Step responses for two-dimensional electromagnetic models

Abstract

We have computed the magnetic field step response for a 2-D body in a conductive host via numerical modeling. The numerical method for computing the step response is a modified version of our previous finite difference scheme that computes the impulse response. By comparing the responses of a suite of models, we observe that basically the step and the impulse responses are affected by the host in a similar manner; a homogeneous host delays and attenuates the peak responses, and a conductive overburden accentuates those effects even more. Both the step and impulse response exhibit similar shape of profiles and ability to detect a target. However, the step response exhibits profiles with a smaller dynamic range, and a detectability window that occurs earlier than the impulse response. As a result, measurements of step response require less time, which makes data collection more efficient, and which may minimize natural noise contamination. At early times, the step response of a good conductor stands out, while its impulse response is buried in noise. Therefore, the step response may have some practical advantages over the impulse response, especially for interpretation of a complex model. The late-time decay of 2-D response is closer to a power law than to an exponential. Although it has some limitations, the 2-D modeling is still useful for interpretation.