Correlating Petrophysical Well Logs Using Fractal‐based Analysis to Identify Changes in the Signal Complexity Across Neutron, Density, Dipole Sonic, and Gamma Ray Tool Types

Abstract:

Typical petrophysical well log correlation is accomplished by manual pattern recognition leading to subjective correlations. The change in character in a well log is dependent upon the change in the response of the tool to lithology. The petrophysical interpreter looks for a change in one log type that would correspond to the way a different tool responds to the same lithology. To develop an objective way to pick changes in well log characteristics, we adapt a method of first arrival picking used in seismic data to analyze changes in the character of well logs. We chose to use the fractal method developed by Boschetti et al[1] (1996). This method worked better than we expected and we found similar changes in the fractal dimension across very different tool types (sonic vs density vs gamma ray). We reason the fractal response of the log is not dependent on the physics of the tool response but rather the change in the complexity of the log data. When a formation changes physical character in time or space the recorded magnitude in tool data changes complexity at the same time even if the original tool response is very different. The relative complexity of the data regardless of the tool used is dependent upon the complexity of the medium relative to tool measurement. The relative complexity of the recorded magnitude data changes as a tool transitions from one character type to another. The character we are measuring is the roughness or complexity of the petrophysical curve. Our method provides a way to directly compare different log types based on a quantitative change in signal complexity. For example, using changes in data complexity allow us to correlate gamma ray suites with sonic logs within a well and then across to an adjacent well with similar signatures. Our method creates reliable and automatic correlations to be made in data sets beyond the reasonable cognitive limits of geoscientists in both speed and consistent pattern recognition.

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[1] Fabio Boschetti, Mike D. Dentith, and Ron D. List, (1996). A fractal-based algorithm for detecting first arrivals on seismic traces. Geophysics, Vol.61, No.4, P. 1095-1102.

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