薄圆管压电换能器瞬态响应及其在井中激发声场

The transient response of a cylindrical piezoelectric transducer and the excited wavefield in a borehole

针对声波测井中采用的柱状薄圆管压电换能器,提出一种研究换能器响应的解析方法.该方法考虑了轴向与径向振动之间的耦合作用,导出置于耦合液体中压电换能器径向位移满足的微分方程和频域传递函数,比较分析了不同激励源作用下换能器的位移响应特性.利用波数域实轴积分法,计算了换能器在弹性地层井孔中激发的声场,研究了不同地层中的波形差异.与前人在假定声源强度的模型下只能求出波场的相对幅度不同,本文得出在一定激励电压作用下换能器在井孔中激发声场的幅度值.这为说明声波测井响应信号的强弱及仪器的声系设计提供了依据,对估计动电效应测井信号的强弱有参考意义.

An analytical method is proposed to study the transient response of a cylindrical thinwalled 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 seismoeleetrie logging signals.