Field observations and core data reveal that natural fractures may not be perfectly vertical but are commonly inclined, yielding an effective tilted transversely isotropic (TTI) medium. Neglecting TTI symmetry can lead to erroneous stress prediction results, which are important for hydrocarbon exploration and development. We have developed a Bayesian Fourier coefficient (FC) inversion approach to estimate gravity-induced stress parameters in TTI media, specifically horizontal stress and the differential horizontal stress ratio (DHSR). The gas-bearing reservoir with dipping fractures is modeled as a linearly elastic, homogeneous TTI material. Under the assumption of no lateral strain, we combine fracture-effective medium models with the generalized Hooks law to establish the relationship between gravity-induced stress parameters and TTI elastic and fracture parameters. Based on seismic scatter theory, we derive a linearized PP-wave reflection coefficient and corresponding FC expressions parameterized by P- and S-wave moduli, density, fracture density, and fracture dip in TTI media. Furthermore, we present a Bayesian FC inversion constrained by a joint multivariable Cauchy prior model to estimate these model parameters, which are then used to calculate gravity-induced stress parameters. A synthetic example demonstrates that Bayesian FC inversion under the TTI model assumption produces more reliable estimates of gravity-induced stress parameters compared to those obtained under the horizontal transversely isotropic (HTI) model assumption. Additionally, a real data set from a gas-bearing reservoir is employed to demonstrate the feasibility of our method. Results indicate that our method yields reasonable estimates of gravity-induced stress parameters with good lateral continuity. The proposed method could aid in identifying optimal zones for hydraulic fracturing of a subterranean formation with TTI symmetry.
Read full abstract