## 1 Introduction
This dual limitation hinders detailed analysis of beach-bar formation processes [19; 20]. To overcome these methodological constraints, this study employs the following multi-dimensional technical framework: Quantitative paleoenvironmental reconstruction, utilizing the abundance and assemblage characteristics of micro-paleontological fossils (e.g., algae, spores, and pollen) to establish evolutionary curves of the paleo-lacustrine environment to quantitatively restore paleo-water depth. This provides high-resolution constraints on the depositional dynamics governing beach-bar development. Precise provenance tracing, addressing multi-source convergence challenges in complex tectonic regions, employs LA-ICP-MS zircon U-Pb dating to systematically acquire detrital zircon age spectra [21; 22]. Correlation of these spectra and isotopic signatures with potential source terranes enables effective sediment source tracing and elucidation of provenance-tectonic coupling mechanisms. Through multi-parameter cross-validation and multi-scale data fusion, this integrated approach achieves synergistic quantification of the controlling factors (paleoenvironment, provenance, tectonics). The resulting models provide a scientific basis for understanding beach-bar sandbody genesis in complex geological settings and hold significant practical implications for hydrocarbon exploration target prediction. The HHK Depression is situated in the southeastern Bohai Bay Basin (Figure 1a,b), covering approximately 3300 km\({}^{2}\) (Figure 1c). It is bounded to the south by the Kendong Uplift and the Laibei Uplift, to the north by the relatively Bonan Uplift, and is axially traversed by the Tan-Lu Fault Zone [23]. The depression exhibits a composite fault system comprising NNE-NE trending strike-slip fault systems and EW-NEE trending extensional fault systems, which partition the depression into the following four secondary structural units: the northern steep slope zone, southern gentle slope zone, central strike-slip zone, and central uplift zone. These faults further sub-divide the depression into southwestern subsag, northwestern subsag, and eastern sag (Figure 1c). The Paleogene sequence in the HHK Depression (from bottom to top) comprises the Shahejie Formation Members 4 to 1 (E\({}_{2}\)s\({}_{4}\)-E\({}_{2}\)s\({}_{3}\)E\({}_{3}\)s\({}_{2}\)-E\({}_{3}\)s\({}_{1}\)), and Dongying Formation Members 3 to 1 (E\({}_{3}\)d\({}_{3}\)-E\({}_{3}\)d\({}_{2}\)-E\({}_{3}\)d\({}_{1}\)), overlain by Neogene Guantao (Ng) and Minghuazhen (Nm) formations and Quaternary (Q) deposits, absent the Kongdian Formation (E\({}_{1}\)k). Notably, the fluvial-deltaic, fan-delta, and shore-shallow lacustrine beach-bar facies are extensively developed within the Shahejie and Dongying Formations. Through integrated analysis of three-dimensional seismic data, well logs, and lithological records, the following six key chronostrigraphic surfaces in the Paleogene were identified: the base boundary of Shahejie Member 2 (SB\({}_{5}\), T\({}_{5}\)), the top boundary of Shahejie Member 2 (SB\({}_{4}\), T\({}_{4}\)), the base boundary of Dongying Member 3 (SB\({}_{3}\), T\({}_{3}\)), the intra-Dongying Member 3 boundary (SB\({}_{3}\)\({}^{\mathrm{L}}\), T\({}_{3}\)\({}^{\mathrm{L}}\)), the base boundary of Lower Dongying Member 2 (SB\({}_{3}\)\({}^{\mathrm{M}}\), T\({}_{3}\)\({}^{\mathrm{M}}\)), and the top boundary of Lower Dongying Member 2 (SB\({}_{3}\)\({}^{\mathrm{U}}\), T\({}_{3}\)\({}^{\mathrm{U}}\)) (Figure 1d). During the Paleogene, lithospheric extension and thinning in eastern China were induced by roll-back of the Pacific Plate subduction beneath the Eurasian Plate [24]. The Bohai Bay Basin, located within the superimposed zone of the right-lateral strike-slip motion along the Tan-Lu Fault Zone and destruction of the North China Craton, developed a unique composite stress field dominated by NW-SE extension and NE-oriented shear, with its Cenozoic tectonic history comprising four superimposed phases.