Parameterized inversion of frequency sounding data in horizontally stratified transverse isotropic medium

Abstract

In this paper, we advance a fast iterative inversion algorithm of frequency electromagnetic sounding data to simultaneously reconstruct the horizontal and the vertical conductivities and interface each bed in the horizontally stratified transversely isotropic (TI) medium. First, applying the analytic expression of the electromagnetic dyadic Green's functions in the TI medium, we realize the forward modeling of the frequency sounding via the fast algorithm of Sommerfeld integral. Then using the perturbation principles and Fourier inversion transform, we establish an efficient computation of Frchet derivatives of the frequency sounding data with respective to all the model parameters. And we use the least square criterion, the normalization and singular value decomposition to iteratively recovery all model parameters. Finally, numerical results validate the inversion algorithms and their antinoise ability.

Designing shielded radio-frequency phased-array coils for magnetic resonance imaging

“…To overcome the extra error introduced by the assumption, finite length coils can be designed without approximation by expanding the current density in a Fourier series. [13] The ill-conditioned integral equation is properly solved with a regularization strategy, [14][15][16] in which penalty functions including minimum power, [17] minimum inductance, [18,19] minimum stored energy, [20] and minimum curvature [21] are applied.…”