To assist experts in fault diagnosis, a sound signal coupling modulation model is proposed for compound faults caused by damage at different positions in a two-stage planetary gear system with a single-stage parallel gearbox. When compound faults occur in a wind turbine gearbox, their characteristic frequencies affect the meshing frequencies of different gear stages in the form of amplitude modulation and frequency modulation. Therefore, this paper proposes a coupling modulation model for the amplitude of sound signals in the wind turbine gearbox under compound faults. By utilizing a parameter identification approach, the modulation coefficients for different gear stages in the proposed coupling modulation model are determined. An energy ratio of sidebands index is constructed to evaluate the effectiveness of the identification. Finally, the reconstructed spectrum of the sound signal coupling modulation model is used to determine the location of compound faults, achieving auxiliary fault diagnosis. Experimental and field data analysis show that the sideband energy ratio indicators for evaluating the identification results are 0. 948, 0. 972, 0. 977, and 0. 964 3, effectively. These results effectively demonstrate the validity of the model identification, laying a foundation for automatic diagnosis of gearbox compound faults.