An averaging procedure is proposed to account for spectral features of
correlated one-dimensional systems in the presence of nonmagnetic imp
urities. The dynamical spin structure factor for a corresponding rando
m ensemble of Heisenberg chain segments is calculated by exact numeric
al diagonalization. It is shown that a few-mode approximation is suffi
cient to describe the numerical results. By examination of the disorde
r-induced pseudogap, the loss of spectral weight, and the discrete pea
k structures due to smallest-cluster contributions, the underlying imp
urity distribution function can be determined.