确定古应力场的断层擦痕分析法力学原理

THEORETICAL BASIS OF A METHOD FOR THE DETERMINATION OF PALEOTECTONIC STRESS FIELD FROM FAULT STRIATION ANALYSIS

利用断层擦痕方向判断区域构造应力场是最近几年发展起来的一种方法。本文详细介绍了这种方法的历史发展、使用步骤和适用条件以及作为方法基础的力学原理。方法的主要点是从野外测量得到区域中诸断层面上的擦痕方向,并按 Bott 原则将这些方向视为当时将出现断层的那些截面上的剪应力的方向。根据这些实测数据,利用连续介质力学给出的区域应力与任一截面上剪应力之间的关系式,并采用数学中的最优化处理方法,可以求出区域应力场的三个主应力方向和一个主应力差的比值。若要确定三个主应力的大小,则尚须辅以其它方法定出一个应力差的值和各向等应力的值,此时方能具有足够的方程来全面确定所求的区域构造应力场。

Determination of regional paleotectonic stress from fault striation anal- ysis is a newly developed method.This article gives a detailed account of the method including its history of development,the conditions as weIl as the steps concerning its usage,and its theoretical background set up from continuum mechanics.The main point of the method consists of measuring the directions of striae on various fault planes in the field of a given re- gion and taking these directions,according to Bott's principle,as the direc- tions of the shearing stresses acting on the cross-sectional planes where the fault planes were about to occur.With these data measured in the field, three principal directions of the state of regional stress and one ratio of stress differences can be determined by using the relation between the re- gional stresses and the shearing stress on any cross section of the region from continuum mechanics and by using methods of optimization in mathematics. If the magnitudes of three principal stresses are wanted,additional methods should be devised for finding out the amounts of other two quantities, namely,one of the stress differenees and the hydrostatic stress,and the number of equations will then be sufficient to give a complete solution of the required regional stress field.