Chapter 4 Modelling induction log responses in 3D geometries using a fast integral equation approach

• Published in: Methods in Geochemistry and Geophysics Vol. 35; pp. 55 - 63
• Main Authors: Avdeev, D.B., Kuvshinov, A.V., Pankratov, O.V., Newman, G.A., Rudyak, B.V.
• Format: Book Chapter
• Language: English
• Published: Elsevier Science & Technology 2002
• ISBN: 9780444504296; 044450429X
• ISSN: 0076-6895
• DOI: 10.1016/S0076-6895(02)80086-5

We present modelling results for the electromagnetic logging problem. Our numerical solution calculates the log responses for three-dimensional earth models that include a deviated/tilted borehole, including invaded beds. The solution accounts for both displacement currents and electrical anisotropy of the formation. Our solution exploits the modified iterative dissipative method that is based on a convergent Neumann series expansion. To achieve solution convergence, the conventional scattering integral equation is modified using a spectral shift and a change of variable, which are based on an inequality for the Green's dyadic function. For deviated boreholes in layered formations, there are no known analytical solutions. Therefore, our solution was first validated against the mode-matching solution for a vertical borehole model in a layered formation. In this model we varied the eccentricity of the 50 MHz two-coil sonde. Comparison to the 10 kHz, 160 kHz and 5 MHz responses from a staggered-grid finite difference solution was then conducted for a 45-degree deviated borehole that crosses a formation boundary. All comparisons showed excellent agreement, and demonstrate verifiable induction log responses in the presence of displacement currents and deviated boreholes. Results for a sonde with a resistive case are also reported.