INFORMATION ABOUT THE ERRORS IN THE OBSERVATIONS IS ESSENTIAL TO SOLVE ANY INVERSE PROBLEM; OTHERWISE, IT IS IMPOSSIBLE TO ESTIMATE TRUE MODEL. IN PRACTICE, HOWEVER, ESPECIALLY WITH SINGLE REALIZATION OF EXPERIMENT, ONE SELDOM HAS A DIRECT ESTIMATE OF THE DATA ERRORS. HERE WE EXPLOIT THE TRADE-OFF BETWEEN DATA PREDICTION AND MODEL OR DATA STRUCTURE TO DETERMINE BOTH MODEL-INDEPENDENT AND MODEL BASED ESTIMATES OF THE NOISE CHARACTERISTICS FROM A SINGLE REALIZATION OF THE DATA. NOISE ESTIMATES WITH OTHER INFORMATION ABOUT MODEL PARAMETERS ARE THEN USED TO CONSTRUCT CONFIDENCE INTERVALS ABOUT THE FINAL MODEL THAT ARE TIGHTER THAN PRIOR INFORMATION AND AGREE WITH PRIOR CONSTRAINTS. WE ILLUSTRATE OUR METHODS WITH SYNTHETIC EXAMPLE OF VERTICAL SEISMIC PROFILING (VSP).