Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Fault strength and rupture process controlled by fault surface topography

Nature Geoscience volume 16, pages 94–100 (2023)Cite this article

Subjects

Abstract

Faults are rarely completely smooth, with topographic undulations coming from the distribution of asperities along the fault surface. Understanding the effects of fault surface topography on fault strength and earthquake source properties has been limited due to a lack of in situ observations in the field. Here we use simulated earthquake cycles on metre-scale laboratory faults to show the effects of the degree of fault topographic heterogeneity, especially on macroscopic peak strength represented by the shear force required to commence macroscopic failure. Our results demonstrate that the less heterogeneous fault is weaker, due to its lower macroscopic peak strength, and produces a larger stress drop on average than the more heterogeneous fault. Rupture along the less heterogeneous fault tends to propagate at subshear speed while the more heterogeneous fault accommodates a wider range of rupture speeds, including slow slip and supershear rupture. These results reveal how fault topographic heterogeneity affects macroscopic peak strength at rupture initiation and stress drop during rupture propagation, which has important implications for understanding natural faults and earthquakes.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Experimental set-up and features of macroscopic force and local stress.
Fig. 2: Representative rupture behaviours on faults with different degrees of topographic heterogeneity.
Fig. 3: Rupture source properties on faults with different degrees of topographic heterogeneity.
Fig. 4: Likely rupture scenarios for faults with less and more topographic heterogeneity.

Similar content being viewed by others

Data availability

The source data for Figs. 1–3, Extended Data Figs. 3–8 and Supplementary Figs. 2,4–7 are available via Zenodo at https://doi.org/10.5281/zenodo.7128164.

Code availability

The numerical code SEM2DPACK used in the study is available at https://github.com/jpampuero/sem2dpack.

References

  1. Anderson, E. M. The Dynamics of Faulting and Dike Formation with Application to Britain (Oliver and Boyd, 1951).

  2. Brace, W. F. & Byerlee, J. D. Stick-slip as a mechanism for earthquakes. Science 153, 990–992 (1966).

    Article  Google Scholar 

  3. Scholz, C. H. The Mechanics of Earthquakes and Faulting 3rd edn (Cambridge Univ. Press, 2019).

  4. Byerlee, J. Friction of rocks. Pure Appl. Geophys. 116, 615–626 (1978).

    Article  Google Scholar 

  5. Di Toro, G. et al. Fault lubrication during earthquakes. Nature 471, 494–498 (2011).

    Article  Google Scholar 

  6. Yamashita, F. et al. Scale dependence of rock friction at high work rate. Nature 528, 254–257 (2015).

    Article  Google Scholar 

  7. Sibson, R. H. A note on fault reactivation. J. Struct. Geol. 7, 751–754 (1985).

    Article  Google Scholar 

  8. Gao, X. & Wang, K. Strength of stick-slip and creeping subduction megathrusts from heat flow observations. Science 345, 1038–1041 (2014).

    Article  Google Scholar 

  9. Hardebeck, J. L. Stress orientations in subduction zones and the strength of subduction megathrust faults. Science 349, 1213–1216 (2015).

    Article  Google Scholar 

  10. Wang, K. & Hu, Y. Accretionary prisms in subduction earthquake cycles: the theory of dynamic Coulomb wedge. J. Geophys. Res. 111, B06410 (2006).

    Google Scholar 

  11. Dielforder, A., Hetzel, R. & Oncken, O. Megathrust shear force controls mountain height at convergent plate margins. Nature 582, 225–229 (2020).

    Article  Google Scholar 

  12. Xu, S. Recognizing fracture pattern signatures contributed by seismic loadings. Interpretation 8, SP95–SP108 (2020).

    Article  Google Scholar 

  13. Lambert, V., Lapusta, N. & Perry, S. Propagation of large earthquakes as self-healing pulses or mild cracks. Nature 591, 252–258 (2021).

    Article  Google Scholar 

  14. Kohlstedt, D. L., Evans, B. & Mackwell, S. J. Strength of the lithosphere: constraints imposed by laboratory experiments. J. Geophys. Res. 100, 17587–17602 (1995).

    Article  Google Scholar 

  15. Rice, J. R. in Fault Mechanics and Transport Properties in Rocks (eds Evans, B. & Wong, T.-F.) 475–503 (Academic Press, 1992).

  16. Rowe, C. D. & Griffith, W. A. Do faults preserve a record of seismic slip: a second opinion. J. Struct. Geol. 78, 1–26 (2015).

    Article  Google Scholar 

  17. Petley-Ragan, A. et al. Dynamic earthquake rupture in the lower crust. Sci. Adv. 5, eaaw0913 (2019).

    Article  Google Scholar 

  18. Brodsky, E. E. et al. The state of stress on the fault before, during, and after a major earthquake. Annu. Rev. Earth Planet. Sci. 48, 49–74 (2020).

    Article  Google Scholar 

  19. Lay, T. et al. Depth-varying rupture properties of subduction zone megathrust faults. J. Geophys. Res. 117, B04311 (2012).

    Google Scholar 

  20. Madariaga, R. On the relation between seismic moment and stress drop in the presence of stress and strength heterogeneity. J. Geophys. Res. Solid Earth 84, 2243–2250 (1979).

    Article  Google Scholar 

  21. Ben-Zion, Y. Stress, slip, and earthquakes in models of complex single-fault systems incorporating brittle and creep deformations. J. Geophys. Res. 101, 5677–5706 (1996).

    Article  Google Scholar 

  22. Dieterich, J. H. & Smith, D. E. Nonplanar faults: mechanics of slip and off-fault damage. Pure Appl. Geophys. 166, 1799–1815 (2009).

    Article  Google Scholar 

  23. Fang, Z. & Dunham, E. M. Additional shear resistance from fault roughness and stress levels on geometrically complex faults. J. Geophys. Res. Solid Earth 118, 3642–3654 (2013).

    Article  Google Scholar 

  24. Wang, K. & Bilek, S. B. Fault creep caused by subduction of rough seafloor relief. Tectonophysics 610, 1–24 (2014).

    Article  Google Scholar 

  25. Bletery, Q. et al. Mega-earthquakes rupture flat megathrusts. Science 354, 1027–1031 (2016).

    Article  Google Scholar 

  26. Lockner, D. A., Morrow, C., Moore, D. & Hickman, S. Low strength of deep San Andreas fault gouge from SAFOD core. Nature 472, 82–86 (2011).

    Article  Google Scholar 

  27. Collettini, C., Tesei, T., Scuderi, M. M., Carpenter, B. M. & Viti, C. Beyond Byerlee friction, weak faults and implications for slip behavior. Earth Planet. Sci. Lett. 519, 245–263 (2019).

    Article  Google Scholar 

  28. Bruhat, L., Fang, Z. & Dunham, E. M. Rupture complexity and the supershear transition on rough faults. J. Geophys. Res. 121, 210–224 (2016).

    Article  Google Scholar 

  29. Tal, Y., Hager, B. H. & Ampuero, J.-P. The effects of fault roughness on the earthquake nucleation process. J. Geophys. Res. Solid Earth 123, 437–456 (2018).

    Article  Google Scholar 

  30. Cattania, C. & Segall, P. Precursory slow slip and foreshocks on rough faults. J. Geophys. Res. Solid Earth 126, e2020JB020430 (2021).

    Article  Google Scholar 

  31. Yamashita, F. et al. Rupture preparation process controlled by surface roughness on meter-scale laboratory fault. Tectonophysics 733, 193–208 (2018).

    Article  Google Scholar 

  32. Yamashita, F. et al. Two end-member earthquake preparations illuminated by foreshock activity on a meter-scale laboratory fault. Nat. Commun. 12, 4302 (2021).

    Article  Google Scholar 

  33. Xu, S., Fukuyama, E. & Yamashita, F. Robust estimation of rupture properties at propagating front of laboratory earthquakes. J. Geophys. Res. Solid Earth 124, 766–787 (2019).

    Article  Google Scholar 

  34. Bürgmann, R. The geophysics, geology and mechanics of slow fault slip. Earth Planet. Sci. Lett. 495, 112–134 (2018).

    Article  Google Scholar 

  35. Fineberg, J. & Marder, M. Instability in dynamic fracture. Phys. Rep. 313, 1–108 (1999).

    Article  Google Scholar 

  36. Xu, S. et al. Strain rate effect on fault slip and rupture evolution: insight from meter-scale rock friction experiments. Tectonophysics 733, 209–231 (2018).

    Article  Google Scholar 

  37. Brodsky, E. E., Gilchrist, J. J., Sagy, A. & Collettini, C. Faults smooth gradually as a function of slip. Earth Planet. Sci. Lett. 302, 185–193 (2011).

    Article  Google Scholar 

  38. Ben-Zion, Y. & Sammis, C. G. Characterization of fault zones. Pure Appl. Geophys. 160, 677–715 (2003).

    Article  Google Scholar 

  39. Ohnaka, M. & Shen, L. F. Scaling of the shear rupture process from nucleation to dynamic propagation: implications of geometric irregularity of the rupturing surfaces. J. Geophys. Res. Solid Earth 104, 817–844 (1999).

    Article  Google Scholar 

  40. McLaskey, G. C. Earthquake initiation from laboratory observations and implications for foreshocks. J. Geophys. Res. Solid Earth 124, 12882–12904 (2019).

    Article  Google Scholar 

  41. Dunham, E. M., Favreau, P. & Carlson, J. M. A supershear transition mechanism for cracks. Science 299, 1557–1559 (2003).

    Article  Google Scholar 

  42. Burridge, R. Admissible speeds for plane-strain self-similar shear cracks with friction but lacking cohesion. Geophys. J. Int. 35, 439–455 (1973).

    Article  Google Scholar 

  43. Andrews, D. J. Rupture velocity of plane strain shear cracks. J. Geophys. Res. 81, 5679–5687 (1976).

    Article  Google Scholar 

  44. Xia, K., Rosakis, A. J. & Kanamori, H. Laboratory earthquakes: the sub-Rayleigh-to-supershear rupture transition. Science 303, 1859–1861 (2004).

    Article  Google Scholar 

  45. Fukuyama, E. & Olsen, K. B. A condition for super-shear rupture propagation in a heterogeneous stress field. Pure Appl. Geophys. 159, 2047–2056 (2002).

    Article  Google Scholar 

  46. Liu, Y. & Lapusta, N. Transition of mode II cracks from sub-Rayleigh to intersonic speeds in the presence of favorable heterogeneity. J. Mech. Phys. Solids 56, 25–50 (2008).

    Article  Google Scholar 

  47. Barras, F., Geubelle, P. H. & Molinari, J. F. Interplay between process zone and material heterogeneities for dynamic cracks. Phys. Rev. Lett. 119, 144101 (2017).

    Article  Google Scholar 

  48. Houston, H., Delbridge, B. G., Wech, A. G. & Creager, K. C. Rapid tremor reversals in Cascadia generated by a weakened plate interface. Nat. Geosci. 4, 404–409 (2011).

    Article  Google Scholar 

  49. Xu, S., Fukuyama, E., Yamashita, F. & Takizawa, S. Evolution of fault-interface Rayleigh wave speed over simulated earthquake cycles in the lab: observations, interpretations, and implications. Earth Planet. Sci. Lett. 524, 115720 (2019).

    Article  Google Scholar 

  50. Ben-David, O., Cohen, G. & Fineberg, J. The dynamics of the onset of frictional slip. Science 330, 211–214 (2010).

    Article  Google Scholar 

  51. Paterson, M. S. & Wong, T.-F. Experimental Rock Deformation—The Brittle Field (Springer-Verlag, 2005).

  52. Bouchon, M. et al. Faulting characteristics of supershear earthquakes. Tectonophysics 493, 244–253 (2010).

    Article  Google Scholar 

  53. Wang, D., Mori, J. & Koketsu, K. Fast rupture propagation for large strike-slip earthquakes. Earth Planet. Sci. Lett. 440, 115–126 (2016).

    Article  Google Scholar 

  54. Ye, L., Lay, T., Kanamori, H. & Rivera, L. Rupture characteristics of major and great (Mw ≥ 7.0) megathrust earthquakes from 1990 to 2015: 1. Source parameter scaling relationships. J. Geophys. Res. Solid Earth 121, 826–844 (2016).

    Article  Google Scholar 

  55. Chounet, A., Vallée, M., Causse, M. & Courboulex, F. Global catalog of earthquake rupture velocities shows anticorrelation between stress drop and rupture velocity. Tectonophysics 733, 148–158 (2018).

    Article  Google Scholar 

  56. Otsuki, M. & Matsukawa, H. Systematic breakdown of Amontons’ law of friction for an elastic object locally obeying Amontons’ law. Sci. Rep. 3, 1586 (2013).

    Article  Google Scholar 

  57. Yamashita, F., Fukuyama, E. & Xu, S. Foreshock activity promoted by locally elevated loading rate on a 4-meter-long laboratory fault. J. Geophys. Res. Solid Earth 127, e2021JB023336 (2022).

    Article  Google Scholar 

  58. Fukuyama, E., Xu, S., Yamashita, F. & Mizoguchi, K. Cohesive zone length of metagabbro at supershear rupture velocity. J. Seismol. 20, 1207–1215 (2016).

    Article  Google Scholar 

  59. Kilgore, B. D., McGarr, A., Beeler, N. M. & Lockner, D. A. in Fault Zone Dynamic Processes: Evolution of Fault Properties During Seismic Rupture (eds Thomas, M. Y. et al.) 151–169 (AGU and Wiley, 2017).

  60. Ampuero, J.-P. SEM2DPACK—a spectral element method tool for 2D wave propagation and earthquake source dynamics. https://github.com/jpampuero/sem2dpack (2012).

  61. Bizzarri, A. Rupture speed and slip velocity: what can we learn from simulated earthquakes? Earth Planet. Sci. Lett. 317–318, 169–203 (2012).

    Google Scholar 

  62. Freund, L. B. Dynamic Fracture Mechanics (Cambridge Univ. Press, 1990).

  63. Fukuyama, E. et al. Spatiotemporal complexity of 2-D rupture nucleation process observed by direct monitoring during large-scale biaxial rock friction experiments. Tectonophysics 733, 182–192 (2018).

    Article  Google Scholar 

  64. Ohnaka, M. Earthquake source nucleation: a physical model for short-term precursors. Tectonophysics 211, 149–178 (1992).

    Article  Google Scholar 

Download references

Acknowledgements

We thank Y. Ben-Zion (USC), L. Ye and T. Yang (SUSTech) for helpful discussions. This study was supported by the NIED research project ‘Large Earthquake Generation Process’ and JSPS KAKENHI grants JP17H02954 and JP16H06477. S.X. acknowledges fund support by NSFC grant 42074048 and National Key R&D Program of China 2021YFC3000700.

Author information

Authors and Affiliations

  1. Department of Earth and Space Sciences, Southern University of Science and Technology, Shenzhen, China

    Shiqing Xu

  2. National Research Institute for Earth Science and Disaster Resilience, Tsukuba, Japan

    Shiqing Xu, Eiichi Fukuyama, Futoshi Yamashita, Hironori Kawakata, Kazuo Mizoguchi & Shigeru Takizawa

  3. Department of Civil and Earth Resources Engineering, Kyoto University, Kyoto, Japan

    Eiichi Fukuyama

  4. College of Science and Engineering, Ritsumeikan University, Kusatsu, Japan

    Hironori Kawakata

  5. Central Research Institute of Electric Power Industry, Abiko, Japan

    Kazuo Mizoguchi

Authors
  1. Shiqing Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Eiichi Fukuyama
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Futoshi Yamashita
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hironori Kawakata
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Kazuo Mizoguchi
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Shigeru Takizawa
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

S.X., E.F., F.Y., H.K., K.M. and S.T. conducted the experiments. S.X. performed the numerical simulations. S.X. conceived the idea, analysed the strain and acoustic data and wrote the manuscript. E.F. oversaw the entire work. F.Y. processed the image data of the fault surface. S.X., E.F. and F.Y. discussed the results and finalized the manuscript.

Corresponding author

Correspondence to Shiqing Xu.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Geoscience thanks Seth Saltiel and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editors: Louise Hawkins and Rebecca Neely, in collaboration with the Nature Geoscience team.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Experimental setup and sensor configurations.

a, Three load cells at the top of the upper rock block measure the total normal force Fn, while one load cell at the western edge of the upper rock block measures the total shear force Fs. During the experiments, normal load was first applied, then the shaking table was instructed to drag the lower rock block toward west, whereas their motion was resisted by the interfacial friction against the upper rock block. b, Configurations of strain gauge (SG) array and piezoelectric (PZT) acoustic sensor array installed at the side surface(s) of the lower rock block. Figure adapted with permission from ref. 36 under a Creative Commons license CC BY-NC 4.0.

Extended Data Fig. 2 Examples of shear stress waveforms and their characteristics.

a, Numerically-simulated shear stress waveforms evaluated at a given location for three rupture events. Left: a subshear rupture. Middle: a subshear-to-supershear rupture via mother-daughter transition (MDT). Right: a subshear-to-supershear rupture via direct transition (DT). b, Evolutions of rupture speed Vr and the magnitude of shear stressing rate \(|\dot \tau |\) for three numerically-simulated rupture events. For each event, four versions of \(|\dot \tau |\) are investigated (see their definitions in a). Results in a and b are derived from the three events shown in Supplementary Fig. 3. c, Experimentally-observed shear stress waveforms (recorded 20 mm off the fault) evaluated at a given location for three rupture events. By comparing the observed waveforms in c with the synthetic ones in a, one can estimate the arrival of rupture front and several other quantities (for example, stress drop ∆τ and shear stressing rate \(|\dot \tau |\)), as discussed in the Methods.

Extended Data Fig. 3 One example of rupture behaviors on the less heterogeneous fault.

a, b, Evolution of local shear stress waveforms during two time intervals for one event. c, d, Evolution of acoustic emission (AE) waveforms during the same time intervals as in a and b. The amplitude of AE waveforms has been normalized by the maximum value. In the scale bar, a.u. stands for arbitrary unit. In b and d, purple dotted curve indicates the SG-estimated trajectory of rupture front, while vertical double arrow denotes the size of nucleation zone.

Extended Data Fig. 4 One example of rupture behaviors on the more heterogeneous fault.

a, b, c, Evolution of local shear stress waveforms during three time intervals for one event. d, e, f, Evolution of AE waveforms during the same time intervals as in a, b, and c. The amplitude of AE waveforms has been normalized by the maximum value. In the scale bar, a.u. stands for arbitrary unit. Red dashed curve in e depicts the PZT-estimated migration path of foreshocks. In a, b, d, and e, purple dashed curve indicates the SG-estimated trajectory of rupture front during the precursory stage, while vertical double arrow denotes the size of nucleation zone. In c and f, purple dotted curve indicates the SG-estimated trajectory of rupture front during the mainshock stage. Red arrows in a and d indicate the locations of 4 prominent asperities. In this example, a moderate foreshock occurred near A3, which caused recognizable stress drops in the nearby SGs. On the other hand, the magnitude of stress drop around A3 was relatively small, and there were no big foreshocks near A2 or A4. As a result, the mainshock, which later started near A1, could successfully transit into a supershear rupture along the western portion of the fault.

Extended Data Fig. 5 Another example of rupture behaviors on the more heterogeneous fault.

a, b, c, Evolution of local shear stress waveforms during three time intervals for a second rupture event. d, e, f, Evolution of AE waveforms during the same time intervals as in a, b, and c. The amplitude of AE waveforms has been normalized by the maximum value. In the scale bar, a.u. stands for arbitrary unit. In a, b, d, and e, purple dashed curve indicates the SG-estimated trajectory of rupture front during the precursory stage, while vertical double arrow denotes the size of nucleation zone. In c and f, purple dotted curve indicates the SG-estimated trajectory of rupture front during the mainshock stage. Red arrows in a and d indicate the locations of 4 prominent asperities. In this example, two big foreshocks sequentially occurred near A4 and A2, which caused quite large stress drops in the nearby SGs. As a result, although the mainshock initially could propagate as a supershear rupture near A1, later it decelerated to a subshear rupture and remained so along the western portion of the fault.

Extended Data Fig. 6 Rupture nucleation on the less heterogeneous fault.

a, Spatiotemporal distributions of mainshock nucleation site and foreshock activity for 30 events on the less heterogeneous fault. The length of horizontal bar represents the spatial extent of foreshock rupture zone, with an uncertainty of ± 25 mm (set by SG interval). The upper limit for displaying foreshock stress drop is truncated at 0.06 MPa (the maximum value is 0.1224 MPa). b, Evolutions of rupture trajectory and foreshock hypocenter during mainshock nucleation. For the plots on the left, the vertical axis is normalized by the time duration of the corresponding nucleation process. For the plots on the right, the size of nucleation zone is defined by the distance between two opposite rupture fronts at the end of the nucleation process. From top to bottom, results are grouped for ruptures that nucleated in the western portion (Supplementary Fig. 4), central portion (Supplementary Fig. 5), and eastern portion (Supplementary Fig. 6), respectively.

Extended Data Fig. 7 Rupture nucleation on the more heterogeneous fault.

a, Spatiotemporal distributions of the initiation site of slow slip, foreshock activity, and mainshock hypocenter for 89 events on the more heterogeneous fault. The length of horizontal bar represents the spatial extent of foreshock rupture zone, with an uncertainty of ± 25 mm (set by SG interval). The upper limit for displaying foreshock stress drop is truncated at 0.25 MPa (the maximum value is 0.5243 MPa). b, Evolutions of rupture trajectory and foreshock hypocenter during mainshock nucleation. For the plot on the left, the vertical axis is normalized by the time duration of the corresponding nucleation process. For the plot on the right, the size of nucleation zone is defined by the distance between two opposite rupture fronts (including fault edge or halted rupture front) at the end of the nucleation process. In a and b, red arrows indicate the locations of 4 prominent asperities.

Extended Data Fig. 8 Distributions of initial stress, rupture initiation site, stress drop and fault gouge during or after the two target experiments.

a, Spatiotemporal distributions of τ0, |σ0|, τ0/|σ0| (evaluated at the late inter-seismic stage right before each rupture), and rupture initiation site for selected events on each fault. Note, the results near the western and eastern edges may not be meaningful, since the SGs there could be outside the contacting surface (Extended Data Fig. 1b). For the less (more) heterogeneous fault, 58 (212) events were used for examining the initial stress state, among which 30 (89) were selected for further analysis. For clarity, stress state evaluated at Tp was displayed for the more heterogeneous fault. Nevertheless, an alternative use of stress state evaluated at Tm could yield a very similar pattern, and hence would not change the fundamental contrast against the less heterogeneous fault. b, Distribution of stress drop Δτ on each fault. The results for LB12-012 were derived from the mainshock stage. c, Distribution of fault gouge after each target experiment. The scale for Y has been exaggerated by a factor of 4. The weight of the collected gouge was 0.014 g after LB12-006, and 0.154 g after LB12-012.

Extended Data Table 1 Loading conditions during the LB12 series (up to LB12-012)
Full size table
Extended Data Table 2 Mean values of various quantities
Full size table

Supplementary information

Supplementary Information

Supplementary Notes 1–3 and Figs. 1–7.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xu, S., Fukuyama, E., Yamashita, F. et al. Fault strength and rupture process controlled by fault surface topography. Nat. Geosci. 16, 94–100 (2023). https://doi.org/10.1038/s41561-022-01093-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41561-022-01093-z

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing