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为了提高地震道反演结果的稳定性，减少反演工作的计算量，降低所需计算机内存资源，本文在经典共轭梯度算法的基础上，提出了可适应更复杂情形的地震道反演问题的广义共轭梯度算法。核算法精度高、运算速度快、抗病态能力强。此外，还针对地震道反演这一具体问题，对灵敏度矩阵进行深入剖析，推导出了不再需要合成灵敏度矩阵的递推算法，从而大大节约了计算机内存资源。由于新算法可将灵敏度矩阵运算分解成褶积和相关运算，使整个递推过程完全由向量运算来完成，因而更进一步地提高了递推过程的运算速度。
In order to improve the stability of seismic trace inversion results, reduce the computational complexity and reduce the required computer memory resources, this paper presents the seismic trace inversion problem that can be adapted to more complicated cases based on the classical conjugate gradient algorithm Generalized Conjugate Gradient Algorithm. High precision nuclear algorithm, computing speed, ability to resist disease. In addition, aiming at the specific problem of seismic trace inversion, the sensitivity matrix is further analyzed, and the recursive algorithm which no longer needs the synthesis sensitivity matrix is deduced, which greatly saves computer memory resources. Because the new algorithm decomposes the sensitivity matrix operations into convolution and correlation operations, the entire recursion process is completely performed by vector operations, which further improves the operation speed of the recursion process.