用线状被动标志物向分布估测岩石总体应变的最优化方法

在一些假设下提出了利用线状被动标志物的方向数据估测岩石总体应变的最优化方法。该方法等同地考虑到每个测量数据对应变估计的贡献，从而能够较好地反映出岩石的总体应变。它具有较好的稳健和广泛的适用对象。实验表明，观察数据大约在80个或更少时估测的应变椭圆轴比的相对误差小于20％，超过160个观察数据一般小于5％－10％。

Determination of Bulk Strain in Rocks from Linear Passive Markers: An Optimum Approach

The information on bulk strain is recorded by the final distribution in azimuth of nonisometric minerals or mineral aggregates in tectonites. With the increase of strain in rocks, they became more evidently aligned to the direction of the maximum principal strain axis. However, besides the bulk strain, the final distribution in azimuth of particles are dependent upon the distribution prior to the strain in azimuth of particles, difference in viscosity between the particles and the matrix, the deformation within the particles, strain path, temporal relationship between the growth of minerals and the bulk strain, etc. All these factors are likely to produce an extremely complicated or even indeterminable relationship between the final distribution in azimuth of particles and the bulk strain in rocks. 　　Under some assumptions, the authors have established a simple quantitative model of orientations of passive strain markers which is deterministically associated with the bulk strain in rocks. We use the modern technique of anneal modeling to estimate the bulk strain from observed orientations of passive strain markers. It is robust and has a wide application, especially in the general cases where no or few strain markers are available to other methods for strain analysis. It can make a better estimation of bulk strain in rocks since each observation is equally weighted in calculation. 　　In order to validate our method, artificial orientation data of passive strain markers were generated by Monte Carlo sampling under some given bulk strains, which then were used to estimate the bulk strains in our method. As we expected, the accuracy of estimated bulk strains tends to increase with the number of observations, and seems to increase or reach a relatively stable state when the number is no less than ca. 160. This implies that at least 160 observations should be required for an accurate estimation of the bulk strain in rocks. When the number of observations is equally set, large bulk strains estimated seem less accurate than small ones, but there is no apparent difference in proportional errors between both estimated bulk strains. Estimated axial ratios of strain ellipse in artificial examples have a proportional error of less than 5～10% when the number of observations exceeds 160, and of less than 20% when less than 80. Furthermore, estimated concentration index (к) in von Mises distribution have a good linear relation to estimated axial ratios (R) of strain ellipse. Their empirical equation is к＝0.402×R－0.087. 　　As an example, deformed graptolite branches in the Ordovician shale from Ramsay and Huber (1984) are studied respectively by our method and maximum-minimum angle method to estimate the bulk strain in rock. There is no apparent difference in estimated axial ratios of strain ellipse between both methods but a relatively great difference in estimated orientations of maximum principal strain axis.