GNGTS 2017 - 36° Convegno Nazionale

534 GNGTS 2017 S essione 3.1 geostatistical approaches are being actively investigated, where a priori knowledge is derived from two-point or multi-point statistics (i.e. Zunino et al., 2014). In this work, we apply an inversion method that uses a regularization strategy to insert additional geological (structural) constrains into the inversion procedure. This approach, that we name structurally-constrained inversion (SCI), involves identifying the angle of structural orientation at all inverted locations. We then construct a series of regularization operators that are locally aligned parallel and perpendicular to the structural orientation. These operators force the model to honour the local structure. For computationally feasibility reasons, we limit our attention to a target-oriented inversion, which uses the amplitude versus angle (AVA) response extracted along the top reflection of the investigated reservoir, to infer the petrophysical properties of the reservoir layer. In particular, the implemented AVA-petrophysical inversion uses a previously defined linear rock-physics model (RPM) to rewrite the linear Aki and Richards (1980) AVA equation in terms of contrasts of petrophysical properties at the reflecting interface. This reformulation allows us to directly derive the petrophysical properties around the target zone from AVA data. The proposed approach is applied to 3D onshore seismic data for the characterization of a clastic, gas-saturated, reservoir. The method. The Aki and Richards (1980) equation expresses the P-P wave reflection coefficients ( Rpp ) as a function of the incidence angle ( θ ) under the assumption of weak elastic contrasts at the reflecting interface: (1) where Vp and Vs are the P-wave and S-wave velocities, respectively, ρ is the density, whereas α Vp ( θ ), α Vs ( θ ), and α ρ ( θ ) are given by: (2) where and are the average P-wave and S-wave velocities over the interface. In matrix notation equation 1 can be written as: Rpp = ADm (3) where the matrix D is the differential matrix operator, while the sparse matrix A contains discrete samples of α Vp (θ) , α Vs (θ) and α ρ (θ) . To rewrite Eq. 1 in terms of petrophysical contrasts at the reflecting interface, we use a linear rock-physics model that links the natural logarithm of the elastic properties to the petrophysical properties of interest: (4) where e is a given elastic properties (i.e. Vp , Vs or density), whereas Sw , Sh and represent water saturation, shaliness and porosity, respectively; a , b , c , and d are numerical coefficients that express the influence of each petrophysical properties in determining a given elastic property. This linear rock-physics model can be derived by means of a multilinear stepwise regression applied to available well log data. By combining Eq. 1 with the previously defined rock-physics model (Eq. 4), we can re-write the P-P wave reflection coefficients as: (5) where fφ , f Sw and f Sh express the influence of each petrophysical property in determining the reflection coefficient at different incidence angles. Using the matrix notation, we can re-write Eq. 5 as: Rpp = ABDr = FDm = Gm (6) where B is a sparse matrix containing the numerical coefficients a , b , c , and d of Eq. 4, F contains discrete time samples of fφ , f Sw and f Sh , while the vector m contains the petrophysical properties of interest m =[ Sw , Sh , φ ] T . After deriving the forward modelling operator, we can define the objective function E ( m ) to be minimized. It can be written as: