Seismic wave reflection amplitudes are used to detect fluids and fracture properties in reservoirs. This paper studies the characterization of a vertically fractured fluid-filled reservoir by analyzing the reflection amplitudes of P-waves with varying incident and azimuthal angles. The reservoir is modeled as a horizontal transversely isotropic medium embedded in an isotropic background, and the linearized P-waves reflection coefficient are considered. The conditioning of the inverse problem is analyzed, and fracture density is found to be the best conditioned parameter. Using diffraction tomography under the Born approximation, an inversion procedure is proposed in the transformed k–ω domain to detect fracture density variations within the reservoir. Seismic data are rearranged in pairs of incident and reflected plane waves, enlightening only one spectral component of the fracture density field at a time. Only the observable spectral components are inverted. Moreover, working in the transformed domain, picking reflection amplitudes is not required. An example of the inversion applied to a synthetic data set is presented. The limitation of source and receiver numbers and the finite bandwidth of the wavelet produce a loss of resolution, but the overall fracture density variations are recovered correctly.

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