GNGTS 2018 - 37° Convegno Nazionale

714 GNGTS 2018 S essione 3.3 Synthetic inversion tests. We start with the post-stack inversion in which only the Ip values (in addition to the number of layers) are considered as unknowns (Fig. 2). We use actual well log data to compute the observed stack trace via a 1D convolutional forward operator. A 45-Hz Ricker wavelet and a sampling interval of 0.002 s are employed. Note that the prior probability p ( m | n ) is defined around a very smoothed version of the true impedance. This low-frequency trend is the so-called low frequency model. Indeed, it is well known that the definition of a correct low-frequency model is crucial in any inversion strategy based on a convolutional operator. We note that the mode of final estimated PPD correctly reproduces the vertical variability of the actual Ip values (Fig. 2a). In Fig. 2b we represent the sample-by- sample width of the 95% confidence interval derived from the PPD of Fig 1a. We observe that the higher uncertainties coincide with the higher Ip contrasts (especially at 1375 and 1385 ms). Fig. 1 - Flowchart of the implemented transdimensional MCMC inversion. Iter max and chain max represents the maximum number of iteration and chains, respectively. N iter and N chain are the actual iteration and chain numbers, respectively. Fig. 2 - Results for the post-stack inversion. See the text for details.