In highly dimensional model spaces, it is common practice reparametrizing the parameter space to reduce the dimension of the inverse problem. However, part of the information in the original parameter space is lost in the reduced space, thus meaning that the model parameterization must constitute a compromise between model resolution and model uncertainty. We use the Discrete Cosine Transform (DCT) to reparametrize linear and nonlinear Bayesian amplitude versus angle (AVA) inversions. In this framework the unknown parameters become the series of coefficients associated to the DCT base functions. In this work, linear inversions allow for an exact quantification of the trade-off between model resolution and posterior uncertainties with and without the model reduction. Then, we employ the DCT to reparametrize non-linear AVA inversions numerically solved through the Differential Evolution Markov Chain and the Hamiltonian Monte Carlo algorithms. The linear inversions demonstrate that the same level of model accuracy, model resolution, and data fitting can be achieved by employing a number of DCT coefficients much lower than the number of model parameters lying in the unreduced space. The non-linear inversions demonstrate that an optimal model compression significantly reduces the number of models needed to attain stable posterior estimations.

Discrete Cosine Transform for Parameter Space Reduction in Linear and Non-Linear AVA Inversions

Aleardi Mattia;Alessandro Salusti
2021-01-01

Abstract

In highly dimensional model spaces, it is common practice reparametrizing the parameter space to reduce the dimension of the inverse problem. However, part of the information in the original parameter space is lost in the reduced space, thus meaning that the model parameterization must constitute a compromise between model resolution and model uncertainty. We use the Discrete Cosine Transform (DCT) to reparametrize linear and nonlinear Bayesian amplitude versus angle (AVA) inversions. In this framework the unknown parameters become the series of coefficients associated to the DCT base functions. In this work, linear inversions allow for an exact quantification of the trade-off between model resolution and posterior uncertainties with and without the model reduction. Then, we employ the DCT to reparametrize non-linear AVA inversions numerically solved through the Differential Evolution Markov Chain and the Hamiltonian Monte Carlo algorithms. The linear inversions demonstrate that the same level of model accuracy, model resolution, and data fitting can be achieved by employing a number of DCT coefficients much lower than the number of model parameters lying in the unreduced space. The non-linear inversions demonstrate that an optimal model compression significantly reduces the number of models needed to attain stable posterior estimations.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1060990
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