地雷达小波域偏移处理程序，并把该程序应用于三个球体空洞的3-D正演结果及实际的雷达数据中，通过对比偏移处理前后的雷达资料，得知该三维偏移算法能使3-D正演剖面中的反射波归位、绕射波收敛，极大地提高了雷达剖面的分辨率，有利于探地雷达资料的地质解释．

英文摘要：

This paper elaborated on the standard and nonstandard forms of matrix multi-resolution analysis theory in detail, and taking Hilbert operator as an example, explained the compression result of operator with multi-resolution form. It laid a good theoretical foundation for migration algorithm of wavelets domain. Then, setting out from the three-dimension radar wave equation, and making use of the bursting reflection theory and floating coordinate transform, we have deduced the finite difference format of GPR three-dimension wave equation. Through equation splitting and multi-resolution wavelets theory, and solving the extrapolate matrix of wave field in the wavelets domain, we have also got the migration algorithm of GPR three-dimension wave equation in wavelets domain. Based on this, the authors developed the migration program of GPR three- dimension wave equation, and applied this program to three-dimensional forward modeling result of three spheric caverns and practical GPR data. Through comparing the radar data before and after the migration processing, it is known that this three-dimension migration algorithm could make the reflection wave return to original position, and make the diffraction wave converge in the three-dimension sections. The lateral resolution of radar sections could be highly enhanced, and the migration algorithm could make the radar three-dimension detection more reliable and precise, which is propitious to the geology explanation of GPR data.