用L₁模线性规划算法恢复地下波阻抗

Subsurface impedance recovering by L₁-norm linear programming algorithm

1. 大庆石油学院,安达 151400;2. 中国新星石油公司石油物探研究所,南京 210014

Daqing Petroleum Institute, Anda 151400

首先详细地阐述了用L₁模线性规划算法恢复地下波阻抗的数学原理, 指出了在层状地球模型假定下限制波阻抗具有极小结构的形式, 与数学上用L₁模线性规划算法计算地层反射系数序列是相一致的。然后用理论模型、测井记录以及野外地震资料进行了反演计算, 证实了该算法是行之有效的。最后对如何引进约束条件进行了简单的讨论, 指出它对于反演解的正确性和可靠性是至关重要的, 对于减少解的非唯一性也是必不可少的。

We expound the mathematical principle of recovering subsurface impedances by L1-norm linear programming algorithm. It is pointed out that under the assumption of layered Earth models, restricting impedances to be of minimum structure form is consistent with computing stratigraphic reflec-tivity series by the L1-norm linear programming algorithm in mathematics. Inversion computations of theoretical models, well logs and field seismic data prove the effectiveness of this algorithm. Finally we simply discuss how to introduce constraint conditions, and point out that this is very important for correctness and reliability of inversion solutions and indispensable for reducing the ambiguity of solutions.