## 1 Introduction  
The Northern Shaanxi mining area is a shallow close-distance coal seam (SCDCS) in western China [1]. Due to historical mining activities, interval mining in the upper coal seams has left a large number of residual coal pillars of various sizes, forming a large area of shallow interval goat [2]. As the upper coal resources are exhausted, the coal resources under interval goat urgently need to be mined. However, the lower coal seam working face will inevitably pass through the interval goat. Production practice confirms that when the lower coal seam working face passes through the residual coal pillars of the goats in the upper coal seams, it is extremely prone to IRS instability induction linked to the instability of overburden rock (OR) in the upper coal seam goat. The transient large-scale collapse of the roof rock strata in the composite goafs of the upper and lower coal seams can cause dynamic hazards such as mine tremors, air blasts, coal wall spalling, and roof cutting and caving, as well as significant compression of the supports and columns, which poses serious threats to the safety of the working face [3; 4; 5; 6; 7; 8; 9; 10; 11; 12]. [PERSON] et al. [13; 14] analyzed the characteristics of the load transfer from the \"activated\" structure in the roof caving of the upper coal seam to the working face of the lower coal seam and classified the roof structures in shallow coal seam groups based on the interval mining ratio. [PERSON] et al. [15] proposed three types of structures, i.e., the load-bearing structure of surrounding rock, the mine pressure movement structure, and the working face protection structure, for the pressure arch in the stope. [PERSON] et al. [16], [PERSON] et al. [17], and [PERSON] et al. [18] analyzed the conditions for the existence of the \"vousoir beam\" and \"cantilever beam\" structures of the main roof based on whether there is a main roof structure between the closely spaced coal seams. [PERSON] et al. [19] and [PERSON] et al. [20] studied the evolution law of mining-induced stress and the catastrophic mechanism of hydraulic support under room-and-pillar goaf in shallow buried coal seams and summarized the sudden instability laws of residual coal pillars in shallow room-and-pillar mining. [PERSON] et al. [21] established a universal model for the bearing movement characteristics of the voussoir structure under discontinuous uniform load in the room-and-pillar goaf, and a typical model for the stress movement characteristics of the composite structure system of the \"main roof-multiple coal pillars-immediate roof-support\" under the room-and-pillar goaf. [PERSON] et al. [22], [PERSON] et al. [23], and [PERSON] et al. [24] classified the key strata structures of the OR in an SCDCS and revealed the reasons for the dynamic pressure in the working face when mining over valleys and exiting coal pillars. Also, they studied the dynamic instability process of room-and-pillar coal pillar groups, elucidated the dynamic mine pressure mechanism of mining under room-and-pillar coal pillars, and found that room-and-pillar coal pillars are more prone to instability and failure than concentrated coal pillars. [PERSON] et al. [25] established a model for the stress transfer law of the composite floor of shallow buried room-and-pillar coal pillars and explored the OR structure when exiting coal pillars. [PERSON] et al. [26] investigated the deformation and failure characteristics of the room-and-pillar coal pillar group and OR, analyzed the dynamic process of rebound impact instability of the advanced coal pillar group under the influence of mining, and revealed the impact instability mechanism during mining in an SCDCS. This paper studied the instability characteristics of the IRS in the 30103 working face of Naliang Coal Mine, which passes through the interval goaf of the overlying \(2^{-2}\) coal seam.