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.

It is shown how attenuation changes with porosity according to Biot theory.Frame modulus versus porosity relation based on experiment data set is adopted.It is found that attenuation coefficient of the fast compressional wave increases first,then decreases smoothly to zero,and finally increases sharply.To explain the zero-attenuation phenomenon,the relative motion between the solid frame and the pore fluid is studied when an elastic wave propagates in a fluid-saturated porous medium.It is shown that there can be porous formations that satisfy the dynamic compatibility condition.When a fast compressional wave propagates in such formations,there will be no relative motion between the two constituent phases,and thus no attenuation.A related revelation from this mechanism is about electrokinetic effect in porous media:there can be no coupling between the fast compressional wave and the electromagnetic wave in a dynamically compatible medium,even when there are surplus charges in the saturating fluid of the formation.

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.