| Abstract: | Calculations of emf induced in a vertical axis coil by a current step in a straight wire segment of finite length were carried out using an equivalent dipole placed along the source wire. An approximation is valid for homogeneous and layered earth models. The location of the equivalent dipole is calculated by forcing the early- and late-time asymptotes of the transient sounding curve of the equivalent dipole to match those of the finite wire. This approximation works because the early-time asymptote of the emf depends on the component of the receiver position which is parallel to the wire while the late-time asymptote does not. Analytical integration of the early-time asymptote yields an expression for the equivalent dipole location in closed form. The coil can be placed anywhere in the vicinity of the finite wire. Square or rectangular loop sources can be simulated by one or more finite wire segments depending on the source-receiver geometry. The equivalent radius calculated for central loop soundings agrees well with the value derived using a circular loop with the same area as the square loop. Results show that acceptable sounding curves can be generated by the equivalent dipole for coils placed as close as 0.5 source lengths from the finite wire segment. Higher accuracy can be obtained by splitting the finite wire into two or more subsegments. Results for layered models are slightly better than homogeneous earth models when the resistivity increases with depth and slightly worse for models with resistivity decreasing with depth. Approximate calculations are about 10 times less expensive than exact calculations depending on the method used for the numerical integration. |
