İstanbul’s Hagia Sophia is a monumental structure with multiple sub-spaces coupled to one another through arches. Its architectural elements have undergone alterations as its function has changed from that of a church to a mosque, a mosque to a museum, and back to a mosque. This study makes use of Hagia Sophia’s rich formal and material characteristics to conduct a comprehensive investigation of room acoustics coupling. The methodology involves the application of the diffusion equation model (DEM) for sound energy flow analysis. Energy flow decays and energy flow dips are examined for almost 1000 receiver positions distributed throughout the various sub-spaces of the building. Ray-tracing (Ray-t) simulations are used to support the energy flow decay analysis conducted using DEM. The Ray-t data are subjected to Bayesian analysis to identify the decay parameters and the degree of acoustical coupling. Among the many variables, the source-receiver distance and positioning within different sub-spaces appear to be the underlying determinant of multi-slope sound decay pattern. On the other hand, the cases of multi-slope decays identified within the structure tend to weaken and single-slope cases increase when the overall absorption area increases in the mosque state due to the carpeted floor.

中文翻译：

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伊斯坦布尔圣索菲亚大教堂不同状态的室内声学耦合探索

伊斯坦布尔的圣索非亚大教堂（Hagia Sophia）是一座纪念性建筑，具有多个子空间，这些子空间通过拱形相互连接。随着其功能从教堂变成清真寺，从清真寺变成博物馆，再到清真寺，其建筑元素发生了变化。本研究利用圣索非亚大教堂的丰富形式和材料特性对室内声学耦合进行了全面研究。该方法涉及将扩散方程模型（DEM）应用于声能流分析。针对分布在建筑物各个子空间中的近1000个接收器位置，检查了能量流衰减和能量流骤降。射线追踪（Ray-t）模拟用于支持使用DEM进行的能量流衰减分析。对Ray-t数据进行贝叶斯分析以识别衰减参数和声学耦合程度。在许多变量中，源-接收器的距离和在不同子空间中的位置似乎是多坡度声音衰减模式的根本决定因素。另一方面，当由于地毯地板而使整体吸收面积在清真寺状态下增加时，在结构内识别出的多坡度衰减情况趋于减弱，而单坡度情况则增加。