Based on a model of attenuative cracked rock, we derive a simplified and frequencydependent stiffness matrix in the case that the rock contains aligned partially saturated cracks, and in the stiffness matrix we also involve the effect of pressure relaxation that is a sensitive fluid factor directly influenced by fluid viscosity and saturation. Using perturbation in stiffness matrix for an interface separating two attenuative cracked media and relationship between scattering potential and reflection coefficient, we propose a linearized reflection coefficient in the case of P-wave incidence and P-wave scattering, which is a azimuth- and frequency-dependent function of dry rock elastic property, dry fracture weaknesses and pressure relaxation related parameter. Using difference in the reflection coefficients between azimuthal angles, we derive an expression of Quasi-difference in Elastic Impedance (QδEI) that is mainly affected by dry fracture weaknesses and pressure relaxation related parameter. Using the derived QδEI, we establish an inversion approach of employing frequency-dependent differences in seismic amplitudes to estimate dry fracture weaknesses and pressure relaxation related parameter. Applying the established approach to synthetic datasets, we conclude the approach can obtain acceptable inversion results of dry fracture weaknesses and pressure relaxation related parameter in the case of generated synthetic data containing a moderate signal-to-noise ratio (SNR). Test on a real data set reveals that the inversion results of dry fracture weaknesses provide a reliable tool in fracture prediction, and the estimated pressure relaxation related parameter appear as an additional proof for the discrimination of fluids in cracks.
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