The anomalous fields from a buried cylindrical inhomogeneity in an otherwise uniform half‐space are analyzed. The problem is rendered two‐dimensional by assuming that the uniform line source of current is parallel to the subsurface cylinder. The multipole scattered field coefficients are obtained from the numerical solution to the associated singular Fredholm integral equation of the second kind. The horizontal magnetic field amplitude, the vertical magnetic field phase, and the amplitude and phase of the ratio of horizontal to vertical magnetic fields are shown to be diagnostic of the location of the inhomogeneity. The results have possible applications to electromagnetic location in mine rescue operations and to geophysical prospecting.

It is shown that the dominant singularity of the electric Green's dyadic is proportional to the irrotational part of the unit delta dyadic. Contrary to statements in the literature, this term does not vanish identically away from the source. Therefore in the full three-dimensional eigenfunction expansion of the Green's dyadic, one must account for the contribution due to the irrotational vector wave functions, even in a source free region. In the recent literature on this subject this point is in controversy. The apparent contradications are discussed and the differences resolved. COMPONENTOF ELECTRIC GREEN'S DYADIC 963

Hunka, J.F., and Barber, T.D.,* Schlumberger Well Services;Rosthal, R.A., Logging While Drilling; Minerbo, G.N., Schlumberger-Doll Research; Head, E.A., *Howard Jr., A.Q., and Hazen, G.A., Schlumberger Well Services; and Chandler, R.N., Etudes and Productions Schlumberger Abstract A new induction logging system has been developed that represents a fundamental departure from the technology and application of previous induction-based resistivity tools. The AIT* Array Induction Imager tool abandons the concept of fixed-focused sensors and is constructed of several independent arrays with main coil spacings ranging from a few inches to several feet. The AIT tool is operated simultaneously at several frequencies; in-phase and quadrature signals are acquired from every array at the frequencies suitable for that array length. The presented log curves range in median depth of investigation from 10 in. to 90 in. Each log uses all the measured channels, combined with a nonlinear processing algorithm, to virtually eliminate environmental effects such as cave effect, shoulder effect, and skin effect. Reliable logs can be obtained even in difficult cases of bad borehole and extreme invasion. These logs are available at resolution widths of 6 ft and 2 ft. Because of the large number of measurements made by the AIT tool, deep two-dimensional quantitative imaging of formation resistivity is possible. These images expose bedding and invasion features in a clear and quantitative manner. The resistivity in the part of the formation undisturbed by fluid invasion is accurately obtained without making any prior assumptions about the invasion profile. New invasion description parameters conveying more profile. New invasion description parameters conveying more meaningful information about the presence of transition zones and annuli are a result of this imaging capability. Using established interpretation principles, this quantitative information about the invasion can be converted into a two-dimensional image of water saturation. Introduction In recent years, the most troublesome environmental features of induction tools have been corrected by tools such as the Phasor* Induction tool. Vertical resolution has been improved from 8 ft to 2 ft; automatic correction for borehole effect is available at the wellsite; and inversion of the three measurements (deep induction, medium induction, and Spherically Focussed (SFL*) log or laterolog) into R, estimates has been made automatic. With the elimination of the grosser environmental distortions, some remaining effects that can introduce errors in difficult logging situations have received more attention. The most troublesome of these are: Cave effect in irregular boreholes, andDetermining Rt in the presence of invasion transition zones. Cave effect is produced when an induction toolen counters a washout or cave in a borehole with high formation resistivity to mud resistivity contrast. Induction arrays normally have response peaks very close to the tool that are very sensitive to conductivity. These responses are cancelled in smooth boreholes, but they do not cancel in rugose holes. Large excursions on the logs can occur when one of these sensitive areas encounters a washout or other irregularity. These "hot spots" are present in all previous induction tools. An invasion transition zone is any radial resistivity profile other than a simple step profile. Transition zones profile other than a simple step profile. Transition zones can be produced by any fingering or mixing of mud filtrate with connate fluids over some radial distance or by the formation of an annulus. Dual induction tools can detect some transition zones, and recent field log evidence suggests that transition zones may be more common than previously realized. previously realized. P. 295

A general method of obtaining the free space particular solution and the required homogeneous solution decomposition in closed region problems in electromagnetics is described. This allows the singular nature of the kernel function to be handled analytically. The remaining homogeneous solution which is expressed in an eigenfunction series is rapidly convergent. The method should be of particular value in vector integral equation formulations where the dyadic kernel is highly singular. The method is applied to the rectangular cavity dyad.

Electromagnetic modeling of an induction sonde (1–100 kHz) in a dipping‐bed environment is a 3-D problem. The capability for such an analysis is necessary for interpretation of oil‐well logs in offshore environments where most holes are deviated. 3-D geometrical effects require vector field analysis. The method accounts for transverse magnetic mode (TM) coupling arising from surface charges deposited by eddy currents passing through bed boundaries. If borehole and invasion effects are included, the only available rigorous analytical methods are finite elements or finite‐difference techniques. These approaches require large‐scale computing. In contrast, our method is approximate and is an extension of the geometrical‐factor theory and Born approximation. The variational method does not require matrices and is numerically simpler than the more rigorous finite element method. The method uses a new electric field vector integral equation developed by Chew. The formulation accounts for low‐frequency behavior at bed boundaries where current channeling and surface charge phenomena dominate the interactions. The receiver voltage has two parts, a volumetric term [Formula: see text] and a surface term [Formula: see text]. The term [Formula: see text] reduces to the Born result when the dip angle goes to zero; [Formula: see text] accounts for the surface charge effect and is only significant when the receivers are in close proximity to a bed boundary. The local nature of the charge interaction results from double scattering events, which are necessary to produce this effect. The charge term is second order as explained intuitively in terms of polarization. The bed boundary interaction is proportional to the factor [Formula: see text], where [Formula: see text] is the dip angle, and [Formula: see text] and [Formula: see text] are the conductivities of the adjacent beds. Since the charge interaction is strongly nonlinear in conductivity, common induction log interpretation, which assumes linearity, is expected to fail near bed boundaries. Results for dip angles up to 60 degrees for variational results and eigenfunction solutions for the case of no borehole or invasion show good agreement. A few 3-D results are computed with simultaneous layering, dip, and invasion.