We discuss approaches to mapping lateral apparent conductivity variations at different periods from magnetic observatory data using multipoint transfer operators as nonlocal functions of the EM response. The multipoint operators provide correlation of three magnetic field components recorded at all observatories. The inversion procedure was applied to Sq observatory data for 1964-68 and records of 30 magnetic storms for 1957-2001. To obtain lateral conductivity patterns, data on diurnal Sq variations and global magnetic storms were processed with the spherical harmonic analysis. The same data were used to estimate the coefficients of first harmonics in the SH series of diurnal lateral variations of Earth's apparent conductivity.