The influence of a conductive host on two‐dimensional borehole transient electromagnetic responses

Abstract

We have computed transient borehole electromagnetic (EM) responses of two‐dimensional (2-D) models using a direct and explicit finite‐difference algorithm. The program computes the secondary electric field which is defined as the difference between the total field and the primary (half‐space) field. The time derivative of the vertical magnetic field in a borehole is computed by numerical differentiation of the total electric field. These models consist of a thin horizontal conductor with a finite width, embedded in a conductive half‐space. Dual line sources energized by a step‐function current lie on the surface of the half‐space and simulate the long sides of a large rectangular loop. Numerical results substantiate several important features of the transient impulse response of such models. The peak response of the target is attenuated as the resistivity of the host decreases. A sign reversal in the secondary electric field occurs later in time as the resistivity of the host decreases. The peak response and the onset of late‐time behavior are delayed in time as well. Secondary responses for models with different host resistivities (10–1000 Ω-m) are approximately the same at late time. If the target is less conductive, the effects of the host, i.e., the attenuation and time delay, are less. It is readily apparent that there exists a time window within which the target’s response is at a maximum relative to the half‐space response. At late time the shape of the borehole anomaly due to a thin conductive 2-D target appears to be independent of the conductivity of the host. The late‐time secondary decay of the target is neither exponential nor power law, and a time constant computed from the slope of a log‐linear decay curve at late time may be much larger than the actual value for the same target in free space.