GNGTS 2022 - Atti del 40° Convegno Nazionale

GNGTS 2022 Sessione 3.3 507 DEEP PRECONDITIONERS FOR SEISMIC INVERSE PROBLEMS WITH APPLICATION TO DEBLENDING V. Lipari 1 , P. Bestagini 1 , M. Ravasi 2 , S. Tubaro 1 1 Dipartimento di elettronica informazione e Biongegneria, Politecnico di Milano, Italy 2 Earth Science and Engineering, King Abdullah University of Science and Technology, Arabia Saudita Introduction. Seismic processing and imaging generally involve ill-posed inverse problems which require regularization techniques to drive their solutions with available prior knowledge. Among these techniques we can include sparsity promoting inversion coupled with fixed basis sparsifying transforms. The underlying idea is that in a transformed domain seismic data and seismic images can be represented with few non-zero coefficients. Despite the remarkable results achieved by these techniques, they rely on handcrafted assumptions imposed on the useful signal to be recovered. Therefore, they sometimes fail to adapt to the highly complex features of seismic data. Alternatively, data driven sparse dictionaries can be learned directly from the dataset. In recent years, sophisticateddata-drivenbasedmethods basedondeep learning techniques have been introduced for seismic processing tasks. However, despite the effectiveness of CNN based methods most of these techniques face generalization issues and need to collect proper training field datasets or to build appropriate synthetic training datasets, which is a hard task. Deep preconditioners (Ravasi, 2021) represent an alternative approach that combines the advantages of sparsifying inversion with the ability of deep CNNs to learn compact representations of N-dimensional vector spaces. First, a convolutional autoencoder (AE) (Goodfellow et al. , 2016). is trained to learn a sparse representation of the desired outcome. Subsequently the trained decoder is used as a non-linear preconditioner for the inverse problem to be solved. The effectiveness of the method is demonstrated through the problem of seismic deblending. Method. We aim at inverting a geophysical linear problem of the form: y = Ax where x ∈ m and y ∈ n are model and data vector, respectively; and A : m → n is a linear mapping between these two spaces. Unfortunately, most geophysical problems are ill-posed (i.e. several models explain the data) and require some form of prior information, to find a stable and satisfactory solution. A standard way is to find a regularized least square solution of the form: and R is a regularization operator. Alternative to regularization is preconditioning, where the search is carried out in a projected space: and the solution is then found as xˆ = Pzˆ . The design of regularizers and preconditioners is usually driven by experience. A popular choice of preconditioner is a transform that projects the model into a space where the model can be explained by a small number of non-zero coefficients leading to sparsity promoting inversion (Candes, 2006). However, fixed coefficient transforms sometimes