Analytical expressions are derived for the electromagnetic (EM) fields observed in the vicinity of a vertical dipole source, due to the response of resistive layer embedded in a conductive background. The analytical expressions for the fields observed at zero offset are validated by comparison to the numerical integration of the Bessel-Fourier integral. It is found that the structure of the fields is remarkably different compared to that observed at far offsets, which is described by the residue of the Bessel-Fourier integral at the position of the so called resistivelayer pole. Indeed the cylindrical wave front behavior of the far offset fields does not apply anymore at close distances from the source. The derived expressions show that at near offsets it is not possible to identify a preferential radial propagation direction, where furthermore the energy flux appears to change direction with offset. The spectral and spatial distribution of the fields are very similar to that of the image of the primary source, this suggests that the response of the layer can be replaced by a another superimposing image component.
As the CSEM method applied to off-shore hydrocarbon exploration matures, the interest grows around designing more effective surveys by seeking a compromise between measurement configurations and sensitivity to the response of the target. In particular a vertical electric dipole source and vertical electric field time domain measurement has been proposed (Barsukov et al., 2007) to discriminate deep resistive targets even at very close transmitter receiver offsets (fig. 1). Naturally the fundamental understanding of the behavior of the structure of the electromagnetic (EM) fields arising in this (and other) configuration has also received a great deal of attention. In this context the concepts developed in the early work of Sommerfeld (1909) and Banos (1966) have been revisited (Weidelt (2007)) in order to explain the spatial distribution of the so called EM airwave field (fig. 2(a)), which appears at long offset measurements, in horizontal source and receiver configuration. FurthermoreWeidelt (2007) has introduced the concept of a resistive layer wave guide which propagates EM energy laterally inside the resistive layer, and leaks out diagonally (fig. 2(b)) into the more conductive surrounding medium. In this context it is easy to show that the dominant contribution of the long offset response of the resistive layer is that arising as a residue of a pole singularity in the integral kernels of the TM polarization of the fields. Therefore for example, for a vertical electric dipole excitation, the electric field and magnetic fields observed above the layer are described by, (super-indices (S) and (I) indicate source and image component) while inside the layer are given by, where the superposition of upward and downward progressing fields is evident. In both eqns.1,2 the behavior of the Hankel function at far offsets (|?0r >>1) determines the cylindrical and radially propagating-decaying (r-1/2e-i ?0r) character of the contribution of the pole, which is representative of a slower attenuating guided type of wave.
