見かけの傾斜から真の傾斜を求める数値処理法

抄録

This paper presents the principles and BASIC program to estimate numerically the ‘true dip’ of a bed (real dip and strike of a bed) from two sets of the ‘apparent dips’ of the beds exposing on geological sectionssuch as cliff walls.
1. Introducing a term “apparent bed” as a line of intersection between abed and a section (which may be inclined at any angle), we classifyed theapparent dip into three types:
type I : apparent dip-angle of the apparent bed observed from the front of the section.
type II : inclination-angle of the apparent bed measured on the section.
type III : two locations of outcrops of the bed.
2. We defined two characteristic vectors in the section; a dip-vector of the apparent bed dv (a vector which is oriented in the direction parallel to the apparent bed), and a normal-erector of the apparent bed ea (avector which is normal to the apparent bed and also is oriented in the direction toward the upper side of the bed) . The dip-vector and thenormal-vector of the apparent bed can be obtained from the observationof each type of the apparent dip.
3. The outer product of two dip-vectors of the apparent bed dv gives thenormal-vector of the bed e (a vector which is normal to the bed and alsois oriented in the direction toward the upper side of the bed) . The truedip (dip and strike) of the bed can be calculated from the components of the normal-vector e. The normal-vectors of the apparent bed ea are usedto determine the sense of the resultant normal-vector e, because thenormal vector must be directed toward the upper side of the bed.
4. The presented BASIC program calculates a true dip from two sets of apparent dips and also illustrates the calculation processes and theresult on a stereo-net diagram.