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Inverse Theory and Applications in Geophysics (2nd Edition)
The 2nd Edition of this book brings together fundamental results developed by the Russian mathematical school in regularization theory and combines them with the related research in geophysical inversion carried out in the West. It presents a detailed exposition of the methods of regularized solution of inverse problems based on the ideas of Tikhonov regularization, and shows the different forms of their applications in both linear and nonlinear methods of geophysical inversion. Its the first book of its kind to treat many kinds of inversion and imaging techniques in a unified mathematical manner.
eBook
Dictionary of mathematical geosciences : with historical notes
This dictionary includes a number of mathematical, statistical, and computing terms and their definitions to assist geoscientists and provide guidance on the methods and terminology encountered in the literature. Each technical term used in the explanations can be found in the dictionary which also includes explanations of basics, such as trigonometric functions and logarithms.
eBook
Generalised Latent Assimilation in Heterogeneous Reduced Spaces with Machine Learning Surrogate Models
Reduced-order modelling and low-dimensional surrogate models generated using machine learning algorithms have been widely applied in high-dimensional dynamical systems to improve the algorithmic efficiency. In this paper, we develop a system which combines reduced-order surrogate models with a novel data assimilation (DA) technique used to incorporate real-time observations from different physical spaces. We make use of local smooth surrogate functions which link the space of encoded system variables and the one of current observations to perform variational DA with a low computational cost. The new system, named generalised latent assimilation can benefit both the efficiency provided by the reduced-order modelling and the accuracy of data assimilation. A theoretical analysis of the difference between surrogate and original assimilation cost function is also provided in this paper where an upper bound, depending on the size of the local training set, is given. The new approach is tested on a high-dimensional (CFD) application of a two-phase liquid flow with non-linear observation operators that current Latent Assimilation methods can not handle. Numerical results demonstrate that the proposed assimilation approach can significantly improve the reconstruction and prediction accuracy of the deep learning surrogate model which is nearly 1000 times faster than the CFD simulation.
Journal Article
Geoscience Mathematics Self-Efficacy Scale (GeoMSES) for Majors-Level Undergraduates: Psychometric Data
Self-efficacy is often investigated as a key attitudinal component of academic persistence and performance, and self-efficacy surveys can serve in research models as efficient and non-threatening assessment tools to augment or substitute for achievement or performance measures. The Geoscience Mathematics Self-Efficacy Scale (GeoMSES) builds on prior work in measurement of self-efficacy for mathematics by focusing specifically on students’ capacity to apply mathematical skills to typical problems encountered in majors-level undergraduate geoscience courses or in professional geoscience settings. The scale was developed as part of program evaluation research for a set of learning modules designed to augment existing geoscience curricula. In samples of undergraduate students in courses at 20 institutions (n = 351), data collected using the new 18-item scale had good psychometric properties including normal distributions, high internal reliability and stability, and significant predictive correlations with mathematics performance. Responses to particular items were highly intercorrelated yet not redundant; the questions may be useful when used individually or in subsets for targeted assessment of self-efficacy for particular skills. The GeoMSES may serve as a research or program evaluation tool or as a classroom assessment tool for instructors interested in using student self-efficacy to help them plan or assess their teaching.
Journal Article
Bayesian Gaussian Mixture Linear Inversion for Geophysical Inverse Problems
A Bayesian linear inversion methodology based on Gaussian mixture models and its application to geophysical inverse problems are presented in this paper. The proposed inverse method is based on a Bayesian approach under the assumptions of a Gaussian mixture random field for the prior model and a Gaussian linear likelihood function. The model for the latent discrete variable is defined to be a stationary first-order Markov chain. In this approach, a recursive exact solution to an approximation of the posterior distribution of the inverse problem is proposed. A Markov chain Monte Carlo algorithm can be used to efficiently simulate realizations from the correct posterior model. Two inversion studies based on real well log data are presented, and the main results are the posterior distributions of the reservoir properties of interest, the corresponding predictions and prediction intervals, and a set of conditional realizations. The first application is a seismic inversion study for the prediction of lithological facies, P- and S-impedance, where an improvement of 30% in the root-mean-square error of the predictions compared to the traditional Gaussian inversion is obtained. The second application is a rock physics inversion study for the prediction of lithological facies, porosity, and clay volume, where predictions slightly improve compared to the Gaussian inversion approach.
Journal Article
Reverse annealing for nonnegative/binary matrix factorization
It was recently shown that quantum annealing can be used as an effective, fast subroutine in certain types of matrix factorization algorithms. The quantum annealing algorithm performed best for quick, approximate answers, but performance rapidly plateaued. In this paper, we utilize reverse annealing instead of forward annealing in the quantum annealing subroutine for nonnegative/binary matrix factorization problems. After an initial global search with forward annealing, reverse annealing performs a series of local searches that refine existing solutions. The combination of forward and reverse annealing significantly improves performance compared to forward annealing alone for all but the shortest run times.
Journal Article