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Upper-plate rigidity determines depth-varying rupture behaviour of megathrust earthquakes


Seismological data provide evidence of a depth-dependent rupture behaviour of earthquakes occurring at the megathrust fault of subduction zones, also known as megathrust earthquakes1. Relative to deeper events of similar magnitude, shallow earthquake ruptures have larger slip and longer duration, radiate energy that is depleted in high frequencies and have a larger discrepancy between their surface-wave and moment magnitudes1,2,3. These source properties make them prone to generating devastating tsunamis without clear warning signs. The depth-dependent rupture behaviour is usually attributed to variations in fault mechanics4,5,6,7. Conceptual models, however, have so far failed to identify the fundamental physical causes of the contrasting observations and do not provide a quantitative framework with which to predict and link them. Here we demonstrate that the observed differences do not require changes in fault mechanics. We use compressional-wave velocity models from worldwide subduction zones to show that their common underlying cause is a systematic depth variation of the rigidity at the lower part of the upper plate — the rock body overriding the megathrust fault, which deforms by dynamic stress transfer during co-seismic slip. Combining realistic elastic properties with accurate estimates of earthquake focal depth enables us to predict the amount of co-seismic slip (the fault motion at the instant of the earthquake), provides unambiguous estimations of magnitude and offers the potential for early tsunami warnings.

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Fig. 1: Tectonic structure of the shallow region of two types of subduction zones where tsunamis are generated.
Fig. 2: Convergent margin structure and P-wave velocity at the lower part of overriding plates.
Fig. 3: Predicted earthquake rupture and energy release characteristics.
Fig. 4: Conceptual model of megathrust seismogenic zone domains.

Data availability

Source data for Figs. 2 and 3 and for Extended Data Figs. 48 are provided with the paper. The digitized values of P-wave seismic velocity above interplate boundary versus depth and seafloor depth along the 48 wide-angle seismic profiles used here are available at the public research data repository figshare (

Code availability

The scripts necessary to process the data and reproduce the main results and figures presented in this work are available at the public research data repository figshare (


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This work was done in the framework of projects ZIP (reference 604713), funded by the E.C. in the call for proposals FP7-PEOPLE-2013-ITN and FRAME (reference CTM2015-71766-R), funded by the Spanish Plan of Research and Innovation. We thank D. Klaeschen and R. von Huene (Geomar) for providing a copy of the P849 seismic data displayed in Fig. 1, T. Lay for his review, and J.-P. Ampuero for his comments on a preliminary version of the work.

Author information




V.S. had the original idea, conceived the physical model, selected and digitized the P-wave velocity profiles, performed the calculations, made the figures except Fig. 1, and wrote the first draft of the manuscript. C.R.R. made the geological interpretation of the physical model, contributed to identifying its implications, processed and pre-stack depth-migrated Java 07 and interpreted both seismic images on Fig. 1, and contributed to writing the manuscript.

Corresponding author

Correspondence to Valentí Sallarès.

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Competing interests

The authors declare no competing interests.

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

Peer review information Nature thanks Thorne Lay and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Extended data figures and tables

Extended Data Fig. 1 Location map of seismic profiles and recent great and tsunami earthquakes.

Colour-coded relief map of seafloor (blue-green) and emerged land (grey). Circles indicate location of the trench-crossing refraction and wide-angle reflection seismic (WAS) profiles used in this study. Yellow-filled circles are in erosional margins and red-filled circles in accretionary margins. The location, type of margin and references for all profiles are listed in Extended Data Table 1. Numbered white stars show locations of 12 events recognized as tsunami earthquakes according to the definition of Kanamori11: (1) Mw 7.6, 1992 Nicaragua; (2) Mw 7.6, 1960 Peru; (3) Mw 7.5, 1995 Peru; (4) Ms 7.2, 1947 Hikurangi; (5) Mw 7.1, 2010 Solomon; (6) Mw 7.6, 1994 Java; (7) Mw 7.8, 2006 Java; (8) Mw 7.8, 2010 Mentawai; (9) Mw 8.0, 1896 Sanriku; (10) Mw 7.5, 1975 Kurile; (11) Mw 7.8, 1963 Kurile; (12) Mw 8.2, 1946 Aleutian. Orange polygons display the rupture areas of the six largest megathrust earthquakes since 1960: Mw 9.5, 1960 Valdivia; Mw 9.2, 1964 Alaska; Mw 9.1, 2004 Andaman Islands; Mw 9.1, 2010 Tohoku-Oki; Mw 8.8, 2010 Maule; Mw 8.7, 1965 Rat Island. Hypocentral location, date, magnitude and references for all these earthquakes are listed in Extended Data Table 2. This figure has been created using the GMT software package46. The topographic and bathymetric relief data have been taken from the GEBCO Digital Atlas data set47. Authors are not aware of any disputed territories shown.

Extended Data Fig. 2 Superposition of multichannel seismic image and P-wave velocity model.

Example of superposition of a VP model (colour, see scale) on a spatially coincident multichannel seismic image (shading) along profile NIC-20, acquired in the convergent margin of Nicaragua. This profile crosses the rupture area of the 1992 Nicaragua tsunami earthquake (Extended Data Fig. 1). Black lines show isovelocity contours with their corresponding velocity values. White circles indicate the approximate location of the interplate boundary, where megathrust earthquakes take place.

Extended Data Fig. 3 Resolution of VP models and wavelength of rupture stress wavefield.

The light red polygon displays the width of the Fresnel zone as a function of depth, assuming VP(z) in Fig. 2a and energy sources with minimum (maximum) peak frequency fs = 8 Hz (12 Hz). The blue-lilac polygon indicates the approximate wavelength of the stress wavefield associated to earthquake rupture propagation (λw), assuming VS(z) in Extended Data Fig. 5c as propagation velocity, and near-field ground motion spectra with minimum (maximum) peak frequency fsw = 1 Hz (4 Hz) (see Methods for details).

Extended Data Fig. 4 Physical properties versus interplate boundary depth.

a, Red (yellow) circles show VP as a function of z. It is obtained by averaging digitized VP values of accretionary and erosional margins (red and yellow circles, respectively, in Fig. 2b). b, White circles show density (ρ) just above the interplate boundary, as a function of z, obtained by applying Brocher’s ρ(VP) relationship19. c, Red circles show shear-wave velocity (VS) just above the interplate boundary, as a function of z, obtained by applying the VS(VP) relationship from Brocher (ref. 19). The shaded polygon covers the range of possible mode III rupture velocities, as a function of z, according to field observations: u(z) = (0.7–0.9)VS(z). The black line is a fourth-order polynomial regression fit of the VP(z), ρ(z) and VS(z) values, respectively. The size of the error bars in all cases is one standard deviation. Source data

Extended Data Fig. 5 P-wave velocity and rigidity gradients.

a, Red line shows the depth gradient of VP as a function of interplate boundary depth, \(\partial {V}_{{\rm{P}}}(z)/\partial z\). It corresponds to the derivative of the VP(z) polynomial regression fit (black line in Fig. 2c). b, Blue line shows the depth gradient of μ as a function of interplate boundary depth, \(\partial \mu (z)/\partial z\). It corresponds to the derivative of the μ(z) polynomial regression fit (black line in Fig. 2d). Source data

Extended Data Fig. 6 Corner frequency and moment rate spectra.

a, Coloured circles show corner frequency as a function of interplate boundary depth (z), for events of Mw = 5.8-8.6. Δσ = 3 MPa is used in the calculations, and VS(z) is taken from Extended Data Fig. 3c. The colour scale indicates Mw. b, Solid lines show calculated moment rate spectra for three events of Mw = 6.4 (bottom), 7.4 (mid) and 8.4 (top). Black, blue and red lines correspond to Vs at z = 1 km, 6 km and 25 km, respectively, for each event. Coloured circles indicate corner frequency according to colour code in Extended Data Fig. 6a. Vertical dashed lines indicate periods of 250 s and 20 s, reference to calculate Mw and Ms, respectively. In all cases, note the high-frequency depletion at shallow depths. Source data

Extended Data Fig. 7 Source duration of circum-Pacific megathrust earthquakes.

a, White circles show scaled source duration of 525 moderate size (Mw 5.0–7.5) shallow megathrust subduction earthquakes from around the circum-Pacific, as a function of depth. Black circles show the same source parameters for six large tsunami earthquakes. Data are from ref. 21. This article contains all the information on the procedure followed to calculate the source parameters. b, Red circles are the normalized source duration in a averaged within a 2-km-thick sliding window. Blue circles correspond to relative rupture duration in Fig. 3b scaled to fit average normalized rupture duration within the regular domain in a (approximately 3.5 s), and shifted 4.5 km down to compensate for the difference between depth below sea surface and depth below seafloor. Error bars are one standard deviation. Source data

Extended Data Fig. 8 Range of variation of Mw for a given Ms.

White circles show Mw for events occurring at different interplate boundary depth b.s. that have the same spectral amplitude at 20 s (hence equivalent Ms). Source data

Extended Data Table 1 Location of seismic profiles and margin type
Extended Data Table 2 Location and magnitude of circum-Pacific megathrust earthquakes

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Sallarès, V., Ranero, C.R. Upper-plate rigidity determines depth-varying rupture behaviour of megathrust earthquakes. Nature 576, 96–101 (2019).

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