Inversion of electromagnetic well-log data at microwave frequencies

Earth formations can be modeled as a layered medium with each layer having its own electromagnetic properties (e.g., conductivity, permittivity). In a typical well-logging operation, a hole - about 15 to 30 cms in diameter - is drilled through the Earth formation to a depth that may extend to a few kilometers. To measure conductivity and permittivity of the formation, a sensor, consisting of an array of transmitters and receivers, is lowered in the borehole. We consider an antenna array, with two transmitters and two receivers, symmetrically located, operating at 1 GHz. The transmitters are sequentially energized and the phase and attenuation between receivers are measured. The measured phase and attenuation are then inverted for formation properties, namely layer-thickness, conductivity and dielectric constant. We describe a multi-channel Wiener deconvolution method to extract formation properties from the measured phase shift and attenuation. A nonlinear anisotropic diffusion filter to smooth intra-layer variations follows the deconvolved results.