System and method for determining formation characteristics using electrical arc modeling

A method, comprising:

• performing a pulsed drilling operation in a wellbore using:
• a drill bit including a first electrode and a second electrode electrically coupled to a pulse-generating circuit to generate electrical arcs between the first and second electrodes based on pulse drilling signals received from the pulse-generating circuit during pulsed drilling operations, the electrical arcs occurring at random azimuthal locations between the first and second electrodes;
• and
• a sensor to record responses to electromagnetic waves or acoustic waves produced by the electrical arcs;
• obtaining a first plurality of measurements representing first responses recorded by the sensor during the pulsed drilling operation;
• generating a model of a source of the electrical arcs based on the first plurality of measurements;
• obtaining an additional measurement representing a second response recorded by the sensor during the pulsed drilling operation;
• determining a first characteristic of a formation in proximity to the drill bit using an inversion based on the model and on the additional measurement;
• determining a respective value of at least the first characteristic of the formation at at least one azimuthal angle;
• and
• constructing an image depicting values of at least the first characteristic of the formation with respect to the at least one azimuthal angle.

A sensor analysis system, comprising:

• a processor;
• and
• a computer readable storage medium storing program instructions that when read and executed by the processor cause the processor to:
• receive a first plurality of measurements representing first responses to electromagnetic waves or acoustic waves recorded by a sensor during a pulsed drilling operation in a wellbore, the electromagnetic waves or acoustic waves produced by electrical arcs generated between first and second electrodes of a drill bit during the pulsed drilling operation based on pulse drilling signals;
• generate a model of a source of the electrical arcs based on the first plurality of measurements;
• obtain an additional measurement representing a second response recorded by the sensor during the pulsed drilling operation;
• determine a first characteristic of a formation in proximity to the drill bit using an inversion based on the model and on the additional measurement determine a respective value of at least the first characteristic of the formation at at least one azimuthal angle;
• and
• construct an image depicting values of at least the first characteristic of the formation with respect to the at least one azimuthal angle.