SUMMARY Nominally continuous data in space and/or time is obtained in various observations in geophysics. Due to an enhanced technology of computers, we can now invert such observed data with a very high sampling rate. Densely sampled observed data are usually not completely independent of each other, and so we must take this effect into account. As for seismic waveform data, they have at least temporal correlation due to the effect of inelastic attenuation of the Earth. Taking the data covariance into account, we have developed a method of seismic source inversion and applied it to teleseismicP-wave data of the 2003 Boumerdes-Zemmouri, Algeria earthquake. From the comparison of the final slip distributions inverted with and without the covariance components, we found that the effect of covariance components is crucial for a data set of higher sampling rates (≥5 Hz). If we neglect the covariance components, the inverted results become unstable due to overestimation of the information from observed data. So far, it has been widely believed that we can obtain a finer image of seismic source processes, by inverting waveform data with a higher sampling rate. However, the covariance components of observed data originated from inelastic effect of the Earth give a limitation on the resolution of inverted seismic source models.