GNGTS 2023 - Atti del 41° Convegno Nazionale

Session 3.3 ______ ___ GNGTS 2023 The downside of this procedure is that derivatives need to be evaluated for each sampled model, and with large model and data spaces the Hessian and Jacobian matrices become computationally intractable. A suitable strategy to reduce the computational complexity of this type of inverse problem is to compress the model and data spaces through appropriate reparameterization techniques, such as the DCT . The DCT of a signal indicates the energy distribution of the signal in the frequency domain spectrum. Usually, most of the energy of the signal is expressed by low-order DCT coefficients and consequently, this mathematical transformation can be used for model compression, which is accomplished by setting the coefficients of the base function terms beyond a certain threshold equal to zero. For the estimation of the optimal number of DCT coefficients needed to approximate the model and data spaces, we quantified how the variability of the model and data changes as the number of DCT coefficients varies: we have computed the variability as the ratio between the variance of the approximated model and data and the one of the uncompressed model and data (Aleardi, 2021). SYNTHETIC INVERSION We have applied the proposed GB-MCMC elastic FWI method to a 2D synthetic model with two layers and with some lateral velocity variations. The model parameters to be estimated are the Vp and Vs values, and we are considering the density constant all over the model. The grid size for generating the observed data is 280( nx 0 ) x 44( nz 0 ), with a grid spacing of 0.44 x 0.44 m , so 24640 parameters form the full model space. A Ricker wavelet with the peak frequency at 15 Hz is used as the source. We have simulated 5 shots equally spaced along the horizontal axis and each shot is recorded by 101 receivers with a 1.2 m receiver interval. Sources and receivers are all placed at the surface. The time interval is of 0.4 ms and the registration time is 300 ms . Uncorrelated Gaussian white noise is added to the observed data. The elastic forward modelling has been performed using Devito , a new domain-specific language for implementing high performance finite difference partial differential equation solvers (Louboutin, 2019). In order to reduce the computational cost of the calculation of the Jacobian matrix using the finite difference approach, we have used the Multiprocessing Python package, which allows to parallelize the execution of a function across multiple input values, distributing the input data across processes (data parallelism). The data and models must be projected onto the DCT space, where the MCMC sampling runs.