Numerical models employed in ground VLF modeling use a normally incident (homogeneous) plane wave as a primary field. We show that these models are not directly applicable to modeling the impedance and wavetilt in the air, quantities needed in the interpretation of airborne VLF resistivity measurements. Instead, the primary field must be replaced by an inhomogeneous plane wave incident on the ground at an angle close to 90 degrees in order to provide the correct behavior of the apparent resistivities in the air. VLF magnetic polarization parameters, however, can be modeled in the air using the normally incident plane wave as a primary field. We also show that the plane‐wave analysis provides the same attenuation characteristics for the wavetilt in the air that is predicted by the Norton’s surface wave obtained by using the vertical electric dipole as a source. Use of the inhomogeneous plane wave introduces the vertical component of the electric field in the model. A 2‐D modeling technique based on the network solution is used to demonstrate the effects of the vertical electric field in the H‐polarization case. The vertical electric field generates charge distributions on the horizontal boundaries of conductors. In the case of a vertical sheet‐like conductor, these charges cause a slight asymmetry in apparent‐resistivity anomalies. Attenuation characteristics of various VLF anomalies with altitude are also presented. The H‐polarization anomalies attenuate much more rapidly in the air than those for E‐polarization due to the difference in the dominating source of EM fields in each polarization.
Fast inhomogeneous plane wave algorithm for the fast analysis of two-dimensional scattering problems
