地震波形约束的蒙特卡洛—马尔科夫链随机反演方法

以地质统计学为基础、以测井资料为条件数据的地震随机反演方法的分辨率高于常规确定性反演，因此迅速得到广泛应用，但是提高计算效率以及消除随机性一直是难点。为此，提出了基于地震波形约束的蒙特卡洛—马尔科夫链（MCMC）随机反演方法。充分利用观测地震数据和待反演参数之间的地球物理映射关系，应用相关系数，根据已知的地震波形之间的相似性特征指导井数据进行伪普通克里金插值模拟，建立具有地震波形指示的初始模型；在此基础上，进一步在贝叶斯框架下构建观测地震数据和测井数据协同约束的后验概率密度分布，结合Metropolis-Hastings采样算法多次随机模拟具有地震波形指示的初始模型参数，利用后验均值作为模型参数的最优解。该方法有效地提高了反演稳定性和横向连续性，降低了随机性，有效地弱化了地震噪声对反演结果的影响，并且极大地加快了马尔科夫链的收敛速度，有效地提高了运算效率和估算精度。模型试算和实际资料反演效果表明，基于地震波形约束的MCMC随机反演方法具有较好的抗噪性，有效提高了反演精度，对识别调谐尺度内薄互储层具有一定优势，在提高纵向分辨率的同时也提高了横向分辨率。

Monte Carlo-Markov Chain stochastic inversion constrained by seismic waveform

The resolution of seismic stochastic inversion based on geostatistics and logging data is higher than that of conventional deterministic inversion, so the former is quickly and widely used, but it is difficult to improve calculation efficiency and eliminate randomness. This paper proposes a Monte Carlo-Markov Chain (MCMC) stochastic inversion method based on the constraint of seismic waveform. By making full use of the geophysical mapping relationship between seismic data and parameters to be inversed, and a correlation coefficient to guide pseudo ordinary Kriging interpolation to well data according to the similarity of known seismic waveforms, an initial model is established; then the posterior probability density distribution is constructed under the constraints of seismic data and logging data on the Bayesian framework, and the initial model which can indicate seismic waveforms is randomly simulated multiple times by using the Metropolis-Hastings sampling algorithm. The posterior mean value is the optimal solution to the model parameters. This method effectively improves inversion stability and lateral continuity, reduces randomness, effectively weakens the impact of seismic noises on inversion results, and greatly accelerates the convergence of the Markov chain, which effectively improves computing efficiency and estimation accuracy. Applications on model and real data have proved the MCMC stochastic inversion method constrained by seismic waveforms has good noise resistance, can effectively improve inversion accuracy, and are advantageous in identifying thin reservoirs within a tuning scale. It improves both vertical resolution and ho-rizontal resolution.