The seismic attributes of water-rich sandstone contain much information about the rock's physical properties and seismic wave parameters. They are commonly used to predict the rock's physical properties (e.g. porosity). However, the seismic attributes of water-rich sandstone are affected by porosity, water saturation and thickness. To eliminate the influence of thickness on the porosity prediction of water-rich sandstone and improve the accuracy of the porosity prediction, the authors propose a Lambert W–R transform method to isolate the contribution of thickness and porosity from seismic attributes. First, a rock physical model is used to calculate the equivalent elastic parameters of water-rich sandstones with different porosity values and water saturation levels. Second, the seismic attribute dataset of water-rich sandstone is established by forward modelling the seismic response of the wedge-shaped water-rich sandstone model, and the selection of sensitive physical properties is completed. Then, the transformation parameters (ζ_AhR_s and η_AhR_s) are obtained by Lambert W–R transformation, which is exponentially related to instantaneous amplitude. ζ_AhR_s and η_AhR_s are sensitive to thickness and porosity, respectively. Finally, an interpretative template for porosity prediction of water-rich sandstone is established by cross-plot analysis (ζ_AhR_s and η_AhR_s) and verified by a practical case. The verification results show that the porosity predicted by the interpretation template is consistent with drilling fluid consumption. However, it is lower than the porosity of logging constrained P-wave impedance inversion.

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基于Lambert W-R模型的薄层富水砂岩地震属性转换及孔隙度预测

富水砂岩的地震属性包含了大量关于岩石物理性质和地震波参数的信息。它们通常用于预测岩石的物理特性（例如孔隙度）。然而，富水砂岩的地震属性受孔隙度、含水饱和度和厚度的影响。为了消除厚度对富水砂岩孔隙度预测的影响，提高孔隙度预测的准确性，作者提出了一种Lambert W - R变换方法，将厚度和孔隙度与地震属性的贡献分开。首先，利用岩石物理模型计算不同孔隙度值和含水饱和度的富水砂岩的等效弹性参数。其次，通过对楔形富水砂岩模型的地震响应进行正演模拟，建立富水砂岩地震属性数据集，完成敏感物性的选取。然后，通过Lambert W - R变换得到变换参数（ζ _Ah R _s和η _Ah R _s ） ，该参数与瞬时幅度呈指数关系。❖ _Ah R _s和❖ _Ah R _s分别对厚度和孔隙率敏感。最后，通过交会图分析（z _Ah R _s和η _Ah R _s）建立了富水砂岩孔隙度预测的解释模板，并通过实例进行了验证。验证结果表明，解释模板预测的孔隙度与钻井液用量相符。但低于测井约束纵波阻抗反演的孔隙度。