A comparisonal study in the context of seismic fracture characterization based on effective stiffness and compliance methods

摘要

The use of rock physics modeling in seismic fracture characterization offers a relative advantage of reducing the number of unknown parameters during seismic inversion. This advantage can be used more constructively if the chosen rock physics model is able to relate the parameters of fractures to the effective elastic constants and makes much more physical sense. We have investigated the predictions of commonly used rock physics models (T-matrix, Hudson's model, and non-interacting approximation) for fractured porous media within the context of seismic fracture characterization. Our reservoir model consists of a single set of aligned vertical fractures making a medium of horizontally transversely isotropic (HTI) symmetry. Seismic amplitude versus angle and azimuth (AVAZ) data was computed in the form of reflection coefficients using Ruger's approximation. A Bayesian inversion method is then applied to seismic AVAZ data to estimate the fracture parameters and uncertainty involved in estimates. Our forward numerical experiments suggest that the predictions of non-interacting approximation (NIA) approach and T-matrix approach are equivalent to each other at very small fracture densities (< 0.01), while predictions can be very different at higher fracture densities depending on the choice of aspect ratios. The predictions of NIA and T-matrix approach become same when the effect of interactions cancel at higher fracture densities, but T-matrix predictions make much more physical sense when fractures are degenerated to spherical pores. Hudson's and T-matrix model give exactly the same predictions to the first order in fracture density, while the predictions of second-order Hudson's model give an increasing moduli with an increasing fracture density making no physical sense. From inverse numerical experiments, NIA approach is unable to recover true fracture density and the peak of marginal distribution is always shifted towards the right of the true value. The choice of different rock physics models does not affect the estimation of azimuthal fracture orientation, and it can always be recovered with small uncertainty. It is much safer to use an interacting approach like T-matrix based on above findings within the context of seismic fracture characterization.