This study attempts to validate a mathematical formalism of introducing attenuation into Schoenberg’s linear slip model. This formalism is based on replacing the real-valued weaknesses by complex-valued ones. During an ultrasonic experiment, performed at a central frequency of [Formula: see text] on a plate-stack model with [Formula: see text]-thick Plexiglas™ plates, the velocity and attenuation (inverse of the quality factor [Formula: see text]) of P-, SH-, and SV-waves are measured in directions from 25° to 90° with the symmetry axis for dry and oil-saturated models and loading uniaxial pressures of 2 and [Formula: see text]. The velocity and attenuation data are fitted by the derived theoretical functions. The values of the real and imaginary parts of the complex-valued weaknesses are estimated. Thereal parts of the weaknesses, which have a clear physical meaning (they affect the weakening of the material), are three times larger for the dry model than for the oil-saturated one. The imaginary parts of the weaknesses are responsible for attenuation; their values are an order of magnitude smaller than the real parts. The derived expressions for angle-dependent velocities and attenuations can be used to distinguish between dry and oil-saturated fractures. In particular, the P-wave attenuation function in the symmetry-axis direction (normal to fracture planes) is different in dry and saturated media. The experiment shows that the plate-stack model is inhomogeneous because of the nonuniform pressure distribution, which degrades the experimental results and creates difficulties in the inversion for the complex-valued weaknesses — particularly in joint inversion of P- and S-wave data.
Static slip model of the M w 9.0 Tohoku (Japan) earthquake: Results from joint inversion of terrestrial GPS data and seafloor GPS/acoustic data
