Frequency and Scale Effects in the Optimization

Previously formulated scaling laws relating acoustic waveforms in boreholes to frequency, tool size and borehole diameter were investigated by repeated logging of the same test interval with different frequencies, and by logging adjacent boreholes of different diameters with the same logging system. Acoustic source frequency bands were centered on approximately 15, 20 and 34 kilohertz. Borehole diameters were Band 17 centimeters for test intervals located at depths ranging from 100 to 400 meters in granite. Test intervals included zones of homogeneous rock and fracture zones that were independently characterized with acoustic televiewer logs and core from the B centimeter borehole. The high frequency transducer produced waveforms dominated by the tube wave mode in the B centimeter borehole, but by a complicated interference pattern produced by the superposition of three normal modes in the 17 centimeter borehole. The two lower frequency transducers produced waveforms in the 17 centimeter diameter borehole with power spectra dominated by the first normal mode. Various methods for picking shear arrivals produced shear velocities in close agreement with known values for all cases except for the data obtained with the high frequency transducer in the 17 centimeter diameter borehole. This result was attributed to the effects of mode superposition and enhanced attenuation of higher frequencies. Tube wave amplitudes constructed from the data obtained with the higher frequency transducer in the B centimeter borehole provided the most unambiguous indication of open fractures. The superior quality of these amplitude logs was attributed to the strong excitation of tube waves, as opposed to the primary excitation of the first normal mode by the two lower frequency transducers in the 17 centimeter borehole.