We consider lithological tomography in which the posterior distribution of (hydro)geological parameters of interest is inferred from geophysical data by treating the intermediate geophysical properties as latent variables. In such a latent variable model, one needs to estimate the intractable likelihood of the (hydro)geological parameters given the geophysical data. The pseudo-marginal method is an adaptation of the Metropolis-Hastings algorithm in which an unbiased approximation of this likelihood is obtained by Monte Carlo averaging over samples from, in this setting, the noisy petrophysical relationship linking (hydro)geological and geophysical properties. To make the method practical in data-rich geophysical settings with low noise levels, we demonstrate that the Monte Carlo sampling must rely on importance sampling distributions that well approximate the posterior distribution of petrophysical scatter around the sampled (hydro)geological parameter field. To achieve a suitable acceptance rate, we rely both on (1) the correlated pseudo-marginal method, which correlates the samples used in the proposed and current states of the Markov chain, and (2) a model proposal scheme that preserves the prior distribution. As a synthetic test example, we infer porosity fields using crosshole ground-penetrating radar (GPR) first-arrival travel times. We use a (50x50)-dimensional pixel-based parameterization of the multi-Gaussian porosity field with known statistical parameters, resulting in a parameter space of high dimension. We demonstrate that the correlated pseudo-marginal method with our proposed importance sampling and prior-preserving proposal scheme outperforms current state-of-the-art methods in both linear and non-linear settings by greatly enhancing the posterior exploration.
翻译:我们从地球物理数据中推断出(水文)地质学相关参数的后表分布,从地球物理数据中推断出(水文)地质学参数的后表分布。在这种潜伏变量模型中,我们需要根据地球物理数据来估计(水文)地质参数的难测可能性。假边缘法是Metropolis-Hasting算法的调整,其中蒙特卡洛平均从样本中得出这种可能性的不偏袒近似值,这种样本来自在这种环境下,即振动的石油物理关系连接(水文)地质学和地球物理特性。要使方法在数据丰富的地球物理环境中以低噪声水平进行实用化处理。在这种潜伏变量模型模型中,我们证明蒙特卡洛取样必须依赖重要取样分布的重要性,这种分布很接近采样(水)地质物理物理分布分布在取样(水)地质学参数字段周围的表面分布分布。为了达到适当的接受率,我们既依靠(1) 相关的伪海洋学方法,该方法将拟议和当前状态下流储量(水) 的精确度提议与保存先前分布的模型方案进行综合测试,我们使用前的地基地基地基地基地基数据-地基数据分析方法,从而显示前地基-地基-地基数据-地基-地基数据-地基-地基数据-地基数据-地基数据-地基数据-地基数据-地基数据-地基数据-地基数据-地基数据-地基数据-地基数据-地基数据-地基数据-地基数据-地基数据-地基数据-地基数据-地基数据-地基数据-地基数据-地基数据-地基数据-地基数据-地基数据-地基数据-地基数据-地基数据-地基数据-地基数据-地基数据-地基数据-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-高度-我们-我们-我们-我们-我们-我们-我们-我们-