Session: 16-01-01: Government Agency Student Poster Competition

Paper Number: 150110

150110 - Geometric Phase-Based Inverse Problems for the Prediction of Changes in Permafrost Properties Due to Climate Change 

As a result of climate change, the Alaskan permafrost’s thawing and freezing cycles have been rapidly altering over the last several years. In order to monitor the changes in the permafrost’s properties, seismic data can be used for remote sensing. This characterization of the permafrost changes based on seismic signals requires solving an inverse problem that identifies permafrost model parameters based on measured seismic signals. The solution of this inverse problem is complicated by the presence of numerous sources of uncertainties, such as properties of trees, which act as resonators, and variations in soil properties such as ice composition. It is therefore essential to include sources of uncertainties to obtain a robust solution of the inverse problem and predict the changes in permafrost properties . Many quantities, such as time of arrival of seismic waves, could be used to solve this inverse problem. However, in this work, we propose a method based on the geometric phase. Geometric phase is an appealing quantity because it might be sensitive to changes in properties of the medium in which the phase is calculated, therefore helping with the identifiability of the inverse problem parameters. For example, the geometric phase changes abruptly with respect to the seismic waves frequency around tree resonances. A simplified forest model, with a soil modeled as a mass-spring lattice and trees modeled as mass-spring chains, is used to compute the geometric phase. To solve the inverse problem based on the geometric phase, we developed a stochastic optimization that accounts for discontinuities in measured responses. This methodology, which includes several sources of uncertainties, is based on Gaussian processes as a surrogate of our numerical model; clustering of responses and support vector machines to divide the parameter space based on phase changes; and an adaptive sampling scheme that identifies optimal model parameter values at which the model should be evaluated to minimize the number of model calculations needed to converge to a solution of the inverse problem. The poster will provide solutions of inverse problems involving uncertainty in frequency, stiffness of the trees, and stiffness properties of the soil. The optimization problem involves the minimization of the difference between the expected value of the geometric phase changes and a target value. The mean value and standard deviation of the ground stiffness are used as random optimization variables, whereas frequency and properties of the tree stiffness are used as random parameters. The expected values are computed using Monte Carlo simulations efficiently evaluated using the Gaussian process approximations of the geometric phase.

Presenting Author: Harry Mayrhofer University of Arizona

Presenting Author Biography: Harry Mayrhofer is a graduate student in the Physics department at The University of Arizona.

Authors:

Harry Mayrhofer University of Arizona
Samy Missoum University of Arizona
Pierre Deymier University of Arizona
Keith Runge University of Arizona
Araceli Hernandez Granados University of Arizona