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Complex permittivity formulation for induced polarization effect in transient electromagnetics
  • Marco Oliva-Gutiérrez,
  • Luis Alonso Gallardo
Marco Oliva-Gutiérrez
Universitat Politècnica de Catalunya

Corresponding Author:[email protected]

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Luis Alonso Gallardo
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We have studied the relevance of permittivity as an indicator of the IP effect in transient electromagnetics. The approach is based on a mathematical formulation of a dielectric model, where we assume that the free electrons of the induced current are weakly bound electrons included in a complex frequency-dependent permittivity. We combine this dielectric function to Maxwell’s equations in order to obtain a modified Helmholtz equation whose new term contains the polarization parameters of the medium. The resultant convolution in Ohm’s Law was solved by the concept of memory variables transforming the convolution into a set of time-dependent ODE, where the storage of the full-time series of the electric field is no longer needed. The final model allows any Cole-Cole Model (CCM) in the electromagnetic fields through the Debye Function Expansion (DFE) and makes it possible to incorporate additional information into the canonical property of conductivity through the dispersive permittivity.