Sensitivity Kernels for Earthquake Coda-Correlation Wavefield Features and Applications to Global Seismology

The global coda-correlation wavefield is a mathematical representation of the seismic wavefield generated by large earthquakes, computed by cross-correlating the long-lasting coda waves recorded by a worldwide network of seismometers. Unlike the common assumptions that the cross-correlation functions are Green’s functions between station pairs, earthquake coda-correlation features arise from cross-terms of in reverberating body waves of common slowness that share common slowness characteristics a subset of propagation legs (e.g., Hrvoje & Phạm, 2018; Phạm et al., 2018). This wavefield has offered new constrains on the deep Earth's interior (e.g., Hrvoje & Phạm, 2018; Ma & Tkalčić, 2024). However, quantitative interpretation of these features for tomographic imaging has been hindered by the lack of distributed sensitivity kernels relating observed correlation signals to Earth structure heterogeneities.

In this study, we develop a forward modeling framework for the earthquake coda-correlation wavefield bypassing conventional cross-correlation of late-coda waveforms. The forward-modeled correlograms reproduce features obtained through conventional stacking with a significantly improved signal-to-noise ratio. Building on this framework, we derive finite-frequency traveltime banana-doughnut sensitivity kernels using adjoint methods (e.g., Tromp et al., 2010; Fichtner, 2014), which quantify how traveltime measurements of correlation features depend on perturbations in P-wave velocity, S-wave velocity, and density.

We compute sensitivity kernels for prominent correlation features (P*, ScS*, and others) at station separations ranging from 30° to 180°. The kernels reveal extensive sampling of Earth's mantle, outer core, and inner core, with spatial-sensitivity patterns fundamentally different from those of body waves in direct seismic wavefield. For antipodal station pairs, correlation features exhibit strong sensitivity throughout the deep interior, including regions poorly sampled by traditional seismic phases. Our results confirm that correlation features form through constructive interference of body-wave pairs with similar slowness, rather than representing Green's functions between station pairs.

This work establishes the theoretical foundation for coda-correlation tomography, enabling future three-dimensional imaging of Earth’s internal structure with unprecedented sampling of the deep interior. The sensitivity kernels provide a pathway to exploit the wealth of information contained in earthquake coda for high-resolution mantle and core tomography.

Reference
Ma, X. & Tkalčić, H. (2024) Low seismic velocity torus in the Earth's outer core: Evidence from the coda correlation wavefield, Sci. Adv., 10, 35, https://doi.org/10.1126/sciadv.adn55.

Fichtner, A. (2014). Source and processing effects on noise correlations. Geophys. J. Int., 197(3), 1527-1531. https://doi.org/10.1093/gji/ggu093 

Phạm, T-S., Tkalčić, H., Sambridge, M. & Kennett, B.L.N. (2018) The Earth's correlation wavefield: late coda correlation, Geophys. Res. Lett., 45, https://doi.org/10.1002/2018GL077244.

Tkalčić, H., & Phạm, T.-S. (2018). Shear properties of Earth's inner core constrained by a detection of J waves in global correlation wavefield. Science, 362, 329. https://doi.org/10.1126/science.aau7649

Tromp, J., Luo, Y., Hanasoge, S., & Peter, D. (2010). Noise cross-correlation sensitivity kernels. Geophys. J. Int.,183(2), 791-819. https://doi.org/10.1111/j.1365-246X.2010.04721.x