Date Approved

2-25-2026

Embargo Period

2-26-2026

Document Type

Thesis

Degree Name

M.A. Mathematics

Department

Mathematics

College

College of Science & Mathematics

Advisor

Thanh Nguyen, Ph.D.

Committee Member 1

Cheng Zhu, Ph.D.

Committee Member 2

Dat Tran, Ph.D.

Keywords

Electromagnetic Induction;Geophysics;Inverse Problems

Disciplines

Mathematics | Physical Sciences and Mathematics

Abstract

Construction of infrastructure in cold regions poses a significant challenge, particularly due to permafrost degradation, which can lead to significant structural damage and deterioration to facilities and transportation systems. In recent years, the issue of geophysical hazard detection has been instrumental in minimizing ground subsidence risks when con- structing infrastructure in cold regions. As a commonly used technology for geophysical applications, electromagnetic induction (EMI) can be used for (i) detecting ground subsurface layers and (ii) characterizing soil types via electrical conductivities. However, EMI technology tends to struggle with lower resolution at lower frequencies and shallow depth of penetration at higher frequencies. Utilizing multi-frequency EMI (MFEMI) sensors is one way to minimize both issues. This thesis addresses the inverse problem of reconstructing the one-dimensional (1-D) electrical conductivity profile of a horizontally layered earth from data measured by an MFEMI sensor. To solve this inverse problem, a least-squares method was used. This method determines the conductivity profile by minimizing the square error between the magnetic field data collected by the MFEMI sensor and simulated data generated by a 1-D forward model. Several techniques for enhancing the stability of the inversion algorithm are presented. Inversion results from simulated datasets demonstrate that the proposed algorithms were able to reconstruct soil conductivity profiles with high accuracy for synthetic data.

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