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Localization of inelastic strain with fault maturity and effects on earthquake characteristics

Nature Geoscience volume 18, pages 793–800 (2025)Cite this article

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Abstract

Coseismic ruptures release stored elastic strain through a combination of shear displacement along localized, principal faults and distributed bulk inelastic failure of the surrounding material. How inelastic strain localizes as fault systems mature and structurally develop is less well understood owing to the difficulty of measuring the complex, near-field and high-strain regions of coseismic surface ruptures. Here we use radar and optical images to measure the near-field surface displacement field and magnitude of off-fault inelastic strain from 16 historic strike-slip earthquakes that occurred on faults with cumulative displacements and fault slip rates that span almost three orders of magnitude. We show that inelastic shear deformation does localize as fault systems mature: the magnitude of off-fault inelastic strain is largest (34–67%) for fault systems with the lowest cumulative displacements (<3 km) and then rapidly decays to values that saturate around 13–19% for the most ‘mature’ fault systems with cumulative displacements exceeding ~20 km. We find that more localized coseismic ruptures host faster ruptures, generate fewer aftershocks and occur along geometrically simpler fault networks.

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Fig. 1: Inelastic OFD measurements.
Fig. 2: Evidence for decreasing inelastic OFD with increasing fault maturity across different events.
Fig. 3: Correlation of inelastic OFD with fault properties.
Fig. 4: Correlation of inelastic OFD with earthquake properties.

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Data availability

The surface displacement maps, fault slip, rupture traces and strain maps can be found at Zenodo at https://doi.org/10.5281/zenodo.11663566 (ref. 71). The fault slip data measured by us in this study using geodetic imaging that were used to estimate OFD are available via Zenodo at https://doi.org/10.5281/zenodo.12713891 (ref. 79). Field observations of the fault slip and all the fault traces used are available from the UCLA Fault displacement hazard initiative (https://dataverse.ucla.edu/dataset.xhtml?persistentId=doi:10.25346/S6/Y4F9LJ)80. Landsat and high-resolution aerial images are available from the USGS EarthExplorer (https://earthexplorer.usgs.gov/). Sentinel-1 and Sentinel-2 imagery is available at https://dataspace.copernicus.eu/browser/. Archival SPOT imagery is available at https://regards.cnes.fr/user/swh/modules/60. The raw single-look complex data acquired by the UAVSAR platform can be downloaded from NASA/JPL at https://uavsar.jpl.nasa.gov/. Source data are provided with this paper.

Code availability

The 2D horizontal displacement maps produced using optical images were processed using COSI-Corr (http://www.tectonics.caltech.edu/slip_history/spot_coseis/download_software.html) and 3D displacement maps using COSI-Corr+ (https://github.com/SaifAati/Geospatial-COSICorr3D). The radar data were processed using ISCE2 (https://github.com/isce-framework/isce2).

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Acknowledgements

This research was supported by the NASA Earth Surface and Interior focus area and performed at the Jet Propulsion Laboratory, California Institute of Technology (grant 80NM0018D0004). We thank NASA/JPL-Caltech for providing the raw single-look complexes for the UAVSAR images (https://uavsar.jpl.nasa.gov/). We also thank the numerous colleagues who shared their field observations, slip models, remote-sensing datasets and surface mapping, including Y. Li, M. Mai, S. Barbot, W. Xu, K. Chen, D. Yuan, J. Liu-Zeng, Z. Liu, Y. Liu, Y. Klinger, C. Glennie and A. Sarmiento. We acknowledge the use of the open-source Generic Mapping Tools software for all map illustrations.

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  1. California Institute of Technology, Pasadena, CA, USA

    C. Milliner & J. P. Avouac

  2. University of Southern California, Los Angeles, CA, USA

    J. F. Dolan

  3. University of Grenoble Alpes, Grenoble, France

    J. Hollingsworth

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  1. C. Milliner
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Contributions

C.M. and J.P.A conceived and led the study. C.M. performed the optical and radar pixel offset analysis, InSAR data processing and statistical analysis. All authors wrote the paper and participated in the interpretation of the results.

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Correspondence to C. Milliner.

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Nature Geoscience thanks Yuri Fialko and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Tamara Goldin, in collaboration with the Nature Geoscience team.

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Extended data

Extended Data Fig. 1 Surface displacement maps.

Surface displacement maps with color showing motion projected into the direction illustrated by the arrow (surface motion is projected here purely for illustrative purposes). Black points show location of fault slip measured from the displacement maps (with number of points denoted by ng), green points are locations of fault slip measured in the field (number of points denoted by nf). Events are shown in order of ascending cumulative displacement, starting from top left with Ridgecrest Mw 6.4 (a), Monte Cristo Mw 6.5 (b); Chuya Mw 7.3 (c), Ridgecrest Mw 7.1 (d), Napa Mw 6.0 (e), Landers Mw 7.3 (f), Hector Mine Mw 7.1 (g), Kahramanmaraş Mw 7.8 (h), Menyuan Mw 6.6 (i), Kekerengu fault of the Kaikoura Mw 7.8 (j), Duzce Mw 7.2 (k), Neftegorsk Mw 7.1 (l), Yushu Mw 6.9 (m), Izmit Mw 7.6 (n), Kokoxili Mw 7.8 (o) and Denali Mw 7.9 (p).

Extended Data Fig. 2 Maps of OFD.

Off-fault deformation (OFD) for earthquakes in ascending order of cumulative displacement (from top left to bottom right, a-p, with value labeled in bold in corner). OFD is shown as a percent in map view by white-red colored dots with color scale at bottom left. The plots shows how the amount of OFD diminishes with increasing cumulative displacement (from a-p). Black lines are fault traces mapped in the field80. Green dots are locations of fault slip measured in the field.

Extended Data Fig. 3 Along-fault slip profiles.

Along-fault slip profiles for each event showing fault slip in meters (y-axis) as a function of the distance along the rupture in kilometers (x-axis) measured by the geodetic imaging data (blue line) with 1σ uncertainty (blue shaded region), with measurements from all field data (gray dots). Magenta dots are fault slip measured by field surveys that are used in the estimate of off-fault deformation, which are the largest value found within the swath width of the geodetic imaging profile. All error bars denote 1σ uncertainty and measure of center denotes the mean. Panels are in ascending order from a-p) according to cumulative displacement. Green line for Napa event (e) shows measurements which covers the northern third of the rupture using UAVSAR data81.

Extended Data Fig. 4 Unclipped correlation plots.

Same as Fig. 2 of the main text but without clipping negative off-fault deformation values to zero. Panels are in ascending order from a-p) according to cumulative displacement (as denoted by value in top left of each panel).These correlation plots illustrate the differences in the magnitude of fault slip (in meters) measured between wide-aperture geodetic imaging data (x-axis) and narrower aperture field surveys (y-axis) decreases with cumulative displacement (with plots in ascending order of cumulative displacement from a-p with value shown in top left). Blue dots are all measurements, while red dots show spatially resampled points that are weighted averages of measurements (blue points) from evenly spaced bins located along each rupture to correct for the heterogenous sampling of field measurements. Red line is the best fit using least squares regression to the spatially resampled (red) points without clipping applied. Black dashed line has gradient of one (that is, no off-fault deformation [OFD], or a completely localized rupture). Events are shown in order of ascending cumulative displacement, starting from top left with Ridgecrest Mw 6.4 (a), Monte Cristo Mw 6.5 (b); Chuya Mw 7.3 (c), Ridgecrest Mw 7.1 (d), Napa Mw 6.0 (e), Landers Mw 7.3 (f), Hector Mine Mw 7.1 (g), Kahramanmaraş Mw 7.8 (h), Menyuan Mw 6.6 (i), Kekerengu fault of the Kaikoura Mw 7.8 (j), Duzce Mw 7.2 (k), Neftegorsk Mw 7.1 (l), Yushu Mw 6.9 (m), Izmit Mw 7.6 (n), Kokoxili Mw 7.8 (o) and Denali Mw 7.9 (p). Error ellipsoids denote 1σ uncertainty.

Extended Data Fig. 5 Regressions of OFD without clipping.

Same as Fig. 3 of the maintext but without clipping negative off-fault deformation values to zero. Panels a-f show qualitatively similar trends to that in Fig. 3a-f, but include the occurrence of negative OFD values. All error bars denote 1σ uncertainty. Number of samples used to derive mean are shown in each panel of Fig. 2. P-values are estimated using a two-tailed Student’s t-distribution.

Extended Data Fig. 6 Estimates of surface rupture roughness.

Map view of fault traces mapped in the field (red lines) which are used in estimating the root-mean square (RMS) fault roughness with the RMS value labelled in corner of each plot in units of meters (map units are shown in UTM projected co-ordinates from which distances are measured). Black line is the reference line derived using the least-cost path analysis to estimate the distance to adjacent faults. Number of samples used to estimate the RMS and 1σ shown in Fig. 4 is shown in upper left of each plot. Panels are in ascending order of cumulative displacement from top left to bottom right, same as that of Fig. 2 in the main text.

Extended Data Fig. 7 Sensitivity of slip deficit regressions for events with prominent surface rupture.

Assessment of the effect of including events that only rupture the majority of their surface rupture length on the relation between the shallow slip deficit (SSD) with the Mw and off-fault deformation (OFD) (that is, excluding events shown in Fig. 4a and b that do not fully rupture the surface along most of their rupture length). ρP is the Pearson correlation coefficient, red points are the predicted values of the multi-variate model and blue points are observations, labels are consistent with those shown in Fig. 2. Here we show the multi-variate regression results after applying two separate criteria to define whether events rupture the surface along most of their lengths. The first criterion is whether events have a centroid depth of slip (determined from finite fault slip models) that exceeds the half-length of the rupture (panels a and b). The second criterion is a simpler and more arbitrary approach of whether events have Mw ≥ 7 (panels c and d). We find that regressing the same multi-variate model to events classified with either criterion produces overall qualitatively similar results to each other and to that seen in Fig. 4a) and b) (which has all events included). Specifically, for events that satisfy the first category the correlation between the slip deficit and Mw is moderately negative with ρP = −0.68 and p-value = 0.02 (panel a), and there is still no clear correlation between the slip deficit and off-fault deformation (ρP = −0.38 and p-value = 0.25, panel b). While the regression results applied to events with Mw > 7.0 still indicate a negative correlation between the slip deficit and Mw, but marginally weaker (ρP = −0.59 and p-value = 0.1. panel c), and still no clear association between OFD and the slip deficit (ρP = −0.32 and p-value = 0.4, panel d). All error bars denote 1σ uncertainty.

Supplementary information

Supplementary Information

Supplementary Figs. 1–12 and Tables 1 and 2.

Source data

Source Data Fig. 1

Statistical source data.

Source Data Fig. 2

Statistical source data (the zip file contains a series of.txt files containing data for each of the earthquakes plotted in Fig. 2).

Source Data Fig. 3

Statistical source data.

Source Data Fig. 4

Statistical source data.

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Milliner, C., Avouac, J.P., Dolan, J.F. et al. Localization of inelastic strain with fault maturity and effects on earthquake characteristics. Nat. Geosci. 18, 793–800 (2025). https://doi.org/10.1038/s41561-025-01752-x

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