Monitoring networks increasingly aim to assimilate data from a large number of diverse sensors covering many sensing modalities. Bayesian optimal experimental design (OED) seeks to identify data, sensor configurations, or experiments which can optimally reduce uncertainty and hence increase the performance of a monitoring network. Information theory guides OED by formulating the choice of experiment or sensor placement as an optimization problem that maximizes the expected information gain (EIG) about quantities of interest given prior knowledge and models of expected observation data. Therefore, within the context of seismo-acoustic monitoring, we can use Bayesian OED to configure sensor networks by choosing sensor locations, types, and fidelity in order to improve our ability to identify and locate seismic sources. In this work, we develop the framework necessary to use Bayesian OED to optimize a sensor network's ability to locate seismic events from arrival time data of detected seismic phases at the regional-scale. Bayesian OED requires four elements: 1) A likelihood function that describes the distribution of detection and travel time data from the sensor network, 2) A Bayesian solver that uses a prior and likelihood to identify the posterior distribution of seismic events given the data, 3) An algorithm to compute EIG about seismic events over a dataset of hypothetical prior events, 4) An optimizer that finds a sensor network which maximizes EIG. Once we have developed this framework, we explore many relevant questions to monitoring such as: how to trade off sensor fidelity and earth model uncertainty; how sensor types, number, and locations influence uncertainty; and how prior models and constraints influence sensor placement.

翻译：监测网络日益致力于整合覆盖多种传感模态的大量异构传感器数据。贝叶斯最优实验设计旨在识别能够最优降低不确定性、从而提升监测网络性能的数据、传感器配置或实验方案。信息理论通过将实验选择或传感器布设问题表述为优化问题来指导最优实验设计，该优化在给定先验知识和预期观测数据模型的条件下，最大化关于目标量的期望信息增益。因此，在地震声学监测背景下，我们可以运用贝叶斯最优实验设计来配置传感器网络，通过选择传感器位置、类型与精度以提升地震源识别与定位能力。本研究构建了必要的理论框架，利用贝叶斯最优实验设计优化传感器网络基于区域尺度地震波到时数据定位震源事件的能力。贝叶斯最优实验设计需要四个核心要素：1) 描述传感器网络检测概率与走时数据分布的似然函数；2) 基于先验分布与似然函数、利用观测数据反演震源事件后验分布的贝叶斯求解器；3) 在假设先验事件数据集上计算震源事件期望信息增益的算法；4) 寻找能最大化期望信息增益的传感器网络的优化器。建立该框架后，我们深入探讨了监测领域若干关键问题：如何权衡传感器精度与地球模型不确定性；传感器类型、数量与位置如何影响不确定性；以及先验模型与约束条件如何影响传感器布设策略。