The appearance of a seismic record is a function of the signal‐to‐noise ratio. This ratio is expressed quantitatively, but it can not be measured on the record. The quality of the record is expressed by the lineup of events and constancy of character across the record, but is generally not expressed numerically. The appearance of the record is here expressed numerically by the mean phase shift from perfect lineup of various events. A statistical relationship is established between this mean phase shift and the signal‐to‐noise ratio. A seismic record may be approximated by considering the signal to have a sinusoidal waveform and the noise to be a continuous sine wave with the same frequency as the signal and with random phase shift with respect to the signal on various traces. The resulting record will show a random phase shift, the mean value of which is a function of the signal‐to‐noise ratio. A plot of these two values shows that with increasing signal‐to‐noise ratio there is very little change in the mean phase shift, and thus of the quality of the record, until a value of one‐half for the signal‐to‐noise ratio is reached, showing that the noise dominates the record up to this point. For values of the signal‐to‐noise ratio between one‐half and two, there is a large change in the mean phase shift, indicating a strong visual improvement for this range. For a signal‐to‐noise ratio larger than two, the signal predominates visually, and only a slight improvement in quality can be obtained with additional improvements in the signal‐to‐noise ratio. These conclusions are in agreement with experimental data published elsewhere.
Accurate and fast two-step phase shifting algorithm based on principle component analysis and Lissajous ellipse fitting with random phase shift and no pre-filtering