Contributions of poroelastic-wave potentials to seismoelectromagnetic wavefields and validity of the quasi-static calculation: a view from a borehole model

In this study, we theoretically analyse the contributions of the four poroelastic-wave potentials to seismoelectromagnetic (SEM) wavefields, verify the validity of the quasi-static calculation of the electric field and provide a method to calculate the magnetic field by using the curl-free electric field. Calculations show that both the fast and slow P waves and the SH and SV waves have non-negligible contributions to the SEM fields. The S waves have indirect contribution to the electric field through the EM conversion from the magnetic field, although the direct contribution due to streaming current is negligible if EM wavenumbers are much smaller than those of the S waves. The P waves have indirect contribution to the magnetic field through EM conversion from the electric field, although the direct contribution is absent. The quasi-static calculation of the electric field is practicable since it is normally satisfied in reality that the EM wavenumbers are much smaller than those of poroelastic waves. While the direct contribution of the S waves and the higher-order EM conversions are ignored, the first-order EM conversion from the S-wave-induced magnetic field is reserved through the continuity of the electric-current density. To calculate the magnetic field on this basis, we separate the quasi-static electric field into a rotational and an irrotational part. The magnetic-field solutions are derived through Hertz vectors in which the coefficients of the magnetic Hertz vector are determined from the magnetic-field continuities and those of the electric Hertz vector originate from the irrotational part of the quasi-static electric field.