## 2 Materials and Methods  
The integrated dataset comprises three-dimensional seismic data, well logs, core samples, and laboratory analyses including grain size distributions, paleontological assemblages, and geochemical parameters. Within the study area containing 29 drilled wells, 16 wells with complete stratigraphic sub-division data and geophysical logs--including spontaneous potential (SP), natural gamma ray (GR), microlog, and microresistivity--were selected for detailed analysis. These logs provide the fundamental basis for high-resolution stratigraphic correlation and serve as critical constraints for mapping planar sandbody distributions. Log facies interpretation further enables depositional facies characterization. Core observation, description, and cast thin-section analysis of target intervals from the 16 wells were systematically conducted, with emphasis on data from key cored wells (B8-2-a, C4-2-a, C4-3-a, C4-4-e, and C3-1-a). Analyzed attributes encompass lithology, compositional heterogeneity, and sedimentary structures. Continuous core sections document vertical grain size variations, whose cyclicity patterns provide diagnostic criteria for analyzing sandbody architecture and defining depositional microfacies. This approach proves particularly essential in frontier exploration areas with sparse well coverage. Full-azimuth three-dimensional seismic coverage exists across the study area, with data acquired at a 2 ms sampling rate and processed to a 12.5 m (in-line) \(\times\) 25 m (cross-line) bin size using three-dimensional prestack time migration (PSTM). Seismic reflection configurations were analyzed to establish a regional framework for depositional facies interpretation. Integrated with seismic profile characteristics, paleotopography and paleogeomorphology were reconstructed through horizon flattening techniques within the GEOFRAM three-dimensional interpretation system [27; 28], thereby enabling the discrimination of paleo-hydrodynamic conditions and basin physiography (Figure 2). Integrated paleoclimate and paleoenvironmental proxies--including abundant lacustrine algal fossils, palynomorph assemblages, and trace element data from the Paleogene succession--were analyzed using complete datasets from four key wells (C3-1-a, C4-4-3, C4-9-f, and B9-4-b). Sampling details are as follows: Well C3-1-a: 83 cuttings samples from 2895 to 3980 m depth; Well C4-4-3: 26 cuttings samples from 2880-3360 m depth; Well C4-4-3: 26 cuttings  
Figure 2: Representative three-dimensional seismic reflection profile across the HHK Depression (AA\({}^{\prime}\): Nearly south-north reflection seismic profile; BB\({}^{\prime}\): Nearly west-east reflection seismic profile, location see Figure 1c). Well C4-9-f: 24 cuttings samples from 2360-2960 m depth; and Well B9-4-b: 12 cuttings samples from 2725-3005 m depth. A total of 145 cuttings samples were collected at 20 m intervals, spanning the Shahejie Formation Members 2-1 (E\({}_{3}\)g\({}_{2}\)-E\({}_{3}\)s\({}_{1}\)) and Dongying Formation Members 3-1 (E\({}_{3}\)d3-E\({}_{3}\)d\({}_{1}\)). Palynofloral assemblages serve as sensitive paleoclimatic indicators. Palynological analysis provides critical chronostriatgraphic constraints on vegetation dynamics, constituting a primary methodology for paleoclimate reconstruction [29; 30]. Systematic quantification of palynological datasets from the HHK Depression, Bohai Bay Basin, revealed six diagnostic polynofacies assemblages from Shahejie Member 3 through the Dongying Formation. During Dongying Formation deposition, palynofacies indicated deciduous broad-leaved dominance under a subtropical climate, with gymnosperm components showing progressive proliferation of Tsuga and Picea. This succession documents a gradual cooling trajectory within a persistently warm-hot regime, characterized by a climatic shift from arid-thermal to humid-warm conditions with quasi-cyclic oscillations (Table 1).