Abstract: A function that represents data points is derived by creating a matrix (e.g., a Hankel matrix) of an initial rank, where the matrix contains the data points. Singular values are derived based on the matrix, and it is determined whether a particular one of the singular values satisfies an error criterion. In response to determining that the particular singular value does not satisfy the error criterion, the rank of the matrix is increased and the deriving and determining tasks are repeated. In response to determining that the particular singular value satisfies the error criterion, values of parameters that approximate the function are computed.

Abstract: To update a model of a subterranean structure, a partial decomposition is computed of an operator that is used to compute a parameterization representing the update of the model. The partial decomposition of the operator is selected from among a partial eigendecomposition of a Fisher information operator, and a singular vector decomposition of the operator. A term based on additional information is combined with the partial decomposition of the operator to derive an update of the model.