We have developed and numerically tested quantitative misfit criteria for comparison of seismograms. The misfit criteria are based on the time-frequency representation of the seismograms obtained as the continuous wavelet transform with the analyzing Morlet wavelet. The misfit criteria include time-frequency envelope and phase misfits, time-dependent envelope and phase misfits, frequency-dependent envelope and phase misfits, and single-valued envelope and phase misfits.
We tested properties of the misfit criteria using canonical signals. The canonical signals, taken as the reference signals, were specifically amplitude, phase shift, time shift, and frequency modified to demonstrate the ability of the misfit criteria to properly quantify the misfits and recognize the character and cause of the misfits between the reference and modified signals. In all cases the misfit criteria properly quantified and characterized the misfits.
The misfit criteria were also calculated for four different numerical solutions for a single layer over half-space (the scecloh.3 problem) and the reference fk solution. The misfit criteria provided useful insight into the misfits between individual numerical solutions and the reference solution.
The standard rms misfit matches the single-valued envelope misfit only in the case of a pure amplitude modification of the signal. In all other cases rms considerably overestimates the misfits and does not characterize them.