Inverting for the Sources of the Earth's Hum

Abstract:

We develop a technique to invert ambient noise correlations for the space-, time- and frequency-dependent distribution of noise sources, accounting for the 3D heterogeneous structure of the Earth. Noise source inversion mainly serves two purposes: First, it allows us to construct more accurate forward models for cross-correlation waveforms used in ambient noise tomography, and second, it provides new insights for better understanding source mechanisms.

Previous results based on a global dataset of correlations in the hum period band confirm that correlations can be used to map the seasonality of hum excitation. We obtained these results using a simple 1-D model of wave propagation with constant parameters. We now extend this mapping to a first inversion step.

The procedure of the inversion is the following. Starting from a homogeneous source distribution, we evaluate the asymmetry in signal energy between causal and acausal branches. This results in a first set of noise source images. We then construct forward models of correlations with a spectral element wave propagation code. Our approach to construct these models efficiently is to use source-receiver reciprocity and to assume spatial uncorrelation of noise sources. In such a setting, correlations can be calculated from a pre-computed set of Green’s functions between the seismic receivers and sources located at the Earth’s surface.

Besides the resulting hum source model itself, key questions are how the chosen modeling approach compares to previously published approaches and in what way the 3-D structure, compared to a 1-D Earth, influences the resulting correlation waveforms.