声波时差与岩石岩性参数关系的统计分析研究

物理量之间的关系可能是多元函数的关系。本文用统计分析的方法来研究有效压力P、孔隙度φ、岩石密度ρ_b、渗透率κ对声波时差的影响。在实验室测定18个砂岩样品所得的一系列数据进行统计分析,并对于每一个样品,拟合出声波时差和有效压力的关系式。从这些关系式,可以看出声波时差随有效压力的增大而指数衰减,并且所有的样品均很好地满足这种关系式。对于不同的样品,这些关系式里的系数不同。对所有的样品所测得的岩石岩性参数进行综合,得到了最佳多元函数拟合公式。这个最佳拟合经验关系式描述了有效压力、孔隙度、渗透率和岩石密度对声波时差的综合影响。

Study of the Relationships among Acoustic Travel-time Differences and Related Parameters of a Medium Using Statistical Analysis Method

The relationships among physical parameters may be multivariate ones. In this paper, study the influence of effective pressure, porosity, rock density and permeability on the acoustic travel-time differences using statistical analysis method. A large set of data obtained from the laboratory measurements on 18 sandstone samples has been analyzed by statistical analysis. For each sample, the effective pressure dependence formula of the acoustic travel-time differences was obtained by fitting. According to these formulae, the acoustic travel-time differences increase exponentially with the increasing of the effective pressure can be found. and all samples satisfy this kind of relationships very well. The coefficients of the formulae are different for different samples. The best multivariate fitted formula for the combined set of parameter measurements from all samples has been obtained in this paper. This formula describes the integrated influence of effective pressure, porosity, permeability and rock density on the acoustic travel-time differences.