Iterative borehole correction

A non-transitory computer-readable medium including program code that is executable by a processing device for causing the processing device to:

• receive raw signal measurements affected by borehole effects from a downhole tool in a wellbore environment having a borehole size;
• convert the raw signal measurements to ratio signals representing attenuation and phase shift corresponding to the raw signal measurements;
• determine apparent resistivity from at least part of the ratio signals that are the least sensitive to the borehole effects;
• determine mud resistivity based on the apparent resistivity, at least part of the raw signal measurements that are the most sensitive to the borehole effects, and the borehole size;
• determine a true resistivity based on the mud resistivity and the at least part of the ratio signals;
• update the raw signal measurements and the ratio signals based on the true resistivity;
• repeat steps of determining the apparent resistivity, the mud resistivity, and the true resistivity, and updating the raw signal measurements and the ratio signals to determine a corrected true resistivity at least until a ratio of resistivity, which represents a divergence between the apparent resistivity and the corrected true resistivity, is less than a selected threshold value;
• and
• cause an operating characteristic of a well tool to be adjusted based on the corrected true resistivity and the updated raw signal measurements and ratio signals.

A computer-implemented method comprising:

• receiving raw signal measurements affected by borehole effects from a downhole tool in a wellbore environment having a borehole size;
• converting the raw signal measurements to ratio signals representing attenuation and phase shift corresponding to the raw signal measurements;
• determining apparent resistivity from at least part of the ratio signals that are the least sensitive to the borehole effects;
• determining mud resistivity based on the apparent resistivity, at least part of the raw signal measurements that are the most sensitive to the borehole effects, and the borehole size;
• determining a true resistivity based on the mud resistivity and the at least part of the ratio signals;
• updating the raw signal measurements and the ratio signals based on the true resistivity;
• repeating steps of determining the apparent resistivity, the mud resistivity, and the true resistivity, and updating the raw signal measurements and the ratio signals to determine a corrected true resistivity at least until a ratio of resistivity, which represents a divergence between the apparent resistivity and the corrected true resistivity, is less than a selected threshold value;
• and
• causing an operating characteristic of a well tool to be adjusted based on the corrected true resistivity and the updated raw signal measurements and ratio signals.