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Transdimensional and Hamiltonian Monte Carlo inversions of Rayleigh wave dispersion curves: A comparison on synthetic datasets
Near Surface Geophysics ( IF 1.1 ) Pub Date : 2020-04-07 , DOI: 10.1002/nsg.12100
Mattia Aleardi 1 , Alessandro Salusti 1, 2 , Silvio Pierini 1
Affiliation  

ABSTRACT We compare two Monte Carlo inversions that aim to solve some of the main problems of dispersion curve inversion: deriving reliable uncertainty appraisals, determining the optimal model parameterization and avoiding entrapment in local minima of the misfit function. The first method is a transdimensional Markov chain Monte Carlo that considers as unknowns the number of model parameters, that is the locations of layer boundaries together with the Vs and the Vp/Vs ratio of each layer. A reversible‐jump Markov chain Monte Carlo algorithm is used to sample the variable‐dimension model space, while the adoption of a parallel tempering strategy and of a delayed rejection updating scheme improves the efficiency of the probabilistic sampling. The second approach is a Hamiltonian Monte Carlo inversion that considers the Vs, the Vp/Vs ratio and the thickness of each layer as unknowns, whereas the best model parameterization (number of layer) is determined by applying standard statistical tools to the outcomes of different inversions running with different model dimensionalities. This work has a mainly didactic perspective and, for this reason, we focus on synthetic examples in which only the fundamental mode is inverted. We perform what we call semi‐analytical and seismic inversion tests on 1D subsurface models. In the first case, the dispersion curves are directly computed from the considered model making use of the Haskell–Thomson method, while in the second case they are extracted from synthetic shot gathers. To validate the inversion outcomes, we analyse the estimated posterior models and we also perform a sensitivity analysis in which we compute the model resolution matrices, posterior covariance matrices and correlation matrices from the ensembles of sampled models. Our tests demonstrate that major benefit of the transdimensional inversion is its capability of providing a parsimonious solution that automatically adjusts the model dimensionality. The downside of this approach is that many models must be sampled to guarantee accurate posterior uncertainty. Differently, less sampled models are required by the Hamiltonian Monte Carlo algorithm, but its limits are the computational effort related to the Jacobian computation, and the multiple inversion runs needed to determine the optimal model parameterization.

中文翻译:

瑞利波频散曲线的多维和哈密顿蒙特卡罗反演:合成数据集的比较

摘要 我们比较了旨在解决色散曲线反演的一些主要问题的两种蒙特卡罗反演:获得可靠的不确定性评估、确定最佳模型参数化和避免陷入失配函数的局部最小值。第一种方法是跨维马尔可夫链蒙特卡罗,将模型参数的数量视为未知数,即层边界的位置以及每层的 Vs 和 Vp/Vs 比率。采用可逆跳马尔可夫链蒙特卡罗算法对变维模型空间进行采样,同时采用并行回火策略和延迟拒绝更新方案提高了概率采样的效率。第二种方法是考虑 Vs 的哈密顿蒙特卡罗反演,Vp/Vs 比率和每层的厚度作为未知数,而最佳模型参数化(层数)是通过将标准统计工具应用于以不同模型维度运行的不同反演的结果来确定的。这项工作主要具有教学视角,因此,我们专注于仅反转基本模式的合成示例。我们对一维地下模型执行我们所谓的半解析和地震反演测试。在第一种情况下,色散曲线是使用 Haskell-Thomson 方法从所考虑的模型直接计算的,而在第二种情况下,它们是从合成炮点集提取的。为了验证反演结果,我们分析了估计的后验模型,我们还进行了敏感性分析,其中我们从采样模型的集合中计算模型分辨率矩阵、后验协方差矩阵和相关矩阵。我们的测试表明,跨维反演的主要好处是它能够提供自动调整模型维度的简约解决方案。这种方法的缺点是必须对许多模型进行采样以保证准确的后验不确定性。不同的是,哈密顿蒙特卡罗算法需要较少的采样模型,但其限制是与雅可比计算相关的计算工作量,以及确定最佳模型参数化所需的多次反演运行。来自采样模型集合的后验协方差矩阵和相关矩阵。我们的测试表明,跨维反演的主要好处是它能够提供自动调整模型维度的简约解决方案。这种方法的缺点是必须对许多模型进行采样以保证准确的后验不确定性。不同的是,哈密顿蒙特卡罗算法需要较少的采样模型,但其限制是与雅可比计算相关的计算工作量,以及确定最佳模型参数化所需的多次反演运行。来自采样模型集合的后验协方差矩阵和相关矩阵。我们的测试表明,跨维反演的主要好处是它能够提供自动调整模型维度的简约解决方案。这种方法的缺点是必须对许多模型进行采样以保证准确的后验不确定性。不同的是,哈密顿蒙特卡罗算法需要较少的采样模型,但其限制是与雅可比计算相关的计算工作量,以及确定最佳模型参数化所需的多次反演运行。这种方法的缺点是必须对许多模型进行采样以保证准确的后验不确定性。不同的是,哈密顿蒙特卡罗算法需要较少的采样模型,但其限制是与雅可比计算相关的计算工作量,以及确定最佳模型参数化所需的多次反演运行。这种方法的缺点是必须对许多模型进行采样以保证准确的后验不确定性。不同的是,哈密顿蒙特卡罗算法需要较少的采样模型,但其限制是与雅可比计算相关的计算工作量,以及确定最佳模型参数化所需的多次反演运行。
更新日期:2020-04-07
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