A Bayesian formulation for estimating the composition of Earth’s crust

Gailin Pease, Anne Gelb, Yoonsang Lee, and C. Brenhin Keller

Journal of Geophysical Research: Solid Earth , 2023: https://doi.org/10.1029/2023JB026353

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The composition of the continental crust is important for understanding Earth's evolution on global and regional scales. We build on previous work estimating Earth's composition with a new approach using Bayesian statistics, where prior information from rocks sampled at Earth's surface is combined with information from seismic properties to estimate Earth's crustal composition at depth. To connect seismic properties and compositions, we model the seismic properties of rock compositions. Our approach provides rigorous uncertainty estimates for crust composition at depth. By quantifying the sources of this uncertainty, we are able to propose a path forward for future work to further improve compositional estimates for Earth's crust at depth.

Due to the inaccessibility of Earth’s deep interior, geologists have long attempted to estimate the composition of the continental crust from its seismic properties. Despite numerous sources of error including nonuniqueness in the mapping between composition and seismic properties, the corresponding uncertainties have typically been estimated qualitatively at best. We propose a Bayesian approach that uses mineralogical modeling to combine prior knowledge about the composition of the crust with seismic data to give a posterior distribution of the predicted composition at any location, combined with a Monte Carlo simulation to estimate the average composition of the Earth’s crust. Our approach yields an estimated composition of 59.5% silica in the upper crust (90% credible interval 58.9 %–60.1%), 57.9% in the middle crust (90% credible interval 57.2%–58.6%), and 53.6% in the lower crust (90% credible interval 53.0%–54.2%). Our estimate exhibits less compositional stratification over depth and a more intermediate composition in the upper and middle crust than previous estimates. Testing our approach on a simulated crust reveals the importance of prior assumptions in estimating the composition of the crust from its seismic properties, and suggests that future work should focus on quantifying those assumptions.

Suggested citation:
Pease, G., Gelb, A., Lee, Y., & Keller, C.B. (2023). A Bayesian Formulation for Estimating the Composition of Earth’s Crust. Journal of Geophysical Research: Solid Earth<\i>, 128(7), e2023JB026353.