Fracture weaknesses and ﬂuid factor are important parameters to identify the location of underground fractures and the type of ﬂuids. An indirect method to predict fractures and discriminate the ﬂuid is ﬁrst using azimuthal seismic data to estimate the normal and tangential fracture weaknesses and then calculating the fracture ﬂuid factor. The indirect method may create some uncertainties, and the estimated fracture weaknesses are affected by both the ﬂuid and fractures. We demonstrate a direct method to estimate Lamé constants and fracture weaknesses of the dry fractured rock, and ﬂuid term from partially incident angle-stack seismic data, based on azimuthal elastic impedance (EI) parameterization and inversion. Combining stiffness parameter perturbations and scattering function, we ﬁrst derive a linearized PP- wave reﬂection coefﬁcient for the case of an interface separating two horizontal transverse isotropic (HTI) media, which can isolate the effects of fractures and ﬂuids. Using the derived reﬂection coefﬁcient, we propose the expression of azimuthal EI. The estimation of ﬂuid term and fracture weaknesses is implemented as a two-step inversion, which includes inversion of partially-incident-stack seismic data for EI at different azimuths, and the estimation of ﬂuid term and fracture weaknesses from the inverted results of azimuthal EI using a Bayesian Markov-chain Monte Carlo (MCMC) method. Tests on synthetic and real data can conﬁrm the stability of the proposed inversion method, and the inversion method appears to be useful for fracture detection and ﬂuid discrimination.
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