Deconvolution-based enhancement of apparent resistivity and bed boundary identification in borehole resistivity imaging

A well measurement system for locating one or more bed boundaries comprising:

• a downhole tool, wherein the downhole tool comprises:
• a pad;
• an arm, wherein the arm extends the pad from the downhole tool;
• a receiver disposed on the pad;
• and
• a transmitter disposed on the pad;
• a conveyance, wherein the conveyance is attached to the downhole tool;
• and
• an information handling system, wherein the information handling system is configured to:
• measure wellbore wall resistivity with the downhole tool;
• extract a vertical voltage measurement from the wellbore wall resistivity;
• deconvolve the vertical voltage measurement with an impulse response to obtain an apparent resistivity;
• calculate a two-dimensional modeled response of a thin horizontal bed in the two-dimensional plane;
• obtain a two-dimensional ideal system response of the thin horizontal bed;
• and
• construct a two-dimensional impulse response through linearly combining the modeled impulse response and the ideal system response;
• and
• calculate a derivative of the apparent resistivity and find one or more peaks of the derivative to determine the locations of the one or more bed boundaries.

A method for locating one or more bed boundaries in a two-dimensional plane comprising:

• calculating a two-dimensional modeled impulse response of a thin horizontal bed in the two-dimensional plane;
• obtaining a two-dimensional ideal system response of the thin horizontal bed;
• and
• constructing a two-dimensional impulse response through linearly combining the modeled impulse response and the ideal system response;
• and
• determining the location of the one or more bed boundaries using the two-dimensional impulse response.