含裂隙介质中的视电阻率各向异性变化

Apparent resistivity anisotropic variations in cracked medium

我国50多年的视电阻率连续观测结果表明,大地震前近震中区域的视电阻率呈现出与主压应力方位有关的各向异性变化,即:垂直于主压应力方向观测的变化幅度最大,平行方向最小或不明显,斜交方向介于二者之间.目前我国定点台站视电阻率观测的探测范围主要在浅层沉积层以内,通常含有较多的含水裂隙.本文将地下岩土介质简化为由固体基质和含流体/气体裂隙组成的固液气三相介质,且基质、流体和气体具有标量形式的电阻率,推导出了包含基质和流体电阻率、裂隙率、饱和度和裂隙面积率因子的电阻率张量表达式.以裂隙的扩展/闭合表示应力作用下裂隙的变化,得到了电阻率随裂隙变化的微分形式,电阻率变化对裂隙体积变化放大系数的表达式和裂隙横向变化对纵向电阻率影响的横向权系数的表达式.在此基础上得到了介质电阻率和视电阻率的各向异性变化特征:对于含水裂隙介质,无论裂隙如何变化,均是最小主轴方向电阻率的变化幅度大于其他方向;对于含水孔隙介质,沿孔隙主要变化方向的主轴电阻率变化幅度大于其他方向.对于各向异性变化,视电阻率和介质电阻率存在π/2的方向差异.相较于含水岩石,无水岩石介质电阻率的各向异性变化不显著.本文提出的电阻率表达式可以对实验室和野外实际观测的许多结果做出合理的解释.

Observations in China for more than 50 years demonstrate that apparent resistivity near epicenters before major earthquakes show anisotropic variations associated with the principal compressive stress azimuth.Specifically,apparent resistivity vertical to the P axis exhibits maximum anomalous amplitudes,while that parallel to the P axis has the minimum or even indistinguishable anomalies,and that oblique to P axis is between them.The detection range of apparent resistivity in the fixed stations is usually confined to shallow sediments which often contain water-bearing cracks.This work attempts to reveal the relationship between anisotropic variations of apparent resistivity aforementioned and cracked media by mathematical analysis.Rock and soil are simplified as a solid-liquid-gas three-phase model containing solid matrix,liquid and gas in the cracks.The resistivity of solid matrix,liquid,and gas is of a scalar form.We have derived a resistivity tensor expression containing crack porosity,saturation,and the crack area rate factor.Using the growth and closure as crack changes under stress,the differential form of resistivity variation has been derived,as well as the volumetric sensitivities of relative resistivity variations versus crack volume changes,and the lateral weight coefficients of crack lateral volumechanges to the axial resistivity variation.Based on this model,the anisotropic variation characters of resistivity and apparent resistivity have been discussed.For water-containing cracked media,resistivity variation amplitude parallel to the minimum electrical axis is greater than that along the maximum electrical axis,no matter how the cracks change.And apparent resistivity variation amplitude vertical to the minimum electrical axis is greater than that parallel to the minimum electrical axis.For water-containing porous media,resistivity variation amplitude of the electrical axis parallel to the main change direction is greater than that vertical to the change direction.And apparent resistivity variation amplitude vertical to the main change direction is greater than that parallel to the direction.Comparing with the water-containing media,resistivity and apparent resistivity anisotropic variations of anhydrous media are less obvious as the cracks change.The resistivity model proposed in this paper can provide reasonable explanation to results from experiments and field measurements.