2023/05/08 by Trent DeGiovanni, DeGiovanni, Trent, Fernando Guevara Vasquez +3
Earth and Planetary Sciences · Engineering · Mathematics · #35J25 #35Q61 #35R30 #Electrical and Bioimpedance Tomography #FOS: Mathematics #Geophysical and Geoelectrical Methods #Numerical Analysis (math.NA) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2305.05069
openalex publication_date 2023/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We use thermal noise induced currents to image the real and imaginary parts of the conductivity of a body. Covariances of the thermal noise currents measured at a few electrodes are shown to be related to a deterministic problem. We use the covariances obtained while selectively heating the body to recover the real power density in the body under known boundary conditions and at a known frequency. The resulting inverse problem is related to acousto-electric tomography, but where the conductivity is complex and only the real power is measured. We study the local solvability of this problem by determining where its linearization is elliptic. Numerical experiments illustrating this inverse problem are included.