An important element of electromagnetic (EM) prospecting is survey design; numerical modeling algorithms may be used to calculate signal‐to‐geologic‐noise (S/N) ratios to compare different survey configurations and measured responses quantitatively. Our models consist of a prismatic three‐dimensional (3-D) target in a conductive half‐space which may contain an overburden conductor; the models are energized by a time‐varying current transmitted in a loop of wire. The signal is the scattered or anomalous response of the target, while the geologic noise is either the response of the half‐space or the anomalous response of the overburden conductor. For typical loop sizes in exploration, the coincident‐loop configuration has a relatively high S/N ratio and thus a relatively high capability to resolve the target in the case of half‐space noise. Measurements made with the horizontal‐loop, moving‐coil configuration can be just as effective if the coil separation is one and one‐half to two times the depth of burial of the target and the transmitting and receiving coils are on opposite sides of the target. For coil positions on one side of the target, the S/N ratio decreases with increasing separation. The advantage in resolving power provided by the coincident loop’s superior S/N ratio diminishes as the size of the loop increases. For the case of noise due to the overburden conductor, the horizontal‐loop configuration with a large coil separation is optimal. If the depth of the target is unknown, the fixed‐loop, roving‐receiver configuration is useful for detecting the target but poor in resolving its depth because its S/N ratio is the least sensitive to the depth. With the fixed‐loop configuration, galvanic effects enhance the detectability of the target in a conductive half‐space, but inhibit detection if an overburden conductor is present. Regarding the S/N ratio, there does not appear to be any advantage in measuring the step response of a 3-D target in a conductive environment versus measuring the impulse response. The shapes of their respective S/N anomalies are essentially the same and the maximum impulse S/N ratio is 10 to 30 percent larger than the maximum step S/N ratio, though it occurs later in time by a factor of about 1.7. Although transient S/N ratios for a 3-D target in a conductive host reach a maximum value and then decrease with increasing time, harmonic S/N ratios do not necessarily reach a maximum value at an intermediate frequency. For all three survey configurations and both types of noise, target depths, and half‐space conductivities studied here, maximum transient S/N ratios are larger than harmonic S/N ratios. Peak step S/N ratios are 30 to 50 percent larger than corresponding in‐phase ratios in the case of half‐space noise, and several times larger in the case of the overburden conductor. A phase rotation of the target’s response due to the conductive host appears to amplify the quadrature S/N ratio relative to the in‐phase S/N ratio. However, in‐phase S/N ratios are always much larger than quadrature S/N ratios over the range of host resistivities used in this study.
Three-dimensional fundamental solutions for transient heat transfer by conduction in an unbounded medium, half-space, slab and layered media