ABSTRACT In glacial studies, properties such as glacier thickness and the basement permeability and porosity are key to understand the hydrological and mechanical behaviour of the system. The seismoelectric method could potentially be used to determine key properties of glacial environments. Here we analytically model the generation of seismic and seismoelectric signals by means of a shear horizontal seismic wave source on top of a glacier overlying a porous basement. Considering a one‐dimensional setting, we compute the seismic waves and the electrokinetically induced electric field. We then analyse the sensitivity of the seismic and electromagnetic data to relevant model parameters, namely depth of the glacier bottom, porosity, permeability, shear modulus and saturating water salinity of the glacier basement. Moreover, we study the possibility of inferring these key parameters from a set of very low noise synthetic data, adopting a Bayesian framework to pay particular attention to the uncertainty of the model parameters mentioned above. We tackle the resolution of the probabilistic inverse problem with two strategies: (1) we compute the marginal posterior distributions of each model parameter solving multidimensional integrals numerically and (2) we use a Markov chain Monte Carlo algorithm to retrieve a collection of model parameters that follows the posterior probability density function of the model parameters, given the synthetic data set. Both methodologies are able to obtain the marginal distributions of the parameters and estimate their mean and standard deviation. The Markov chain Monte Carlo algorithm performs better in terms of numerical stability and number of iterations needed to characterize the distributions. The inversion of seismic data alone is not able to constrain the values of porosity and permeability further than the prior distribution. In turn, the inversion of the electric data alone, and the joint inversion of seismic and electric data are useful to constrain these parameters as well as other glacial system properties. Furthermore, the joint inversion reduces the uncertainty of the model parameters estimates and provides more accurate results.

中文翻译：

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联合SH地震和地震数据的贝叶斯反演以推断冰川系统特性

摘要 在冰川研究中，冰川厚度、基底渗透率和孔隙度等特性是了解系统水文和力学行为的关键。地震电法有可能用于确定冰川环境的关键特性。在这里，我们通过覆盖多孔基底的冰川顶部的剪切水平地震波源对地震和地震信号的生成进行分析建模。考虑一维设置，我们计算地震波和电动感应电场。然后我们分析了地震和电磁数据对相关模型参数的敏感性，即冰川底部的深度、孔隙度、渗透率、剪切模量和冰川基底的饱和水盐度。而且，我们研究了从一组极低噪声合成数据中推断出这些关键参数的可能性，采用贝叶斯框架来特别关注上述模型参数的不确定性。我们使用两种策略解决概率逆问题：（1）我们计算每个模型参数的边际后验分布，以数值方式求解多维积分；（2）我们使用马尔可夫链蒙特卡罗算法来检索模型参数集合给定合成数据集，遵循模型参数的后验概率密度函数。这两种方法都能够获得参数的边际分布并估计它们的均值和标准差。马尔可夫链蒙特卡罗算法在数值稳定性和表征分布所需的迭代次数方面表现更好。单独的地震数据反演不能比先验分布更进一步地限制孔隙度和渗透率的值。反过来，单独的电数据反演以及地震和电数据的联合反演可用于约束这些参数以及其他冰川系统特性。此外，联合反演降低了模型参数估计的不确定性并提供了更准确的结果。地震和电数据的联合反演有助于限制这些参数以及其他冰川系统特性。此外，联合反演降低了模型参数估计的不确定性并提供了更准确的结果。地震和电数据的联合反演有助于限制这些参数以及其他冰川系统特性。此外，联合反演降低了模型参数估计的不确定性并提供了更准确的结果。