Systems and methods for detecting downhole tool location inside a borehole

A method of logging a wellbore, comprising:

• logging wellbore data with a sensor in a downhole tool including data related to a formation surrounding the wellbore over a period of time, the logged wellbore data correlated with a time parameter;
• determining, using a processor, a lateral position of the downhole tool with respect to the wellbore over the same period of time, the lateral position of the downhole tool correlated with the time parameter, the determining comprising:
• double integrating, using the processor, an acceleration of the downhole tool over the period of time;
• obtaining, using the processor, a displacement of the downhole tool over the period of time from the double integration;
• fitting, using the processor, the displacement of the downhole tool over the period of time to a best fit curve;
• and
• subtracting, using the processor, the best fit curve from the displacement of the downhole tool over the period of time, the difference between the best fit curve and the displacement of the downhole tool being indicative of the lateral position of the downhole tool relative to the wellbore;
• and
• associating, using the processor, the logged wellbore data with the lateral tool position based on the time parameter, generating calibrated wellbore data based on the lateral position of the tool with respect to the wellbore.

A downhole logging system, comprising:

• a downhole logging tool, comprising:
• a sensor configured to log wellbore data including data related to a formation surrounding a wellbore over a period of time, the logged wellbore data correlated with a time parameter;
• and
• an accelerometer configured to obtain a lateral acceleration of the downhole logging tool over the period of time;
• and
• a processing system comprising one or more processors, the processing system configured to:
• determine a lateral position of the downhole logging tool with respect to the wellbore from the lateral acceleration of the downhole logging tool, wherein the lateral position of the downhole logging tool is correlated with the time parameter, by:
• double integrating, using the processor, the lateral acceleration of the downhole tool over the period of time;
• obtaining, using the processor, a displacement of the downhole tool over the period of time from the double integration;
• fitting, using the processor, the displacement of the downhole tool over the period of time to a best fit curve;
• and
• subtracting the best fit curve from the displacement of the downhole tool over the period of time, the difference between the best fit curve and the displacement of the downhole tool being indicative of the lateral position of the downhole tool relative to the wellbore;
• and
• associate the logged wellbore data with the lateral position of the downhole logging tool based on the time parameter, generating calibrated wellbore data based on the lateral position of the tool with respect to the wellbore.