A Scaling Law for Slow Earthquakes
Nature, 2007 · paper · Earth science
Shows that slow earthquake phenomena, including tremor, low-frequency and very-low-frequency earthquakes and slow slip, follow one scaling relationship. Seismic moment is proportional to duration, unlike regular earthquakes, suggesting they form a new earthquake category.
Checked: PDF from courses.washington.edu, fetched 4 Oct 2026. Page numbers are those of that PDF.
4 findings
Reference or label The shallow VLF earthquakes of ref. 26 are located in "the accretionary prism of the Nankai trough26" (Fig. 2 legend) but "within the shallow accretionary prism along the Japan trench26" (text) and "Northeast Japan26" (Table 1).
- p. 3 Figure 2 caption, item b
earthquakes in the accretionary prism of the Nankai trough26
- p. 4 left column, first paragraph
within the shallow accretionary prism along the Japan trench26
- p. 2 Table 1, row Shallow VLF, column Area
Northeast Japan26
- p. 3
b, VLF earthquakes in the accretionary prism of the Nankai trough26.
Only the authors can say what is right here.
Judge's note: All three statements read as quoted on the page 2, 3 and 4 images. The paper elsewhere separates the Nankai trough (western Japan) from the Japan trench / Northeast Japan, so the locations conflict. The title of ref. 26 names no location, so the paper alone does not show which is right; the authors must say. The text presents these events as occurring "in other environments", so the location bears on the argument.
Second check: another model agreed
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Reference or label Two different display equations on p. 3 are both numbered (4): "L^3 = C1T (4)" and "L^2 = C2T (4)"; the later pointer "Equation (4) explains the rupture velocity of 0.1 m s^-1" refers to the second one and is therefore ambiguous. The second label should be (5).
- p. 3 left column, first display equation
L3 5 C1T (4)
- p. 3 left column, second display equation
L2 5 C2T (4)
- p. 3 left column bottom, diffusional model paragraph
Equation (4) explains the rupture velocity of 0.1 m s21
- p. 3 left column, first display equation (low-stress drop model)
L3 = C1T (4)
Judge's note: Checked the page-3 crops: the low-stress-drop relation L^3 = C1T and the diffusional relation L^2 = C2T both carry the label (4). No equation (5) appears anywhere. The sentence 'Equation (4) explains the rupture velocity of 0.1 m s^-1 for L≈100 km, while ... 1 m s^-1 for L≈10 km' sits in the diffusional-model paragraph, and its numbers follow from L/T = C2/L with C2 ≈ 10^4 m^2 s^-1. With C1 ≈ 3×10^8 the values would be 0.03 and 3 m/s instead. This is a numbering and pointer error. The physics is unaffected.
Second check: another model agreed
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Reference or label The afterslip event cited to ref. 27 has two different years: "e, Afterslip of the 1992 Sanriku earthquake27" in the Fig. 2 caption (p. 3) and "after the 1994 Sanriku earthquake27" in the text (p. 4).
- p. 3 Figure 2 caption, item e
e, Afterslip of the 1992 Sanriku earthquake27
- p. 4 left column, first paragraph
1994 Sanriku earthquake27
- p. 3
e, Afterslip of the 1992 Sanriku earthquake27.
- p. 3 Figure 2 legend, item e
Afterslip of the 1992 Sanriku earthquake27
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: that Heki et al. 1997 (ref. 27) describes afterslip of the 1994 Sanriku-Haruka-oki earthquake. I checked the images: the Fig. 2 caption (p. 3) prints 1992 and the p. 4 text prints 1994, and both cite ref. 27 for afterslip. Within the files, the 1992 Sanriku-oki event belongs to ref. 6 (Kawasaki et al., 'The 1992 Sanriku-oki, Japan, ultra-slow earthquake'), which suggests the caption mixes up the two events. Ref. 27's title as listed does not give the year, so the authors would need to confirm which year is correct.
Second check: another model agreed
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Reference or label Reference 3: "Science 26, 503–506 (2006)" gives volume 26 for a 2006 Science paper, while the same list has Science 286 (1999) and 296 and 298 (2002).
- p. 4 reference 3
Science 26, 503–506 (2006)
- p. 4 reference 8
Science 298, 1009–1012 (2002)
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: the true volume and year of Ito et al. (reviewers say Science 315, 503–506, 2007). The page 4 image shows a bold "26", so this is not an extraction artefact. The reference list itself shows 26 cannot be right: refs 23, 1 and 8 give Science volumes 286 (1999) and 296 and 298 (2002), so a 2006 volume would be above 300. The correct volume and year cannot be checked from the files.
Second check: another model agreed
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7 minor (typos and the like; most checked by the judge only)
Wording "The spectra of VLFs, LFEs and tremor all follow f−1 decay at high frequency (Fig. 3b, c)": Fig. 3b is a VLF and 3c an LFE; no tremor spectrum is shown, and the legend claims the result only "For both VLF and LFE".
- p. 2 body text, first paragraph under Figure 1
The spectra of VLFs, LFEs and tremor all follow f
- p. 3 Figure 3 legend
For both VLF and LFE, spectra
Judge's note: Checked Fig. 3 panels and legend on the page 3 image: panel b is station TSAF VLF events, panel c is station KWBH LFEs. No tremor spectrum is plotted. The following sentence cites ref. 13 for stacked LFE spectra and the paper treats tremor as closely related to LFEs, so the claim may be covered implicitly, but the cited panels do not show tremor. Minor overstatement of what the figure shows.
Second check: another model agreed
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Typo Fig. 2 legend: "These follow a scaling relation of M0 ∝ t, for slow earthquakes" uses lower-case t, while the characteristic duration is T in equations (1), (2), (4) and Table 1.
- p. 3 Figure 2 caption
These follow a scaling relation of M0 / t, for
- p. 1 right column, before equation (1)
duration T (in units of seconds)
- p. 3 Figure 2 legend
These follow a scaling relation of M0
- p. 3 Figure 2 caption
M0 / t, for
Judge's note: Crop of the legend shows an italic lower-case t. The text defines the characteristic duration as T and uses t for running time (moment rate function, u(t)). The figure plots characteristic duration, so T is expected, but the text also argues that moment grows in proportion to elapsed time, so lower-case t could be deliberate. Cosmetic.
Second check: none (judge only)
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Typo Malformed clause: "which is not impossible, but in the case of stress drop is much higher than observed for regular earthquakes".
- p. 3 discussion of intersection of scaling relations
but in the case of stress drop is much higher than observed
Judge's note: Read on the page 3 image, right column. The clause lacks a subject after "in the case of stress drop"; the meaning (the stress drop is much higher than observed for regular earthquakes) is clear. Cosmetic wording slip.
Second check: none (judge only)
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Typo Reference 21 prints the fourth author as "Brechenridge, K. S."; reviewers say the name is Breckenridge.
- p. 4 reference 21
Brechenridge, K. S.
- p. 4 reference 21
Brechenridge
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: the spelling of the fourth author of Gladwin et al., J. Geophys. Res. 99 (1994). The page 4 image prints "Brechenridge", so it is not an extraction artefact. The correct spelling cannot be verified from the files.
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Typo Reference 25 prints the fourth author as "Mikilius, A."; reviewers say the name is Miklius.
- p. 4 reference 25
Mikilius, A.
- p. 4 reference 25
Mikilius
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: the spelling of the fourth author of Segall et al., Nature 442, 71–74 (2006). The page 4 image prints "Mikilius". The correct spelling cannot be verified from the files.
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Typo Reference 12 prints "Baba, T., Tanioka, T., Cummins, P. R. & Uhira, K."; reviewers say the second author is Tanioka, Y.
- p. 4 reference 12
Baba, T., Tanioka, T., Cummins, P. R. & Uhira, K.
- p. 4 reference 12
Tanioka, T.
- p. 4 reference 12
Baba, T., Tanioka, T.
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: the initial of the second author of Baba et al., Phys. Earth Planet. Inter. 132, 59–73 (2002). The page 4 image prints "Tanioka, T.". The initial may have been carried over from "Baba, T.", but this cannot be verified from the files.
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Typo Acknowledgements name the funder as "the Ministry of Education, Sports, Science and Technology, Japan", omitting "Culture".
- p. 4 Acknowledgements
the Ministry of Education, Sports, Science and
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: the official English name of the Japanese ministry (Ministry of Education, Culture, Sports, Science and Technology). The page 4 image prints the name as quoted. It may be an informal short form; cosmetic either way.
Second check: none (judge only)