## 1 Introduction  
As the exploration of structural hydrocarbon reservoirs in continental basins becomes increasingly challenging and the issue of reserve succession grows more severe, the focus of oil and gas exploration in these basins has gradually shifted and expanded from structural traps to lithost stratigraphic traps, from shallow targets to deep exploration objectives, and from conventional to unconventional domains [1, 2]. Among these, thin-bedded beach-bar sand bodies have emerged as a key focus for research and exploration in lithologic and unconventional hydrocarbon reservoirs. To date, numerous clastic beach-bar deposits have been identified in China's continental basins, with significant breakthroughs in hydrocarbon exploration [3, 4]. Thin-bedded sand bodies are significant types of sedimentary deposits found in the gentle slope zones of continental rift lake basins. They are characterized by their thin thickness, extensive lateral distribution, diverse sedimentary origins, complex diagenetic features, and unpredictable development patterns. The exploration of unconventional oil and gas resources in China has now entered a meticulous phase, with massive petroleum reserves residing within these thin-bedded sand bodies (defined as having a thickness of less than 10 m) located in subsurface strata [5; 6]. The Bohai Bay Basin, a typical continental sedimentary basin in China, serves as a crucial area for unconventional hydrocarbon exploration [7; 8]. Focusing on the Paleogene system in the HHK Depression of this basin, this study discusses the fine characterization of the boundaries of thin-bedded beach-bar sand bodies, which hold important implications for expanding exploration frontiers in unconventional hydrocarbon reservoirs within continental basins [9; 10]. Currently, identifying thin-bedded sand bodies using conventional geological theories and methods poses considerable challenges. However, through comprehensive seismic sedimentology analysis [11], it is possible to study the lithological characteristics of the sedimentary rocks, identify thin-bedded sand bodies, and determine their sedimentary types and evolutionary processes [12; 13], thereby providing new pathways for the exploration and development of deep unconventional oil and gas resources. The fine characterization of thin-bedded sand body boundaries has become a focal point and a challenge in both oil and gas geological research and applied geophysics. With advancements and the widespread adoption of horizontal well technology and drilling fracturing techniques [14], the previously overlooked thin beds and interbedded reservoirs are garnering increasing attention from the oil and gas exploration and development community. From the perspective of seismic exploration principles, thin sand layers are considered to be strata that strictly fall within the defined tuning thickness. Conventional seismic interpretation methods are insufficient for exploring these thin strata. To effectively predict such layers, it is essential to acquire wideband impedance signals during the inversion process. Furthermore, seismic attribute analysis has emerged as a reliable and efficient technique for interpreting seismic data, particularly in the context of thin-bedded sand body predictions, consistently yielding favorable results [15; 16; 17]. Traditional inversion methods acquire high-frequency components through two primary approaches. The first method utilizes deterministic interpolation models, typically employing techniques such as inverse distance weighting, natural neighbor interpolation, and Kriging [18; 19; 20]. While these models produce deterministic interwell interpolation results, they are inherently constrained by their model assumptions, resulting in low confidence levels [21; 22]. Consequently, their application is primarily limited to reservoirs demonstrating stable lateral continuity and significant stratigraphic thickness.