GNGTS 2024 - Atti del 42° Convegno Nazionale

Session 3.3 GNGTS 2024 constant model for the density. However, for brevity, only the Vs results will be discussed because this is notoriously the most informed model parameters when considering surface wave data. Parallelizaton of the calculaton of the Jacobian matrix across diferent servers was employed to reduce computatonal costs. The seismic data and velocity models must be projected onto the DCT space, where the MCMC sampling runs. For the data, we have notced that 60x45=2700 retained coefcients resulted in a relatve percentage error with respect to the observed data lower than 8%, reducing the the full 250x48x3=36000-D data space to a 60x45x3=8100-D domain (where are considering the same number of DCT coefcients for all the three shots). For the model space instead, 20 and 7 coefcients along the two DCT spatal dimensions explain more than 95% of variability of the model obtained extending the borehole data in the horizontal directon, reducing the 150x276x2=82800-D elastc space to an 20x7x2=280-D domain (i.e., we are considering the same number of DCT coefcients for both the Vp and Vs models). We need to point out that this compression not only reduces the dimensions of the vectors and matrices involved in the inversion procedure (such as the gradient and the Hessian), but also greatly reduces the number of forward evaluatons needed to construct the Jacobian matrix and so, the overall computatonal cost of the algorithm. The implementaton used six cores on an Intel® Core™ i7-8700 CPU @ 3.20GHz. Each iteraton, including computng the Jacobian, the gradient, the Hessian matrix and drawing a sample, takes approximately 8m wall clock tme. A total of 4.000 iteratons for a single chain required approximately 6 days. In our case we used fve MCMC chains to sample the model space, which started from very simple two layered velocity models. Figures 1a and 1c show, respectvely, one of the startng models of the chains used for the GB-MCMC inversion and the posterior mean model, computed considering all the chains. The prior informaton for the Bayesian inversion (prior mean vector and prior covariance matrix) are directly derived from the two layered model displayed in Figure 1a. Fig. 1 (a) One of the startng models used for the GB-MCMC inversion; (b) Posterior standard deviaton map; (c) Posterior mean Vs model considering the fve chains; the dashed black line corresponds to the positon of the available borehole data; (d) The borehole data together with the velocity profle of the predicted model at the horizontal positon of 10m (black).