Abstract: Impedance and thickness of one-layered medium in annular space between casing pipe and formation are selected as two inversion parameters.Equations with the tangent function form of phase-shift and equations with the arctangent function form of phase-shift are regarded as the target functions, respectively.Linear least-square inversion method of impedance and thickness is established.Investigation of error functions and inversion results of synthetical data are given.It is found that linear least square inversion method with the arctangent function form of phase-shift is a stable and effective method which can avoid multi-minimal points and the error function only has one minimum value corresponding to the true value of impedance and thickness.Reversion results are not sensitive to the initial value of impedance and thickness.

Key words: reflected ultrasonic waves, phase-shift, tangent function, impedance, thickness