Table 5.

Distribution parameters of joint characteristics used for the simulated populations

Population*Bivariate normal†Normal†Lognormal†Joint number
Orientation mean (deg.) varianceTrace length mean (m) varianceAperture mean (mm) variance
a0180∠55‡ 4000, 3503.5‡ 1.53‡ 400200
a1180∠55§ 4000, 3503.5§ 1.53§ 400200
b1240∠45‡ 4000, 3503.5§ 1.53§ 400200
c1180∠55§ 4000, 3502.0‡ 1.53§ 400200
d1180∠55§ 4000, 3503.5§ 1.510‡ 400200

*Each population is stored as a 200 (joint numbers/rows) × 4 (joint characteristics/columns) matrix. A row vector represents four characteristics (dip direction/dip angle, trace length and aperture) of a joint. A column vector represents the distribution form of a characteristic of 200 joints.

†Representing distribution forms used to generate corresponding joint population. These distribution forms are used only to demonstrate the functions of the proposed method. Other distribution forms also are acceptable in the method.

‡Representing the data generated in the first time.

§Representing the data generated in the second time with the same parameter.

The data generated in the second time may have some differences from the data generated in the first time although both are generated through the same parameter. Two populations generated through the same parameter of a characteristic in one time will be same (including sequences); for example, the column vectors of trace length of populations a1, b1 and d1 are same.