Fabio Ciabarri

Reservoir Characterization Through Target-Oriented AVA-Petrophysical Inversions with Spatial Constraints

We apply three methods that use different regularization strategies to insert spatial constraints into the seismic-petrophysical inversion. The first method is what we call the structurally constrained inversion (SCI), which directly uses the structural information brought by the seismic stack image to insert geological (structural) constraints into the inversion. The second method is based on anisotropic Markov random field (AMRF) and uses the Huber energy function to reasonably model the spatial heterogeneity of petrophysical reservoir properties. Finally, the last method includes both geostatistical information (describing the lateral variability of reservoir properties) and hard data (i.e. well log data) constraints into the inversion kernel (GHDC inversion). For computationally feasibility, we apply a target-oriented inversion that uses the amplitude versus angle (AVA) responses extracted along the top reservoir reflections to infer the petrophysical properties of interest (i.e. porosity, water saturation and shaliness) for the target layer. In particular, an empirical, linear rock-physics model, properly calibrated for the investigated area, is used to rewrite the P-wave reflectivity equation as a function of the petrophysical contrasts instead of the elastic constants. This reformulation allows for a direct and a simultaneous estimation of petrophysical properties from AVA data. The implemented approaches are tested both on synthetic and field seismic data and compared against the standard method in which each AVA response is inverted independently (laterally unconstrained Bayesian inversion; LUBI). In the case of poor signal-to-noise ratio it turns out that the three considered spatially constrained methods achieve better delineations of reservoir bodies and provide more reliable results than the standard LUBI approach. More in detail, the AMRF recovers sharper geological boundaries than the SCI and GHDC algorithms. The SCI algorithms is more sensitive to data noise, whereas the key advantage of the GHDC consists in analytically providing posterior uncertainties for the model parameters. Finally, for what concerns the computational cost the GHDC and the SCI methods result the most and the least computationally demanding, respectively.

Estimation of reservoir properties from seismic data through a Markov Chain Monte Carlo-AVA inversion algorithm

We formulate the amplitude versus angle (AVA) inversion in terms of a Markov Chain Monte Carlo (MCMC) algorithm and apply it for reservoir characterisation and litho-fluid facies prediction in offshore Nile Delta. A linear empirical rock physics model is used to link the petrophysical properties (porosity, water saturation and shaliness) to the elastic attributes (P-wave velocity, S-wave velocity and density), whereas the exact Zoeppritz equations are used to convert the elastic properties into AVA responses. The exact Zoeppritz equations allow us to take advantage of the long offset seismic acquisition and thus to consider a wide range of incidence angles in the inversion. The proposed algorithm reliably estimates the non-uniqueness of the solution that is the uncertainties affecting the estimated subsurface characteristics (both in terms of litho-fluid facies and petrophysical properties), taking into consideration the uncertainties in the prior information, the uncertainties in the estimated rock-physics model and the errors affecting the observed AVA responses. A blind test, based on available well log information, demonstrates the applicability of the proposed method and the reliability of the results. In addition, comparisons between the results provided by the implemented MCMC algorithm with those yielded by a linear AVA inversion and an analytical approach to facies prediction, show the benefits introduced by wide-angle reflections in better constraining the inverted parameters and in attenuating the noise in the predicted subsurface models. We formulate the amplitude versus angle (AVA) inversion in terms of a Markov Chain Monte Carlo algorithm and apply it for reservoir characterisation and litho-fluid facies prediction in offshore Nile Delta. A blind test, based on available well log information, demonstrates the applicability of the proposed method and the reliability of the results.

Appraisal problem in the 3D least squares Fourier seismic data reconstruction

Least squares Fourier reconstruction is basically a solution to a discrete linear inverse problem that attempts to recover the Fourier spectrum of the seismic wavefield from irregularly sampled data along the spatial coordinates. The estimated Fourier coefficients are then used to reconstruct the data in a regular grid via a standard inverse Fourier transform (inverse discrete Fourier transform or inverse fast Fourier transform). Unfortunately, this kind of inverse problem is usually under-determined and illconditioned. For this reason, the least squares Fourier reconstruction with minimum norm adopts a damped least squares inversion to retrieve a unique and stable solution. In this work, we show how the damping can introduce artefacts on the reconstructed 3D data. To quantitatively describe this issue, we introduce the concept of “extended” model resolution matrix, and we formulate the reconstruction problem as an appraisal problem. Through the simultaneous analysis of the extended model resolution matrix and of the noise term, we discuss the limits of the Fourier reconstruction with minimum norm reconstruction and assess the validity of the reconstructed data and the possible bias introduced by the inversion process. Also, we can guide the parameterization of the forward problem to minimize the occurrence of unwanted artefacts. A simple synthetic example and real data from a 3D marine common shot gather are used to discuss our approach and to show the results of Fourier reconstruction with minimum norm reconstruction.