Abstract The correlation coefficient has inadequacies as a metric for comparison of seismic data to presumed truth in the form of synthetic seismograms or well logs. It is not a direct measure of the information content of a prediction, nor the shared information between the prediction and perfect data. All else being equal, information content (useful or not) of seismic data decreases monotonically with decreasing bandwidth, but the correlation coefficient may vary differently. Quantities from information theory such as cross entropy, variation of information, and channel capacity are measures that can aid in the assessment of the information contained in a prediction and are amenable for use as loss functions in machine learning and other applications. We demonstrate these ideas on real and synthetic data.
Castagna et al. (Thu,) studied this question.