## 3 Materials and Methods
### Well Logging Data Preprocessing  
Quality control of logging data from individual wells, as well as consistency checks of logging data from multiple wells, are integral components of the log data analysis process. This is crucial for establishing reliable rock physics models and ensuring high-quality seismic inversion. The preprocessing of the logging data in this study primarily encompasses environmental correction, outlier management, and curve standardization. Figure 4: Seismic spectrum characteristics of the Lower E\({}_{3}\)d\({}_{2}\) Sub-member in HHK Depression. Consistency checks of multi-well logging data are a vital quality control step in the seismic-constrained inversion process with well calibration. Systematic errors may arise from different generations of logging instruments, variations in the properties of the mud utilized in each well, and influences from wellbore conditions. These factors can result in significant discrepancies in the logging responses of identical logging curves at standard layers across different wells [66]. The presence of such discrepancies suggests that seismic synthetic records calibrated using well data and seismic lithology inversions constrained by multiple wells may involve various uncertainties [67]. Consequently, building upon the quality control of single-well data, the standardization and correction of multi-well data represent essential quality control measures in the integration of well and seismic information [68]. The specific procedure is as follows: A histogram of logging response frequencies or a frequency intersection graph is constructed for the standard layer of the well in question and compared in detail with the corresponding graph for the same standard layer from a key well [69]. If the two sets of values are identical and exhibit similar shapes, this indicates that the curve calibration for the well is accurate. Conversely, if discrepancies are noted, it suggests an error in the calibration of the logging curve for that well [70]. In such instances, the difference between the characteristic values of the standard layer logging curves across each well and the characteristic values from the key well's standard layer is utilized as the correction value for the well's logging curve [71]. Building on this foundation and integrating research requirements with the practical conditions of well logging data, a stable mudstone interval from the lower Dong-2 Member was selected as the reference layer. The core of the mudstone-referenced gamma ray (GR) and density (DEN) curve standardization method lies in establishing a normalization baseline based on the radioactive and density characteristics of mudstone, thereby eliminating the effects of instrumentation, environmental conditions, and lithological variations on logging data [72]. This mudstone interval exhibits lateral stability and distinct logging response features, including high natural gamma ray (GR > 100 API), high density (DEN: 2.0-2.5 g/cm\({}^{3}\)), moderate neutron porosity, and acoustic transit time. Using the GR values of pure mudstone layers as the baseline (120-130 API), the GR offsets for other wells were calculated. Simultaneously, systematic errors in the density curves were corrected based on the average mudstone density (2.3 g/cm\({}^{3}\)). Subsequently, standardization procedures were applied to all of the wells within the study area involved in the inversion analysis. Following the standardization process, the probability histogram matching method was employed for multi-well consistency checks. Probability distribution histograms for natural gamma, density, and other log curves were generated for each well in the study area (Figure 5). These histograms demonstrated good interwell consistency within the region, making them suitable for subsequent rock physics analysis. The environmental correction of the original logging data and the rationality correction of reservoir parameters ensure that we obtained a relatively accurate and reasonable series of key logs.