## 1 Introduction
(2017) established a coupling model of vehicle-track-subgrade considering track irregularity and concluded that the vertical dynamic displacement amplitude of the subgrade surface under the superimposed vibration of a double-track railway is approximately 50% higher than that of a single-track railway. [PERSON] et al. (2017) conducted a comparative analysis of the spectral characteristics and vibration amplitude of subgrade vibrations based on vibration response experiments of high-speed railway embankment-bridge transition sections. Using the characteristics of elastic wave propagation attenuation to detect the health status of an object is a common method in non-destructive testing ([PERSON] et al., 2016; [PERSON] et al., 2017; [PERSON] et al., 2017). Existing research often relies on the attenuation characteristics of indicators exhibited by elastic waves as they pass through different media of rock and soil to identify internal cracks, voids, and damage within the geotechnical body ([PERSON] et al., 2016; [PERSON] et al., 2017; [PERSON] et al., 2017). [PERSON] et al. (2017) discovered that elastic wave attenuation is significant in mined-out areas and decreases after backfilling but is not completely eliminated; this feature can be used to monitor cavities in mining areas. [PERSON] et al. (2017) found through experiments that the main cause of elastic wave attenuation is the compaction degree of mineral particles, followed by the development of joints and bedding, which can monitor the compositional structure of geotechnical bodies. [PERSON] et al. (2017) used crosshole seismic CT techniques to image the P-wave velocities of the limestone stratum, establishing the relationship between the P-wave velocity and geological anomalies, demonstrating that elastic waves can be used for karst detection. [PERSON] et al. (2017) studied the propagation and attenuation characteristics of elastic waves in layered coal rock, pure coal, and pure sandstone using an elastic wave generation device, providing optimized and corrected theoretical foundations for microseismic technology. [PERSON] et al. (2017) introduced the characteristic parameter within the framework of the flicker noise spectrum and analyzed the relationship between the acoustic emission -value and -value, revealing their effectiveness in predicting instability and monitoring dynamic hazards in coal and magnetite formations. [PERSON] et al. [33] explored the detection of roadbed erosion using vibration-excited acoustic waveform arrays on the pavement, analyzing 2D spectra, transient waveforms, and sound field distributions, and found that soil erosion leading to a water layer beneath the pavement alters mode wave characteristics, causing frequency spectrum disconnections and resonance phenomena, which serve as indicators of serious roadbed erosion. Although significant progress has been made in the study of subgrade vibration response, existing research often overlooks the long-term dynamic monitoring of the internal structure of the subgrade during railway operation [34]. Additionally, there is limited research on the dynamic response characteristics of karst subgrades and the use of vibration response to assess the condition of railway subgrades [35]. The formation of karst soil cavities is sudden and unpredictable, and once they reach a state of critical equilibrium, they pose safety hazards. Therefore, dynamic monitoring of the vibration response of the subgrade environment during train operation is essential. This study examines wheel-rail vibration as the vibration source and establishes a three-dimensional finite element model coupling the train, ballastless track, and subgrade foundation. The vibration response characteristics of the surrounding environment are compared when a high-speed train passes over a subgrade without a soil hole and with an underlying soil hole in karst areas.