Stress wave attenuation in shock‐damaged rock

The velocity and attenuation of ultrasonic stress waves in gabbroic rock samples (San Marcos, California) subjected to shock loading in the 2 GPa range were studied. Prom P wave velocity measurements we determined the damage parameter D p and crack density ε of the samples and related these to the attenuation coefficient (quality factor) under dynamic strains of 2×10 −7 and at a frequency of 2 MHz using the ultrasonic pulse‐echo method. A fit to the data yields the P wave spatial attenuation coefficient at a frequency of 2 MHz, α p ( D p ) = 1.1 + 28.2 D P (decibels per centimeter). From the relation between the attenuation coefficient and quality factor, the quality factor Q is given by Q −1 = 0.011(1 + 25.6 D p )(1 − D p ) ½ . Using O'Connell‐Budiansky theory relating crack density to velocity, the parameter in Walsh's theory was determined based on experimental data. An approximate method is also proposed to estimate the average half‐length of cracks based on the attenuation measurements.