一种添加修正项的Gardner公式

Gardner formula with an additional correction term

通过实验研究,基于Gardner经验公式,本文提出一种更加准确的揭示地层密度与纵波速度之间关系的方法。首先用Gardner经验公式估算地层密度;然后计算实测密度与估算密度的差值dt,同时考虑了测井资料中对密度有影响的GR,RD,PE,CNL,AC五条测井曲线,对dt与这五条曲线做多元回归分析,建立误差模型;最后用预测误差值加上Gardner密度预测值,得到最终密度预测值,也就是添加了dt修正项的Gardner公式的密度预测值。将该方法预测结果与Gardner经验公式、Castagna等提出的速度和密度的多项式及指数关系式进行了对比分析。研究结果表明,引入误差修正项dt的Gardner公式的预测精度更高。

Based on Gardner empirical formula,one method is proposed in this paper to reveal a more accurate relationship between the formation density and P-wave velocity through experimental study.First we estimate the formation density with Gardner empirical formula,and then we calculate the error dt between the measured density and estimated density.Taking into account the impact of the five logs GR,RD,PE,CNL,and AC on the formation density,we utilize multiple regression analysis to acquire the relation of these five elements and the error dt,i.e.the error model.Finally,the density of the Gardner formula with an additional correction term dt is obtained with the Gardner predicted value plus the predicted error.We make comparative analysis of the results of the Gardner formula,the polynomial,exponential empirical formula presented by Castagna,and the proposed method.The results show that our method has higher predicted accuracy than others.