基于分形先验信息的非线性反演

Nonlinear inversion based on fractal priori information

基于分形先验信息的非线性反演方法能综合利用测井数据和地震信息,在贝叶斯框架下,通过分形高斯噪音算法得到基于分形理论的先验信息,然后根据地震资料构建似然函数,最终利用基于快速模拟退火算法(Very Fast Simulated Annealing,VFSA)改进的粒子群优化(Particle Swarm Optimization,PSO)算法(VFSA-PSO)实现后验概率密度的抽样。与确定性反演结果相比,该方法能够有效地融合测井资料中的高频信息,提高反演结果的分辨率,并且目标函数的建立融合了确定性反演中的低频约束,从而得到宽频带的反演结果。数值模拟试验表明:基于分形先验的非线性反演结果与理论模型吻合较好,实际资料的应用效果也证明了该反演方法的有效性。

Nonlinear inversion based on fractal priori information is formulated in a Bayesian framework,combining logging data with seismic information.Firstly,we can get the priori information through fractal Gaussian noise algorithm.Then,based on the seismic information,we can construct the likelihood function.Finally we apply VFSA-PSO optimization algorithm to obtain an exhaustive characterization of the posteriori probability density.Compared to deterministic inversion,the method we proposed can integrate the high frequency information of well logging and have a higher resolution.And the establishment of the obj ective function adds constraints of low frequency information using the experience of deterministic inversion for refer-ence,so the inversion results contain the broadband information.According to the numerical calculations,we can conclude that the nonlinear inversion results based on fractal priori information match the model well.The application of real data also proves the effectiveness of the proposed nonlinear inversion method.