I understand you have a signal measured at a different spatial position and you want them to be correlated but you are unable to find that distance successfully. Changing reference station causes zero crossing changes and defeats the objective.
You have already tried using “cross correlation” and “Pearson coefficients” to find the distance. You may establish an axis perpendicular to these signals to get the shortest distance to these signals from the axis plane. Furthermore, you can refer to the following steps to determine the distance at which signals will be measured such that they stay correlated:
- Spatial autocorrelation: Calculate the spatial “autocorrelation function” (ACF) for each signal. The ACF measures the correlation between a signal and its shifted version at different lags. By analyzing the ACF for each signal, you can identify the lag at which the autocorrelation drops below a certain threshold. This lag can estimate the distance at which the signals become uncorrelated.
- Mutual information: Mutual information is a measure of the mutual dependence between two signals. It captures both linear and nonlinear relationships. By calculating the mutual information between the reference signal and each of the other signals, you can identify the point at which the mutual information drops below a certain threshold. This can provide an estimate of the distance at which the signals lose their correlation.
- Spatial correlation analysis: Instead of focusing on individual zero crossings or specific lag values, you can perform a spatial correlation analysis across all pairs of stations. This involves calculating the correlation coefficient or another similarity measure for each pair of stations and then examining the spatial pattern of correlations. By analyzing the spatial distribution of correlations, you may be able to identify a distance or spatial range at which the correlations consistently drop below a certain threshold.
Hope this helps.
