Premium
The distribution of random segment lengths
Author(s) -
Penland Cecile
Publication year - 1988
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/gl015i012p01405
Subject(s) - random variable , distribution (mathematics) , mathematics , constant (computer programming) , combinatorics , set (abstract data type) , expected value , variable (mathematics) , value (mathematics) , simple (philosophy) , geometry , statistics , mathematical analysis , computer science , programming language , philosophy , epistemology
Choice of the correct distribution of sediment thicknesses is necessary in studying reflection of acoustic rays from randomly layered sediments and in many seismic applications. We consider a set of N segment lengths, {1 i }, i=1, 2, 3,..., N, whose combined length is L. Three cases are of interest: 1) L and N are known constants, 2) the number of segments N is a known constant but L is a random variable with given expectation value , and 3) both N and L are random variables with given expectation values and , respectively. The distribution of segments lengths is calculated for each of the three cases under the assumption that any set {1 i } is as probable as any other set fulfilling the same conditions. The expressions are simple and easy to implement.