Convolution effect on TCR log response curve and the correction method for it

Through-casing resistivity (TCR) logging has been successfully used in production wells for the dynamic monitoring of oil pools and the distribution of the residual oil, but its vertical resolution has limited its efficiency in identification of thin beds. The vertical resolution is limited by the distortion phenomenon of vertical response of TCR logging. The distortion phenomenon was studied in this work. It was found that the vertical response curve of TCR logging is the convolution of the true formation resistivity and the convolution function of TCR logging tool. Due to the effect of convolution, the measurement error at thin beds can reach 30% or even bigger. Thus the information of thin bed might be covered up very likely. The convolution function of TCR logging tool was obtained in both continuous and discrete way in this work. Through modified Lyle-Kalman deconvolution method, the true formation resistivity can be optimally estimated, so this inverse algorithm can correct the error caused by the convolution effect. Thus it can improve the vertical resolution of TCR logging tool for identification of thin beds.