Embedding seismic scattering from seismograms

Heterogeneities in the Earth's crust scatter seismic waves at many scales, trapping seismic energy and producing coda waves that encode valuable information on geological structures. In regions such as volcanoes and fault systems, analyzing coda waves is essential for characterizing non-uniform subsurface heterogeneity, improving interpretation and seismic imaging. Here, we apply unsupervised learning to infer properties directly from seismograms. We simulate 7,800 source-receiver seismograms within a realistic physics-based volcanic model of a magmatic plumbing system with complex interactions between dykes and sills. Recent studies suggest that the spectral characteristics of these synthetic seismograms are controlled by the partial resonance of multiply scattered waves. We leverage a deep scattering transform to extract robust, time-invariant representations of seismograms recorded with multiple stations, and use a manifold learning algorithm to visualize and analyze patterns in the scattering coefficients. By examining the connections in the embedded manifold, we reveal how local medium complexity influences recorded wavefields. Our results demonstrate that the proposed method effectively captures local resonant frequency and modulation induced by heterogeneous structures near the sources. We show that the statistical properties of the medium align with the estimated local complexities derived from seismic signals. By analyzing complete seismograms in a data-driven way, our method enhances subsurface heterogeneity characterization and offers a promising approach for improving the space-time monitoring in highly heterogeneous regions.