GNGTS 2018 - 37° Convegno Nazionale

GNGTS 2018 S essione 3.3 715 In other terms, higher uncertainty occurs at the layer interfaces. Fig. 1c represents the facies profile derived from borehole information: different colors code different litho-fluid facies. From Fig. 1d we observe that the transdimensional inversion is able to correctly locate the layer boundaries that mark the major Ip contrasts. The convergence of the algorithms is proved by the good match between the observed and the predicted data derived on the mode of the final PPD (Fig. 1e). This result shows that an impedance discontinuity will induce a higher impedance uncertainty at the discontinuity but that there is also a higher confidence in the location of the discontinuity itself. The results of the pre-stack inversion are shown in Fig. 3. We again employ actual well log data and a convolutional forward modelling based on the full Zoeppritz equations to compute the synthetic and the predicted data. The source wavelet and the sampling interval are the same as in the first example. Note that also in this case it is crucial setting the admissible parameter ranges around a correct low-frequency model. Figs. 3a-c represent the estimated final PPD for Vp , Vs and density. Again, we observe that they accurately follow the vertical variability of the actual properties. As expected the uncertainty is lower for Vp and higher for Vs and density. Still in this application the algorithm efficiently locates the layer boundaries marking the major elastic contrast (Fig. 3d). Note that in this example the facies profile is the same as in Fig. 2c. Finally, the optimal match between predicted and observed data of Fig. 3e proves the convergence of the algorithm. Conclusions. We showed two examples of transdimensional inversions solved through the rjMCMC algorithm. The first test was a simple post-stack inversion in which only the Ip parameter was considered as unknown (in addition to the number of layers). The second test was a pre-stack inversion in which the Vp , Vs and density are simultaneously inverted. In this last case we extended the equations for the acceptance ratio probability to multiparameter inversions. Both examples proved that transdimensional MCMC inversion can successfully estimate model uncertainty, model dimensionality and subsurface parameters. Our results showed that the inversion uncertainty (i.e. uncertainty in subsurface properties and their locations) is related to the contrast in properties across an interface. That is, there is a trade-off between property uncertainty and location uncertainty: A larger elastic or acoustic discontinuity determines more uncertainty in the model property value, but less uncertainty in the location of the discontinuity. The following step of our research is to apply the implemented algorithm to field data. In this context an efficient parallel implementation will be crucial to make the computational cost of the rjMCMC algorithm affordable. Fig. 3 - Results for the pre-stack inversion. See the text for details.