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# Fault strength and rupture process controlled by fault surface topography

## 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.

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## 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.

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## 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

### 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.

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.

## Supplementary information

### Supplementary Information

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

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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

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