An improved algorithm for determining regularized relaxation time (T-1) distributions from inversion-recovery data obtained from fluid-saturated natural porous media(sedimentary rocks), for which the T-1 distribution may be interpreted as a distribution of pore sizes, is reviewed, Because the selection of an appropriate value for the regularization parameter is automatic, requiring no user intervention or subjective choices, the data processing can be routinely applied, pixel by pixel, to multiple relaxation-weighted imaging data, This is illustrated with inversion-recovery data resolved in one spatial dimension y, obtained from experiments on the depth filtration of clay in sedimentary rock cores, A new kind of image results, of mixed physical dimensions (the (y, log(e) T-1) plane), These images reveal details of the clay filtration process not previously available from simple profiles of a mean T-1, in addition to known artifacts arising from blunders in specimen assembly; in some cases information of interest can be resolved even in the presence of gross artifact. The clay filtration results indicate that although clear reductions in mean T-1 result from invasion of the rock pores by suspended clay, significantly larger clay concentrations would be required to distort the overall T-1 distribution sufficiently to confuse invaded large pores with small pores containing practically immobile fluid. (C) 1995 Academic Press, Inc.