Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published May 1, 2020 | Supplemental Material
Journal Article Open

Did Oldham Discover the Core After All? Handling Imprecise Historical Data with Hierarchical Bayesian Model Selection Methods


Historical seismic data are essential to fill in the gaps in geophysical knowledge caused by the low rate of significant seismic events. Handling historical data in the context of geophysical inverse problems requires special care, due to the large errors in the data collection process. Using Oldham's data for the discovery of Earth's core as a case study, we illustrate how a hierarchical Bayesian model selection methodology using leave‐one‐out cross validation can robustly and efficiently answer quantitative questions using even poor‐quality geophysical data. We find that there is statistically significant evidence for the existence of the core using only the P‐wave data that Oldham effectively discarded in his discussion.

Additional Information

© 2020 Seismological Society of America. Manuscript received 20 September 2019; Published online 15 January 2020. The authors would like to thank two anonymous reviewers for their feedback and the SRL Editor‐in‐Chief Allison Bent for managing the review process. The authors would also like to thank Luis Rivera for providing an internal review of this article. J. B. M. would like to thank the General Sir John Monash Foundation and the Origin Energy Foundation for financial support during his graduate studies. Data and Resources: Historical data were taken from Oldham (1906), either from the reported tables of averaged events or by digitizing the presented travel‐time curves. All calculations were performed using the PyStan wrapper of the Stan statistical software package (Carpenter et al., 2017). The supplemental material contains inversion results for the five models not presented in the article (Figs. S1–S5). Additional discussion regarding hierarchical Markov chain Monte Carlo (MCMC) sampling and leave‐one‐out cross validation (LOO‐CV) versus k‐fold CV are also present in the supplement.

Attached Files

Supplemental Material - srl-2019266_supplement_figure_s1.pdf

Supplemental Material - srl-2019266_supplement_figure_s2.pdf

Supplemental Material - srl-2019266_supplement_figure_s3.pdf

Supplemental Material - srl-2019266_supplement_figure_s4.pdf

Supplemental Material - srl-2019266_supplement_figure_s5.pdf

Supplemental Material - srl-2019266_supplementcover.docx


Files (164.4 kB)
Name Size Download all
29.4 kB Preview Download
29.5 kB Preview Download
29.4 kB Preview Download
17.1 kB Download
29.4 kB Preview Download
29.5 kB Preview Download

Additional details

August 19, 2023
October 20, 2023