The geomagnetic activity of the D_st index is analyzed using wavelet transforms and it is shown that the D_st index possesses properties associated with self-affine fractals. For example, the power spectral density obeys a power-law dependence on frequency, and therefore the D_st index can be viewed as a self-affine fractal dynamic process. In fact, the behaviour of the D_st index, with a Hurst exponent H≈0.5 (power-law exponent β≈2) at high frequency, is similar to that of Brownian motion. Therefore, the dynamical invariants of the D_st index may be described by a potential Brownian motion model. Characterization of the geomagnetic activity has been studied by analysing the geomagnetic field using a wavelet covariance technique. The wavelet covariance exponent provides a direct effective measure of the strength of persistence of the D_st index. One of the advantages of wavelet analysis is that many inherent problems encountered in Fourier transform methods, such as windowing and detrending, are not necessary.