Sensitivity Study of the Immersive Boundary Condition Method

Abstract

Summary In various geophysical applications, it is often required to restrict the wave propagation inside a spatially limited domain which is embedded in a larger background domain. The Immersive Boundary Condition (IBC) method allows one to obtain the exact solution of the wave equation within a spatially limited subdomain, while at the same time accounting for the interactions with the background domain. The IBC method represents the theoretical foundation of a wave-propagation laboratory (WaveLab) built at ETH Zurich in Switzerland. The IBCs implementation in an actual laboratory comes along with practical restrictions. This work focuses on the application of spatial subsampling to the recording surface required by the IBC algorithm. Due to hardware limitations, the implementation of subsampling to simulate the WaveLab is essential in order to analyse the behaviour of the method. Additionally, a number of perturbations need to be studied, such as miscalibration of actuators and receivers, and sensor drop-outs. These results will give us insight into how physical experimentation may be affected by perturbations of the IBC method. From the initial tests, we see that subsampling the recording surface without violating the spatial Nyquist criterion returns acceptable results; and miscalibration of the receivers has a very small effect.