We address an optimal sensor placement problem through Bayesian experimental design for seismic full waveform inversion for the recovery of the associated moment tensor. The objective is that of optimally choosing the location of the sensors (stations) from which to collect the observed data. The Shannon expected information gain is used as the objective function to search for the optimal network of sensors. A closed form for such objective is available due to the linear structure of the forward problem, as well as the Gaussian modeling of the observational errors and prior distribution. The resulting problem being inherently combinatorial, a greedy algorithm is deployed to sequentially select the sensor locations that form the best network for learning the moment tensor. Numerical results are presented and analyzed under several instances of the problem, including: use of full three-dimensional velocity-models, cases in which the earthquake-source location is unknown, as well as moment tensor inversion under model misspecification

翻译：我们通过贝叶斯实验设计处理了地震全波形反演中的最优传感器布置问题，旨在恢复相关矩张量。其核心目标是最优选择用于采集观测数据的传感器（台站）位置。以香农期望信息增益为目标函数，搜索最优传感器网络。由于正问题具有线性结构，且观测误差与先验分布均服从高斯模型，该目标函数可得到闭式解。鉴于该问题本质上的组合特性，我们采用贪婪算法逐步选择能构成学习矩张量最佳网络的传感器位置。针对多种问题实例给出数值结果并进行分析，包括：使用全三维速度模型、震源位置未知的情形，以及模型设定错误条件下的矩张量反演。