In seismic physical modeling, piezoelectric transducers are commonly used as generators and detectors of acoustic waves. Physically, these transducers are thin discs with diameters on the order of 1 to 13 mm. In a typical scale-model experiment where the acoustic medium is water, dominant frequencies are on the order of 500 kHz, and wavelengths are on the order of 3 mm. Even the smallest transducers have diameters which are significant fractions of a wavelength. Because of this, the radiation and reception patterns of disc transducers have pronounced directivities due to wave interference effects. Amplitude information acquired by physical modeling must be corrected to account for both radiation and reception directivities before doing any AVO/AVAZ analysis. This report presents a numerical procedure for determining the directivities of disc-shaped transducers in an acoustic medium such as water. As well, a compact analytical formula for the directivities is derived. Figure 1a shows that the two methods gave almost identical directivities in the x-z plane.
Using the University of Calgary Seismic Physical Modeling facility, ultrasonic CMP gathers were recorded over an acrylic slab immersed in water. Figure 1b shows that the physically-modeled reflected amplitudes, after corrections for directivity, were in good agreement with predictions from both the plane-wave and spherical-wave Zoeppritz equations for incident angles less than critical. The agreement with the spherical wave prediction was good even beyond the critical angle.
View full article as PDF (1.84 Mb)