Systems and methods are provided to obtain multiple resistivity measurements using a resistivity tool eccentered and rotating in a wellbore, which may be used to ascertain information relating to a drilling fluid in the wellbore. One such system includes a resistivity tool and data processing circuitry. The resistivity tool may become eccentered in a wellbore filled with drilling mud at least when the wellbore is at least partially deviated. The resistivity tool may also rotate within the wellbore and to obtain at least two resistivity measurements at different corresponding angles of rotation within the wellbore. The data processing circuitry may determine a mud phase angle by comparing the resistivity measurements obtained by the resistivity tool.
