单程波算子积分解的象征表示

单程波波场延拓算子在地震偏移成像中有重要应用.单程波波场延拓算子按其实现方式可分为Kirchhoff积分、空间隐式有限差分和Fourier变换方法，他们代表了算子的不同表示方法，当截断使用这些方法时会得到不同的精度.象征表示对这些方法的导出和精度分析有重要作用.算子作用于正弦波函数所得函数称为算子的象征.算子的象征是褶积算子Fourier变换的推广.Fourier变换方法则直接用象征函数的可分表示求出.空间隐式有限差分则可以用象征函数的Padè近似或部分分式导出.单程波算子在深度域的积分称为单程波算子积分解.本文推导了单程波算子积分解的象征表达式，给出了算子象征的代数运算的头几阶表达式，这些表达式还未在前人文献中发现.Kirchhoff积分所需格林函数可以通过象征函数和鞍点法导出.基于积分解的象征表达式给出了非对称走时公式，对改善Kirchhoff积分的聚焦性能有重要意义.

Symbol description to integral solution of one-way wave operator

Extrapolation operator of one-way wave field has great application in seismic migration imaging. According to their implement, these operators can be classified into three kinds: Kirchhoff integral method, implicit definite difference in space domain and Fourier transform method. They represent different operator expression methods. Different precisions will be got while using the operators in these methods in different truncate order. Represent in symbol in the method of derivation and accuracy analysis. Symbol of operator is the function of operator acting on sine function. Symbol of operator is the extension of convolution operator's Fourier transform. Fourier transform method can be directly derived from symbol function's separable approximation. Implicit space difference can be solved by padè approximation or part fraction. Integral of one way wave operator in depth domain. The symbol solution of one-way wave integral is deduced, the first several order operator expressions of symbol's algebra operation are given. These expressions haven't been found in any previous reference. Green function that adapts to Kirchhoff integral method could be derived from symbol function and saddle point method. The symbolic expression, which based on integral solution give the equation of asymmetric traveltime, have great significance on focusing capability of Kirchhoff integral method.