Abstract
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, {1i}, 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 <L>, and 3) both N and L are random variables with given expectation values <N> and <L>, respectively. The distribution of segments lengths is calculated for each of the three cases under the assumption that any set {1i} is as probable as any other set fulfilling the same conditions. The expressions are simple and easy to implement.
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