Frequency-dependent ambient seismic source inversion based on cross-correlation waveforms

Ambient seismic signals contain rich information about environmental events and Earth structure. A number of studies have investigated the extraction of environmental, e.g. oceanographic, information from these signals. Moreover, it has been examined how to access them directly for tomographic imaging rather than by the approximation of empirical Green's functions. As several studies have shown, well-constrained models of the ambient source distribution are key for the development of such applications.

Here, we present a method to invert for the spatially and temporally varying power spectral densities (PSDs) of these sources. In a previous study, we adapted techniques from adjoint full waveform inversion to this problem in order to determine the relative geographic importance of the sources of Earth's hum described by a generic Gaussian PSD. We now extend the source parametrization to spatially varying PSDs expressed as a series of orthogonal tapers in the frequency domain.

Based on this parametrization, noise cross-correlations are computed with the help of a stored library of Green's functions between the receivers and all possible source locations to account for the propagation of seismic waves. Observed cross-correlations are then iteratively inverted for the space- and frequency-dependent ambient source model.

To constrain the spectral shape of the PSDs, we require measurements on the cross-correlation waveforms that are appropriate to resolve signals of different frequencies. By synthetic inversion, we investigate the use of measurements that are based on cross-correlation signal energy and cross-correlation envelopes, after filtering the waveforms in different frequency bands.

We will show purely synthetic and real-data applications on regional and global scale, respectively. The final goal of this work is to conduct an inversion for ambient source PSDs for the Sea of Japan on 24-hour stacks of observed cross-correlations in the microseism range.