Transient response of a homogeneous half space with due regard for displacement currents

Abstract

The solution for the half-space model is represented directly in the time domain as computationally stable convolution integrals. The influence of the geoelectric parameters of the earth and transmitter current waveform are then investigated for both infinitesimal and finite-dimensional transmitter loops. Simple empirical formulae are derived to account for the finite duration of the transmitter current turn off time. The whole transient process is divided into three essentially different stages: the propagation stage, the intermediate stage and the diffusion stage. The first is characterized by extremely complicated signal behavior. Apparently, interpretation of the field data using any kind of model fitting inversion algorithm is impossible in this stage. The diffusion stage virtually coincides with that used in the quasi-static case and is, therefore, unsuitable for detecting the dielectric properties of the earth. The intermediate stage is, thus, the only possible time range in which the dielectric properties can be detected using the dynamic characteristics of the signal. The duration of each stage is evaluated depending on the geoelectric parameters of the earth for different transmitter current waveforms.