A resistivity tool for investigating a wall of a borehole drilled with a non-conductive mud includes a tool body adapted to be incorporated in a logging-while-drilling tool assembly; a resistivity sensor disposed on the tool body, wherein the resistivity sensor comprises a sensor pad supporting a current injector electrode, a current return electrode, and an array of measurement electrodes, and a circuitry for controlling current injection from the current injector electrode and for measuring voltage difference between electrodes in the array of measurement electrodes, wherein the current injector electrode and the current return electrode are disposed near opposite ends of the sensor pad and the array of measurement electrodes is disposed between the current injector electrode and the current return electrode, wherein the sensor pad is constructed of an insulating material and includes a conductive shielding member, or wherein the sensor pad is constructed of a conducting material and includes insulating sections around the electrodes.