An electromagnetic resistivity logging tool comprising: a conductive tool body comprising: a first transmitter comprising: a first transmitter annular cavity that encircles the conductive tool body , a first transmitter surface gap that encircles the conductive tool body and electromagnetically couples the first transmitter annular cavity to an external surface of the conductive tool body , and a first transmitter ring of high magnetic permeability material in the first transmitter annular cavity ; a first receiver comprising: a first receiver annular cavity , a first receiver surface gap that electromagnetically couples the external surface of the conductive tool body to the first receiver annular cavity , and a first high magnetic permeability material in the first receiver annular cavity ; a first transmitter module coupled to opposite sides of the first transmitter surface gap to induce an electric current around the first transmitter annular cavity ; and a first receiver module coupled to opposite sides of the first receiver surface gap to detect currents induced around the first receiver annular cavity . a conductive tool body comprising: a first transmitter comprising: a first transmitter annular cavity that encircles the conductive tool body , a first transmitter surface gap that encircles the conductive tool body and electromagnetically couples the first transmitter annular cavity to an external surface of the conductive tool body , and a first transmitter ring of high magnetic permeability material in the first transmitter annular cavity ; a first receiver comprising: a first receiver annular cavity , a first receiver surface gap that electromagnetically couples the external surface of the conductive tool body to the first receiver annular cavity , and a first high magnetic permeability material in the first receiver annular cavity ; a first transmitter comprising: a first transmitter annular cavity that encircles the conductive tool body , a first transmitter surface gap that encircles the conductive tool body and electromagnetically couples the first transmitter annular cavity to an external surface of the conductive tool body , and a first transmitter ring of high magnetic permeability material in the first transmitter annular cavity ; a first transmitter annular cavity that encircles the conductive tool body , a first transmitter surface gap that encircles the conductive tool body and electromagnetically couples the first transmitter annular cavity to an external surface of the conductive tool body , and a first transmitter ring of high magnetic permeability material in the first transmitter annular cavity ; a first receiver comprising: a first receiver annular cavity , a first receiver surface gap that electromagnetically couples the external surface of the conductive tool body to the first receiver annular cavity , and a first high magnetic permeability material in the first receiver annular cavity ; a first receiver annular cavity , a first receiver surface gap that electromagnetically couples the external surface of the conductive tool body to the first receiver annular cavity , and a first high magnetic permeability material in the first receiver annular cavity ; a first transmitter module coupled to opposite sides of the first transmitter surface gap to induce an electric current around the first transmitter annular cavity ; and a first receiver module coupled to opposite sides of the first receiver surface gap to detect currents induced around the first receiver annular cavity . <EOS>