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Similar seismic moment release process for shallow and deep earthquakes


The generation of earthquakes at depths exceeding 60 km remains debated, as rocks at such depths are anticipated to be ductile. Seismological investigations have revealed a variety of rupture characteristics that are distinguishable between shallow (0–60 km), intermediate-depth (60–300 km) and deep-focus (300–700 km) earthquakes, but it is unclear whether different physical mechanisms are controlling earthquake ruptures. Here, we apply machine learning classification to a global database of earthquakes with moderate to large moment magnitudes to show that depth-dependent elastic properties can explain the range of resulting rupture characteristics. We find that the rigidity of the surrounding medium is the primary control of the earthquakes’ source characteristics and that all the analysed earthquakes shared similar moment release processes with the medium effect corrected. Thus, the rupture duration, rupture length and the associated drop in stress scale with depth due to the accompanying changes in rigidity. Our results support a constant strain drop hypothesis, in which the ratio of coseismic slip to the characteristic rupture length remains largely unchanged for earthquakes at all depths and regardless of the nucleation mechanisms. These results also suggest that medium-rigidity-corrected earthquake self-similarity holds for earthquakes of different depths and host-rock types.

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Fig. 1: Global and depth distributions of 3,675 moment magnitude (Mw) > 5.5 shallow, intermediate-depth and deep-focus earthquakes.
Fig. 2: Random forest classification accuracies and interpretation of \(\widetilde {{{{F}}}}_{{{{{\mathrm{m}}}}}}\) and \(\widetilde {{{\boldsymbol{T}}}}\).
Fig. 3: Correlation of STF features with depth, \(\widetilde {{{{F}}}}_{{{{{\mathrm{m}}}}}}\) and \(\widetilde {{{\boldsymbol{T}}}}\).
Fig. 4: Systematic variations in earthquake parameters under the constant strain drop hypothesis.
Fig. 5: Corrected definition of earthquake self-similarity under the constant strain drop hypothesis.

Data availability

The SCARDEC database is available at accessed on 3 March 2022). The STFs dataset generated by kinematic source inversion can be accessed from the supplementary material in ref. 47 (, last accessed on 3 September 2021). The source data of Figs. 2, 3 and 5, and Extended Data Figs. 18, are available via Zenodo at

Code availability

The machine learning algorithms are developed with scikit-learn, an open-source Python package. The code and the input STF features used in this study are available via Zenodo at


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We thank M. Vallée and L. Ye for the STF data. The manuscript benefited from discussion with Z. Peng and R. Wang. We also thank S. Ma for helping with the figures. This research is supported by the National Key R&D Program of China (no. 2021YFC3000704 and 2022YFC3005602) and the National Natural Science Foundation of China (no. 42274063). Y.H. is supported by the Strategic Priority Research Program of Chinese Academy of Sciences (no. XDB42020104).

Author information

Authors and Affiliations



Z.L. conceived the idea and supervised the project. X.C. performed the data analysis and wrote the manuscript draft. All the authors took part in the discussion of the results and contributed to writing the paper.

Corresponding author

Correspondence to Zefeng Li.

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The authors declare no competing interests.

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Nature Geoscience thanks the anonymous reviewers for their contribution to the peer review of this work. Primary Handling Editor: Louise Hawkins, in collaboration with the Nature Geoscience team.

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Extended data

Extended Data Fig. 1 Relationship of dichotomy accuracies and feature importance.

(a), (b) Relationship of dichotomy accuracies of individual features and their random forest feature importance for shallow and deep earthquake classification and for intermediate-depth and deep-focus earthquake classification. Error bars represent the standard deviation of 1,000 iterations of dichotomy.

Extended Data Fig. 2 Classification accuracies of synthetic \(\widetilde F_m\) and \(\widetilde T\).

(a), (b), Classification accuracies of synthetic \(\widetilde F_m\) and \(\widetilde T\) with different noise amplitudes. Error bars represent the standard deviation of 1,000 iterations of dichotomy. S-D: shallow vs deep; ID-DF: intermediate-depth vs deep-focus.

Extended Data Fig. 3 Depth variation of STF features \(\widetilde F_m\) and \(\widetilde T\) and interpretation as Earth’s depth-varying rigidity.

(a) Left panel: depth-dependency of \(\widetilde F_m\). Gray dots represent the \(\widetilde F_m\) of individual earthquakes. Red squares with vertical bars are the average and standard deviation over a 50-km bin. The number of events per bin are 2625, 310, 223, 121, 86, 29, 8, 37, 28, 27, 34, 74 and 62 from shallow to deep depths. Green stars represent large tsunami earthquakes. The blue curve represents the theoretical prediction of \(\widetilde F_m\) using a modified preliminary reference Earth model under a constant strain drop assumption (after Vallée, 2013). Right panel: similar to the left panel for Synthetic \(\widetilde {{{\mathrm{F}}}}_{{{\mathrm{m}}}}\) predicted by the constant strain drop assumption with added Gaussian perturbation (standard deviation 0.18 for 0–60 km and 0.15 for 60–700 km). (b) Similar to (a) but for \(\widetilde T\) (standard deviation 0.22 for 0–60 km and 0.14 for 60–700 km). S-D: shallow and deep earthquake classification; ID-DF: intermediate-depth and deep-focus earthquake classification.

Extended Data Fig. 4 Spearman coefficient relations of STF features and depth for shallow and deep earthquakes.

Spearman coefficient relations of STF features and depth for shallow and deep earthquakes. The number in the top right represents the spearman correlation coefficient.

Extended Data Fig. 5 Spearman coefficient relations of STF features and \(\widetilde F_m\) for shallow and deep earthquakes.

Spearman coefficient relations of STF features and \(\widetilde F_m\) for shallow and deep earthquakes. The number in the top right represents the spearman correlation coefficient.

Extended Data Fig. 6 Spearman coefficient relations of STF features and depth for intermediate-depth and deep-focus earthquakes.

Spearman coefficient relations of STF features and depth for intermediate-depth and deep-focus earthquakes. The number in the top right represents the spearman correlation coefficient.

Extended Data Fig. 7 Spearman coefficient relations of STF features \(\widetilde T\) for intermediate-depth and deep-focus earthquakes.

Spearman coefficient relations of STF features \(\widetilde T\) for intermediate-depth and deep-focus earthquakes. The number in the top right represents the spearman correlation coefficient.

Extended Data Fig. 8 Random forest classification accuracy with an additional feature, scaled energy.

(a) The red dots are the feature importance for shallow and deep earthquake classification (the Y label on the right). The blue dots are the average accuracies of 1,000 iterations of random forest classifications by progressively adding features into the model from the highest to the lowest importance (the Y label on the left). Error bars are standard deviations. (b) Similar to the left panel but for intermediate-depth and deep-focus earthquake classification.

Extended Data Table 1 List of source time function features

Supplementary information

Supplementary Information

Supplementary Text 1 and 2, Supplementary Figs. 1–3 and Supplementary Table 1.

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Cui, X., Li, Z. & Hu, Y. Similar seismic moment release process for shallow and deep earthquakes. Nat. Geosci. 16, 454–460 (2023).

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