GNGTS 2018 - 37° Convegno Nazionale

718 GNGTS 2018 S essione 3.3 of this vertical constraint decreases as the maximum order of the Legendre polynomials increases. However, petrophysical properties are also mutually correlated. This additional constraint is imposed by minimizing the following objective function: (3) where C d is the data covariance matrix, d obs are the observed data derived from logged elastic property values, d pre are the data predicted on the current subsurface model m pre , and C m is the a-priori model covariance matrix that is determined from available well log information. The optimal value for the damping parameter γ is estimated from the L-curve. In the following test, I use a maximum degree for the Legendre polynomials equal to 40 resulting in 41×3 coefficients to be estimated. Fig. 1a shows the results for the considered well. This example shows that the final predicted model fairly reproduces the observed data and reliably predicts the porosity, water saturation and shaliness values associated with the reservoir layer located at 880 ms in two-way-time. As expected the accuracy of the results decreases from porosity, to shaliness and to water saturation that is the parameter that plays the minor role in controlling the observed data. To further demonstrate the reliability of the proposed inversion method, I perform an additional test in which a more standard approach to global optimization is used for inverting the data pertaining to the first blind well. In particular, I now consider Fig. 1 - Seismic-petrophysical inversion: Comparison of the results and data gathers provided by the proposed (a) and the standard approach (b).