用单钻孔资料和岩层复平求面理倾斜的通用公式探讨

用改进的数学公式,便于用单钻孔资料和岩层复平求面理倾斜、求岩层厚度、求地层断距等多个课题。

D ISCUSSION ON THE GENERAL FORMULA FOR EVALUA-TING INCLINATION OF FOLIATION BY THE DATA OF SINGLE DRILL HOLE AND RESUMING HORI-ZONTAL OF STRATUM

Wu Guanglin(1984)improved the mathematical formula(Zimmer, 1963)which evalua-tes inclination of stratum by the data of single drill hole core with scratch mark(see formula(3)and(4)). This paper adjusts the value of 6 and r in formula(3)and(4)by-trigonometrical principle(see formula(1)and(2)), so that we can directly use the relationship between the inclination of drill hole(or normal line of stratum)and the inclination of a plane to reach the purpose of multifunctional calculation Moreover, introducing the known value of(ψ-λ), we can ovoid the handle process of positive and negative, plus and minus of the easy confused values of r before calculating, especially designing, a pair of programs by the calculator which can be designed with more than 38 steps of program(such as CASIO fx-180p etc.), we can evaluate the outcome in about 20 seconds.Formula(1)and(2)are set up the relationship between the inclinations of a line and a plane. When the cross section of the core is horizontal, the inclination of the normal line of the horizontal plane of the drill hole is the triginal inclinating opposite to that of the drill hole(i.e. ψ + 180β), the dip is still. Taking the values of ψ, β, λ, a into formula(1)and(2), we can get D< A. In the same principle, if we know the inclinations of bedding and diagonal bedding of stratum, just exchange the resuming horizontal position of stratun with the inclination of normal line and put it into formula(1)and(2), we can evaluate the inclination of the diagonal bedding. After evaluating the value of A, according to m = L cos A, we can evaluate the thickness(m)of the stratum or the stratigraphic separation(m), where L means the slope distance of the stratum thick ness or slope distance of the bedding planes of the same stratum on both sides of the fault. In addition, we can evaluate the angle relationship between the plane and line, plane and plane, line and line, etc.