The physical grounds are discussed for assessing turbulent structures hidden inside the Earth's liquid core by using a time series of the geomagnetic dipole moment obtained from historical and paleomagnetic data. We propose the idea that the time-averaged wavenumber spectra of electric current density at the core-mantle boundary (CMB) and also velocity near the CMB have relation to the frequency spectrum of the dipole moment. We performed computer simulations of a magnetohydrodynamic spherical dynamo to verify this idea. We show that the frequency spectrum of the dipole moment in the simulation is similar to that inferred by paleomagnetic observations. The simulation results indicate that the underlying kinetic energy spectrum is proportional to m ^−5/3 in a high wavenumber range, where m is the azimuthal wavenumber. We speculate that a similar turbulent energy spectrum may exist in the Earth's core with a peak near m = 5.