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Application of Reversible Jump Markov Chain Monte Carlo Algorithms to Elastic and Petrophysical Amplitude-Versus-Angle Inversions

机译:可逆跳跃马尔可夫链Monte Carlo算法在弹性和岩石物理幅度与角度逆转中的应用

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We infer the elastic and petrophysical properties from pre-stack seismic data through a transdimensional Bayesian inversion. In this approach the number of model parameters (i.e. the number of layers) is treated as an unknown, and a reversible jump Markov Chain Monte Carlo (rjMCMC) algorithm is used to sample the variable-dimension model space. This inversion scheme provides a parsimonious solution, and reliably quantifies the uncertainties affecting the estimated model parameters. Parallel tempering, which employs a sequence of interacting Markov chains in which the likelihood function is successively relaxed, is used to improve the efficiency of the probabilistic sampling. In addition, the delayed rejection updating scheme is employed to speed up the convergence of the rjMCMC algorithm to the stationary regime. Both elastic and petrophysical inversions invert the amplitude versus angle responses and employ a convolutional forward modelling based on the exact Zoeppritz equations. First, synthetic tests are used to assess the reliability of the implemented rjMCMC algorithms, then their applicability is demonstrated by inverting field seismic data acquired onshore. In this case the inversion was aimed at inferring the elastic and petrophysical properties around a gas-saturated reservoir hosted in a shale-sand sequence. In this case, the final outcomes provided by the rjMCMC algorithms are also compared with the predictions of linear Bayesian elastic and petrophysical inversions. The synthetic and field data examples demonstrate that the implemented algorithms can successfully estimate model uncertainty, model dimensionality and subsurface parameters with an affordable computational cost.
机译:我们通过横向贝叶斯反转从堆叠前地震数据中推断出弹性和岩石物理性质。在这种方法中,模型参数的数量(即,图层的数量)被视为未知数,并且可逆跳转马克可河链蒙特卡罗(RJMCMC)算法用于采样可变维模型空间。该反转方案提供了一种解析的解决方案,并且可靠地量化影响估计模型参数的不确定性。并行回火,其采用一系列相互作用的马尔可夫链,其中连续地放松似然函数,用于提高概率采样的效率。另外,采用延迟拒绝更新方案来加速RJMCMC算法的收敛到静止状态。弹性和岩石物理逆转,振幅与角度响应,并基于精确的Zoeppritz方程使用卷积前向建模。首先,使用合成测试来评估所实现的RJMCMC算法的可靠性,然后通过在陆上获取的场地震数据反转来证明它们的适用性。在这种情况下,倒置旨在推断出在页岩砂序列中托管的气体饱和储层周围的弹性和岩石物理性质。在这种情况下,还将RJMCMC算法提供的最终结果与线性贝叶斯弹性和岩石物理反转的预测进行了比较。合成和现场数据示例表明,实现的算法可以以实惠的计算成本成功估计模型不确定性,模型维度和地下参数。

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