Frequency and time-domain analytical expressions are derived for the electromagnetic field response of a resistive layer inserted in an otherwise homogeneous whole-space as observed in the vicinity of an electric dipole source. The analysis of closed-form solutions demonstrated that at near-source-receiver offsets, the spectral and spatial distribution of the fields is better described by a superposition of images, associated with the dipolar character of the charges distributed in the boundaries, rather than the guided mode behavior dominating the response in the far offset regime. Approximate solutions of the fields in the frequency domain were derived using the saddle point method of integration. The formulas describing the fields were in good agreement with semianalytical calculations. However, a lower frequency bound was found, below which the expressions are inaccurate, and thereby they cannot be used to obtain time-domain solutions. A kernel modulation scheme was used instead, which yields an infinite series representation for the fields. The expressions thus derived produce accurate fields to very low frequencies, and thereby they were also used to obtain time-domain formulas. The analysis indicated that for a vertical electric dipole (VED) excitation, the late time response of the image field associated with the charge density induced on the upper boundary appears to cancel the direct field, thus providing the response of the layer. For a horizontal electric dipole (HED) source, the superimposed contributions of the transverse electric (TE) and transverse magnetic (TM) modes appeared to oppose the image field, resulting in the direct field dominating over the response of the layer, and thereby masking any sensitivity to the properties of the layer in this configuration.

This paper compares the sensitivity to, and resolution of the properties of a resistive target using marine controlled source electromagnetic measurements, with the frequency domain horizontal source-receiver method and the recently introduced vertical source-receiver time domain configuration. The problem is addressed from an analytical stand point, i.e. by analyzing closed form solutions of the 1D spatial and spectral distribution of the fields, and numerically, from 1D inversion of synthetic datasets as well as from 2D simulations of the response of finite lateral extent reservoirs. The 1D analysis demonstrates that the far offset measurement of the standard CSEM has more sensitivity to the presence of the resistive layer than the vertical source-receiver time domain measurement done at close offsets from the source. Closed form solutions derived for the guided mode of the fields yields increasing sensitivity of the standard CSEM configuration for thin resistors and increasing offsets from the source. The image term solution for the fields observed in the near offset vertical source-receiver configuration yields increasing sensitivity with decreasing frequency, i.e. towards the late times of the measurement. For the simplified single layer model a threshold offset is establish beyond which the standard CSEM method is more sensitive. However for a more realistic setting of a finite extent 2D reservoir this report shows that the guided mode driving the far offset sensitivity is only dominant for wide enough targets. The vertical source receiver is more sensitive to smaller targets, where the guided mode does not develop, and it has better resolution to the lateral extent of the reservoirs.

This paper studies the problem of electromagnetic fields observed outside of an infinite metallic casing due to dipolar excitations inside the pipe. Closed-form expressions are derived for the hertz vector potential driving the solution of the boundary value problem. The results indicates that the fields outside the casing are due to a distribution of vertical dipoles that decay in strength away from the true source. Analytical expressions are also obtained for the induced source distribution, as a function of the geometry and electric properties of the system. For the transverse magnetic mode (electric dipole source), the sources represent an electric current channeled vertically along the casing, whereas for the transverse electric mode (magnetic dipole source), they represent a distribution of induced magnetic moments. The strength of the current channeling decays exponentially away from the source, whereas the strength of the induced magnetic moment drops within the first few meters. The expressions obtained for the fields due to a magnetic dipole reveals that the effect of the casing yields a multiplicative complex constant, which attenuates the dipolar-type field. This effect has been observed experimentally in crosswell surveys, but it has never been formally proven. The fields due to an electric dipole excitation describe an inhomogeneous cylindrical surface wave propagating and attenuating in the radial and vertical directions.

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 resistive layer 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.