Rise times of attenuated seismic pulses detected in both empty and fluid‐filled cylindrical boreholes

Fourier‐Bessel theory is used to derive filters representing the influence of both empty and fluid‐filled cylindrical boreholes on particle motion induced in rock by a plane P-wave incident perpendicular to the borehole axis. For wavelengths greater than 10 times the borehole circumference, the effect of the borehole on particle motions is shown to be negligible; thus the results have little relevance for the long wavelengths commonly encountered in earthquake seismology. The results are, however, relevant to the study of stress wave propagation at ultrasonic frequencies in rock masses. For small wavelengths (αa > 3.0) the filter representing particle motion on the wave incident site of an empty borehole reduces to a linear phase filter which increases all amplitudes by a factor of 2 while the filter representing fluid stress at the center of a fluid‐filled borehole may be reduced to simple mathematical expressions. Experimental results were obtained for the interaction of a stress wave with either accelerometers mounted in an empty borehole or a hydrophone located centrally in a fluid‐filled borehole. Both theory and experiment show a similar distortion in the rise time of the pulse traveling past the borehole.