SummaryTrace lengths of discontinuities observed on finite exposures are biased due to sampling errors. These errors should be corrected in estimating mean trace length. A technique, which takes into account the sampling errors, is proposed for estimating the mean trace length on infinite, vertical sections from the observations made on finite, rectangular, vertical exposures. The method is applicable to discontinuities whose orientation is described by a probability distribution function. The method requires that the numbers of discontinuities with both ends observed, one end observed, and both ends censored be known. The lengths of observed traces and the density function of trace length are not required. The derivation assumes that midpoints of traces are uniformly distributed in the vertical plane. Also independence between trace length and orientation is assumed. Data on a Pennsylvania shale in Ohio, U. S. A., were used as an example.
[1]
P. J. Pahl,et al.
Estimating the mean length of discontinuity traces
,
1981
.
[2]
Pinnaduwa Kulatilake,et al.
Sampling bias on orientation of discontinuities
,
1984
.
[3]
Kanti V. Mardia,et al.
Statistics of Directional Data
,
1972
.
[4]
S. Priest,et al.
ESTIMATION OF DISCONTINUITY SPACING AND TRACE LENGTH USING SCANLINE SURVEYS
,
1981
.
[5]
Mc Bridges.
Presentation of Fracture Data for Rock Mechanics
,
1975
.
[6]
D. M. Cruden.
Describing the size of discontinuities
,
1977
.
[7]
Nicholas Anthony Lanney,et al.
Statistical description of rock properties and sampling.
,
1978
.