GNGTS 2024 - Atti del 42° Convegno Nazionale

Session 3.3 GNGTS 2024 reduce this problem is to increase the ensemble size (Roe et al., 2016). The DCT, in this sense, helps in lowering the number of ensemble individuals needed to avoid collapse and, as a consequence, the number of forward modelling computatons. We perform the compression through a 2D DCT, applying it in both horizontal and vertcal directons. The choice of the number of DCT coefcients to retain in each directon is made through an analysis of the variability of the original signal that it is preserved afer the compression. The variability is here defned as the rato between the standard deviatons of compressed and uncompressed signal (see Aleardi et al., 2021a). Synthetc inversion We applied the ES-MDA acoustc FWI to a porton of the synthetc Marmousi benchmark model. The considered model extends 4.3 km horizontally and 1.340 km in depth. This is the porton that has been inverted, and it lies below a water layer 0.260 km deep, considered when computng the synthetc seismograms. The inverted porton was discretzed with a grid characterized by a spacing of 20 m in both horizontal and vertcal directon. This results in 216 nodes along the horizontal directon and 68 on the vertcal one. A Ricker wavelet with a central frequency of 5 Hz is considered as the source signature. We simulated 5 shots equally spaced along the horizontal axis, from the lef to the right edge of the considered area and recorded by 200 receivers, with a constant receiver interval of 21.6 m. The tme interval is 4 ms and the record length is 3 s. We added to the observed data uncorrelated Gaussian noise, with a standard deviaton equal to 10% of the standard deviaton of the noise-free data. We observed that retaining 30 DCT coefcients along the frst (horizontal) dimension and 15 along the second (vertcal) one was enough to properly represent about 95% of the variability of the original V p model. In this way, we can compress the model space from 68x216=14688-D to 15x30=450-D. A similar analysis on the seismic data led us to use 55 DCT coefcients along the horizontal and 65 along the vertcal directon. Considering that we simulate 5 shots, the original 751x200x5=751000 parameters are reduced to 65x55x5=17875 in the compressed data space. A test phase has been performed to assess the minimum number of models within an ensemble needed to obtain a good reproducton of the main features of the original velocity model. We notced that a good compromise between the quality of the results and the computatonal tme was possible considering ensembles of 10000 models. Increasing this number does not lead to a considerable improvement of the inversion result, whilst it highly afects the computatonal cost of the procedure. We further observed that 10 iteratons of the algorithm are enough to reach convergence. The computatonal tme required by the EB-FWI is approximately 8 days. The acoustc forward modeling has been performed using Devito, a python package that implements a high performance fnite diference partal diferental equaton solver (Louboutn et al., 2019). We run the serial code implementng the inversion on a server equipped with Intel® Xeon® Silver 4114 CPU @ 2.20 GHz. Fig.2 shows the result of the inversion, comparing the original model, the corresponding model afer the DCT compression, the model used as mean of the prior distributon and the mean of the