Method of the environmental noise estimation by injection tests for ground based gravitational wave detectors

Environmental noise is one of the important issue for the observation of gravitational waves, but it's difficult to predict this in advance. To evaluate how much the environmental noise spoils the detector sensitivity, understanding of the detector response to the environmental noise in actual setup is crucial for both the observation and the future upgrade. In this paper, we introduce and verify the new method of PEM injection based on the post-observation commissioning of KAGRA. This new method (response function model) includes the frequency conversion and non-linearity of power, which effects are not considered in the current model (coupling function model) used in LIGO and Virgo. We also confirmed our method by applying it to the environmental noise enriched dataset and succeeded to reproduce them.