Randomness of Geophysical Log Data – Fractal Approach

Geophysical data allows for measuring a change in petrophysical parameters thought a whole well length. They often exhibit a chaotic behaviour which is difficult to describe and finding a pattern is near impossible. A potential measure of this chaos – correlation dimension – has been examined in the study. The research was carried out for the log data from Williston Basin, USA and the Norwegian Lille-Frigg oil field on the North Sea. Sonic log (DT), neutron porosity log (NPHI), deep resistivity log (LLD) as well as density log (RHOB) were utilised in the study. A python program has been written to measure the change in correlation dimension. Instead of calculating a one value of a correlation dimension for a whole log, a moving range algorithm was developed and implemented. It is based on defining a range for which the dimension is calculated and then moving the range on a geophysical log. In addition, a graph representing change of a correlation dimension with depth is drawn. The influence of data range and range shift were measured. Over 100 correlations have been carried out between rock properties and their dimension. The results indicate that the correlation dimensions change throughout the whole geophysical log and correlate with themselves and other curves in a moderate degree. It allows for determining ranges where a data set is not chaotic. The research shows that properly set range should have a reasonable and representative amount of data points, while the shift should be small for accurate results. Presented analysis creates perspectives for a more precise rock formation description and possible correlation between different oil wells within a single reservoir.