The transient response of a cylindrical piezoelectric transducer and the excited wavefield in a borehole
薄圆管压电换能器瞬态响应及其在井中激发声场

An analytical method is proposed to study the transient response of a cylindrical thin-walled piezoelectric transducer as used in petroleum well logging. The radial displacement transfer function of the transducer is derived, with the coupling effects of axial and radial vibrations being considered. The responses of the radial displacement to different excitation pulses are analyzed. Full acoustic waveforms on the borehole axis excited by the transducer are calculated with the real-axis integration method in different formations. Unlike the literature work, where only the relative amplitude from the source with assumed intensity is available, the current work gives absolute amplitude of the acoustic response for a certain excitation voltage. The work offers an effective theory on the explanation of the intensity of the acoustic logging response signals and on the instrument design as well. The results are also useful in the evaluation of the amplitude of the seismoelectric logging signals.