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.

SH wave field excited by circumferential shear source in cylindrically double layered media is theoretically analysed.Dispersion equation of cylindrical Love waves (guide waves) has been derived.Both existence condition and existence range of cylindrical Love waves are discussed.Dispersion and excitation of cylindrical Love waves are investigated by numerical calculation.It is discovered that the lowest order cylindrical Love waves have cut off frequency,which differs from Love waves in half space with horizontally double layered elastic media.The asymptotic expression of dispersion equation of cylindrical Love waves as well radius r₁→∞ consistently tends to the dispersion equation in the horizontal half space case,and cut off frequency tends to zero.The transient full waveform calculation is also calculated and illustrated, showing that realizing direct shear wave logs through exciting SH wave would be a more forthright way.