Performance of piezoelectric transducers in terms of amplitude and waveform

For seismic physical modeling, piezoelectric transducers (PETs) usually are used as sources and receivers. Their properties affect data significantly, especially if data are processed as seismic data: (1) Strong resonance at one frequency causes a ringy signal and a narrow frequency band; (2) the pronounced directionality effectively limits the offsets at which energy arrives; and (3) because the dimension of the 12-mm transducer is larger than the wavelength (1.5 to 10.0 mm), the recorded waveform changes with offset. To reduce the pronounced directionality of the transducers at ultrasonic frequencies, we designed PETs that have a smaller effective diameter than do traditional ones. To test their applicability for laboratory seismic profiling, we tested their frequency sensitivity, their directionality, and the change of waveform as a function of offset caused by their size relative to the wavelengths. The experiments showed that the PETs produce their best-quality data at frequencies of 350 to 550 kHz and source-receiver offsets of <= 14 cm. For these frequencies, the amplitudes decay to ringing-noise level at incidence angles of < 35 degrees; for a reflector 10 cm deep, that results in a 14-cm source-receiver offset. For these frequencies and offsets, the spacious dimension of the PETs does not cause the waveform to change such that further processing is compromised. We also developed an analytic solution to the changing-waveform problem that predicts the temporal divergence of the signal as an additional resolution limit to the Fresnel effect; the loss of high frequencies is caused not by by attenuation alone, but also by the spacious dimension of the sensors.