Journal of Geophysical Research: Solid Earth
Supporting Information for
Recovering paleoearthquake slip record in a highly dynamic alluvial and tectonic region
(Hope fault, New Zealand) from airborne LiDAR
Manighetti I.(1), Perrin C.(1), Dominguez S.(4), Garambois S.(2), Gaudemer Y. (3), Malavieille J. (4),
Matteo L. .(1), Delor E.(1-2), Vitard C.(1), and Beauprêtre S.(2)
(1) GEOAZUR, Université de Nice Sophia Antipolis, CNRS, OCA, Nice, France; (2) ISTerre, Université Grenoble Alpes,
CNRS, Grenoble, France ; (3) Institut de Physique du Globe de Paris, Sorbonne Paris Cité, Univ Paris Diderot, CNRS,
F-75005 Paris, France; (4) Géosciences Montpellier, CNRS, France.
Contents of this file
Figures S4 to S7
Additional Supporting Information (Files uploaded separately)
Captions for Figures S1 to S3 and for Figure S8
Captions for Tables A to B
Introduction
Here we present the LiDAR data along with the quality 1 and quality 2 reconstructed offset
markers. The LiDAR data have been acquired in 2011 by New Zealand Aerial Mapping Limited.
We show complementary analysis of a small offset using the LaDiCaoz code of Zielke and
Arrowsmith (2012), and detailed statistical analysis of the entire offset data collection. We also
provide additional information on scaling relations and generic properties of earthquakes to
discuss the possible slip-length distributions of the identified paleoearthquakes. Finally two
tables present the cumulative lateral offsets that have been measured on the Eastern and the
Western Hope fault prior to the present study, and the offsets measured in the present study,
along with a detailed description of the offset markers.
<Figure ES1>: Uploaded separately because larger than one page
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Figure ES1. Backslip reconstructions of all offset markers rated as quality 1 and quality 2, not
shown in Fig.3 and 4, and having a lateral offset ≤ 60 m. For clarity, only the preferred, optimal
lateral offset is shown, compared with the present trace of the offset markers. The figures are
combined hillshade and contour plots (1, 0.5 or 0.25 m). The fault is in red. Arrows suggest
either the marker edges or the marker overall trend, or they point onto the lateral offset. Long
white arrows indicate the markers for which we measured the lateral offset (see Table B),
whereas short yellow arrows suggest additional markers that seem to be offset but for which
we did not perform any measurement. Insets showing azimuth, slope or hillshade plots are
added in the few cases where they help to better see the offset marker. The figures have been
grouped to show the series of offsets that are best preserved in the morphology (see Fig. 5 and
text): around 4, 9, 14, 18, 23, 28, and > 30 m. The name of the markers, their lateral offset,
uncertainty and quality are indicated (see Fig. 2 for location). The markers and their offsets are
described in Table B.
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Figure ES2. Application of the LaDiCaoz code of Zielke and Arrowsmith (2012) to our marker
pair 16_17 & no (Fig. 3a and Table B). For this marker, we estimated with the backslip procedure
a lateral offset of 4.3 m -0.5/+1.3 m, which we eventually reported as 4.3 ± 1.3 m in our global
statistical analysis. We have expanded the LaDiCaoz code to: i) readjust many more pairs of
profiles than a single one, so as to “scan” a significant length of each marker section either side
of the fault and examine how this “scanning” reveals the actual overall shape of the marker; ii)
lengthen the profiles to be readjusted, so as to examine the matching of the marker over a
section long enough to encompass both the marker flanks and its adjacent “shoulder surfaces”.
Figure ES2-a shows the position of the 18 profile pairs that we fitted. The fault trace is in pale
blue. Fig. ES2-b-s show the readjustments, presented with increasing distance from the fault
trace. Each figure includes three graphs: the best fit of the two profiles to the left, the GoF
values as a function of lateral displacement in the center (GoF are here calculated as in Zielke
and Arrowsmith, 2012; this GoF depends on the number of points being fitted), and the
topography backslipped by the best-fitting offset to the right. We obtain 18 different bestfitting offset values, in the range 2.2-7.1 m. While the GoF maximums slightly vary from one
adjustment to the other, the adjustment of the profile pairs is of similar quality wherever the
profiles are located (see left plots). This shows that the actual lateral offset lies between 2.2 and
7.1 m. The average offset inferred from all the measurements is 4.7 ± 1.5 m. This value is similar
within uncertainties to our estimate from visual backslipping (4.3 ± 1.3 m). Furthermore, Fig.
ES2-t-u show that a 4.3-4.7 m offset also well readjusts the topography adjacent to the marker.
Therefore, the two methods converge on a similar optimal lateral offset, along with similar
uncertainties.
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Figure ES3. Statistical analysis of the cumulative lateral offsets measured on the A to K fault
segments (Table 2; note that we had to consider together the segments E and F, and the
segments I and J, respectively, to have a reasonable number of offsets along the corresponding
fault sections). The offsets are discriminated from their quality. For clarity, the few offsets
larger than 70 m have been ignored in the plots. Each figure compares the histogram of the
measurements (in green), the individual PDFs (in black), and the summed PDF curve (or COPD
plot, in red). Best‐constrained ‘peak’ offset values (COPD values) are indicated above the peaks.
They are reported in Table 2. See text for discussion.
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Figure ES4. Statistical analysis of the complete lateral offset collection in the full range of the
offset data (Table B). The three quality data subsets are analyzed separately (Fig. ES4a, ES4b,
and ES4c), whereas Fig. ES4d analyzes together the quality 1 and quality 2 offsets. Each figure
compares the histogram of the measurements (in green), the individual PDFs (in black in Fig.
ES4a-b-c; in Fig. ES4d, in orange for quality 1 data and in blue for quality 2 data), and the
summed PDF curve or COPD plot (in red). The best-constrained ‘peak’ offset values (COPD
values) are indicated above the peaks. See text for more details.
Figure ES5. Distribution of the measured lateral offsets along the analyzed fault section, for the
entire range of offsets. Zero is taken at the western tip of the LiDAR stretch. The three data
qualities are discriminated with different symbols. The A-K segments are distinguished with
grey vertical bars. See text for more details on the 0-40 m range.
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Figure ES6, Manighetti et al.
Figure ES6. Generic shape of earthquake and fault slip-length profiles. a) Earthquake sliplength profiles measured at surface (from Manighetti et al., 2005). The plot shows about 40 sliplength profiles (in grey) measured on earthquake ruptures of different slip modes, magnitudes
and locations worldwide. In black is the average curve for the entire profile population,
revealing the generic triangular and asymmetric shape of the coseismic slip-length
distributions. b) Earthquake slip-length profiles measured at depth in source inversion models
(from Manighetti et al., 2005). The plot shows about 70 slip-length profiles (in grey) measured
on earthquake ruptures of different slip modes, magnitudes and locations worldwide. In black is
the average curve for the entire profile population, revealing the generic triangular and
asymmetric shape of the coseismic slip-length distributions. c) Long-term cumulative sliplength profiles measured on geological faults (from Manighetti et al., 2001; 2009; 2015). The
plot shows about 700 cumulative slip-length profiles (in black) measured on active normal faults
of different sizes, ages and locations. In blue is the average curve for the entire profile
population, revealing the generic triangular and asymmetric shape of the long-term slip-length
distributions. See text for use of this figure.
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Figure ES7. Earthquake slip-length empirical scaling functions established by Manighetti et al.,
2007 (their Fig. 5a). Black symbols are surface slip-length measurements for 250 historical,
intraplate earthquakes of various slip modes, magnitudes and locations worldwide. In solid lines
are the four established slip-length scaling functions. Earthquakes have variable slip to length
ratios, and hence variable apparent stress drops, that depend on the maturity of the fault which
they broke. Functions 1 to 4 indicate earthquakes that occurred on faults ranging from
immature (function 1) to mature (function 4). In dotted line is, for comparison, the Wells and
Coppersmith (1994) empirical slip-length scaling function. The red lines indicate the
characteristic coseismic slip measured in this study (4.4 ± 1 m)
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Figure ES8. (a) Slip-length distributions established from individual offset measurements. In
left graphs, only quality 1 and 2 measures are shown, whereas the three quality data are
presented in right graphs. In each plot, the dotted lines suggest the slip-length profiles of the 3
to 4 most recent large earthquakes. These lines are made to run through the quality 1 and 2
offset measures. Scenario 1 is unlikely because it would produce very high stress drop
earthquakes (very short rupture lengths << 100 km), which are unlikely on a mature fault as is
the Hope fault; Scenario 2 is likely and actually shown in greater details in Fig. ES8b (see text);
Scenario 3 is unlikely because it would produce high stress drop earthquakes (short rupture
lengths < 100 km), which are unlikely on a mature fault as is the Hope fault; Scenarios 4a and 4b
are possible provided that the maximum coseismic slip is at most ~5.5 m (see text); Scenario 4c
is unlikely because gentle westward slip tapering cannot occur over the short distance that
separates the LiDAR stretch and the Hanmer step-over; Scenarios 5 to 8 are unlikely because
they would produce very high stress drop earthquakes (large slip to length ratios), which are
unlikely on a mature fault as is the Hope fault. (b) our interpretation of the most likely sliplength distributions for the 4 most recent large earthquakes on the Eastern Hope fault. The sliplength functions are drawn through the quality 1 and 2 offsets, and they are made to satisfy the
entire set of information discussed in section 6.3.
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<Table A>: Uploaded separately because larger than one page
Table A. Published cumulative lateral offsets on the Eastern (Table A-a) and the Western (Table
A-b) Hope fault (i.e., east and west of central Hanmer basin). Offsets reported in Beauprêtre et
al., 2012 are not included for they were measured in our LiDAR data, and they are re-measured
in the present study (see Table B).
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Table B. Measured cumulative lateral offsets. Marker names refer to Figure 2. They are
indicated on both northern and southern sides of the fault trace (columns 2&3). The fault
segments along which the offsets are measured are indicated (column 1, see Fig.2). Columns
4&5 report the latitude-longitude coordinates of the piercing points of the northern and
southern markers against the fault trace. Columns 6, 7, 8 and 9 report the measured cumulative
lateral offset, the maximum and minimum errors on the offset, and the quality rating attributed
to the marker pair matching. Column 10 indicates the color of the markers on Figure 2. Column
11 provides a short description of the markers’ nature, whereas column 12 adds specific
comments on each marker. For most quality 4 offsets, we do not provide any offset
measurement as these measures might be misleading. We however provide a few values for the
clearest of these quality 4 offsets, but these values are ignored in the present analysis.
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