Content uploaded by Shmuel Marco
Author content
All content in this area was uploaded by Shmuel Marco on Dec 15, 2014
Content may be subject to copyright.
Geology
doi: 10.1130/G30685.1
2010;38;303-306Geology
Nadav Wetzler, Shmuel Marco and Eyal Heifetz
sediments
Quantitative analysis of seismogenic shear-induced turbulence in lake
Email alerting services
articles cite this article
to receive free e-mail alerts when newwww.gsapubs.org/cgi/alertsclick
Subscribe to subscribe to Geologywww.gsapubs.org/subscriptions/click
Permission request to contact GSAhttp://www.geosociety.org/pubs/copyrt.htm#gsaclick
official positions of the Society.
citizenship, gender, religion, or political viewpoint. Opinions presented in this publication do not reflect
presentation of diverse opinions and positions by scientists worldwide, regardless of their race,
includes a reference to the article's full citation. GSA provides this and other forums for the
the abstracts only of their articles on their own or their organization's Web site providing the posting
to further education and science. This file may not be posted to any Web site, but authors may post
works and to make unlimited copies of items in GSA's journals for noncommercial use in classrooms
requests to GSA, to use a single figure, a single table, and/or a brief paragraph of text in subsequent
their employment. Individual scientists are hereby granted permission, without fees or further
Copyright not claimed on content prepared wholly by U.S. government employees within scope of
Notes
© 2010 Geological Society of America
on March 25, 2010geology.gsapubs.orgDownloaded from
GEOLOGY, April 2010 303
INTRODUCTION
Earthquake-induced deformation of sedi-
ments, called seismites, is common in the
late Pleistocene lacustrine Lisan Formation
near the Dead Sea (Fig. 1). El-Isa and Mus-
tafa (1986) postulated that the abundant folds
formed when seismic waves deformed the
sediments at the lake bed. The discovery of
turbulent breccia layers (originally called
“mixed layers”) abutting syndepositional faults
(Agnon et al., 2006; Marco and Agnon, 1995)
proved that the breccia layers are seismites,
thus providing a paleoseismic record spanning
70–15 ka (Marco et al., 1996). Additional con-
fi rmation for the identifi cation of these layers
as seismites was found in the temporal correla-
tion of late Holocene breccias with historical
earthquakes (Ken-Tor et al., 2001; Migowski
et al., 2004). The deformation features typi-
cally appear in layers with thickness varying
from centimeters to decimeters. The layers are
folded asymmetrically in trains showing the
same trend of axial plane dips. The deformed
beds are enclosed between undeformed layers
of alternating millimeter-scale laminas with
annual pairs of winter detritus and summer
evaporitic aragonite (Begin et al., 1974).
The tectonic environment of an active plate
boundary in which these layers lay, suggests that
understanding the process of seismite forma-
tion might provide a method to relate sediment
deformation features with earthquake param-
eters. The original sediments consist of stably
stratifi ed water saturated mud. This condition
rules out the role of Rayleigh-Taylor Instability
(requiring an inversion of densities). The asso-
ciation of a specifi c mechanical process with the
seismites under discussion was fi rst presented
by Heifetz et al. (2005), who hypothesized
that, since earthquakes typically induce shear
and the sediments are stably stratifi ed, Kel-
vin Helmholtz Instability (KHI) is a plausible
mechanism. Using linear stability analysis they
showed that strong earthquakes are indeed capa-
ble of setting off the KHI, by providing shear
kinetic energy that exceeds the gravitational
potential energy. While the analysis of Heifetz
et al. (2005) was linear, it is evident that nonlin-
ear processes play a major role in the dynamics
of strong earthquakes, which is the focus of this
paper. We further examine the response of sta-
bly stratifi ed mud to an imposed shear through
direct numerical simulation (DNS), and uses
the KHI hypothesis to explore the possibility of
using these structures as “paleoseismograms.”
POWER SPECTRUM ANALYSIS
The sediment deformations in the study area
(left column of Fig. 2) appear in various forms
of linear waves, billow-like asymmetric folds,
coherent vortices, and turbulent chaotic struc-
tures (breccia).
Because KHI is a non-isotropic phenomena
(with vertical stratifi cation and shear and hori-
zontally directed velocities) its energy power
spectrum does not obey the inertial isotropic
Kolmogorov turbulence power law [E(k) µ k
-a
,
where E(k) is the energy deposited in wave
number k = 2π/λ, where λ is the wavelength,
with a = 5/3]. In other disciplines, such as ocean
fl uid dynamics (e.g., Li and Yamazaki, 2001),
turbulent KHI was found to obey a power law
with a value of ~2. Hence, in order to examine
further the KHI hypothesis, we fi rst analyze the
power spectra of hundreds of observed deforma-
tions in the fi eld.
Unlike analyses of KHI in lab or fi eld
experiments, in which the power spectrum of
the kinetic and potential energy are measured
directly, we have to deduce the energy indirectly
from the motionless deformed layers. After the
deformation ceased, the water was squeezed
out of the sediment, which became solid rock.
Hence, as a proportional proxy for the poten-
tial energy during the dynamic stage (i.e., the
earthquake) we consider the deformation ampli-
tude squared (A
2
), defi ned in Figure 3. Since in
idealized KHI the energy is equally partitioned
between its kinetic and potential components
(e.g., Kundu and Cohen, 2008) it can be approx-
imately related to the eddy kinetic energy.
We photographed more than 300 folds of
all shapes and evolutional stages in the Lisan
Geology, April 2010; v. 38; no. 4; p. 303–306; doi: 10.1130/G30685.1; 4 fi gures.
© 2010 Geological Society of America. For permission to copy, contact Copyright Permissions, GSA, or editing@geosociety.org.
Quantitative analysis of seismogenic shear-induced turbulence in
lake sediments
Nadav Wetzler, Shmuel Marco, and Eyal Heifetz
Department of Geophysics and Planetary Sciences, Tel Aviv University, Tel Aviv, Israel
ABSTRACT
Spectacular deformations observed in lake sediments in an earthquake prone region (Lisan
Formation, pre–Dead Sea lake) appear in phases of laminar, moderate folds, billow-like asym-
metric folds, coherent vortices, and turbulent chaotic structures. Power spectral analysis of
the deformation indicates that the geometry robustly obeys a power-law of –1.89, similar to
the measured value of Kelvin-Helmholtz (KH) turbulence in other environments. Numeri-
cal simulations are performed using properties of the layer materials based on measure-
ments of the modern Dead Sea sediments, which are a reasonable analogue of Lake Lisan.
The simulations show that for a given induced shear, the smaller the thickness of the layers,
the greater is the turbulent deformation. This is due to the fact that although the effective
viscosity increases (the Reynolds number decreases) the bulk Richardson number becomes
smaller with decrease in the layer thickness. The latter represents the ratio between the gravi-
tational potential energy of the stably stratifi ed sediments and the shear energy generated
by the earthquake. Therefore, for thin layers, the shear energy density is larger and the KH
instability mechanism becomes more effi cient. The peak ground acceleration (PGA) is related
to the seismogenic shear established during the earthquake. Hence, a link is made between the
observed thickness and geometry of a deformed layer with its causative earthquake’s PGA.
Figure 1. A: Sampling locations shown
with the background of maximum extent of
Lisan at 26 ka in blue. B: Tectonic plates in
the Middle East. Dead Sea Transform (DST)
transfers the opening motion in the Red
Sea to the Taurus-Zagros collision zone.
C: Landsat image of sampling region.
on March 25, 2010geology.gsapubs.orgDownloaded from
304 GEOLOGY, April 2010
Forma tion outcrops in two locations, Masada
and Peratzim (Fig. 1). For each fold the most
conspicuous lamina is traced and stored in a dig-
ital database. For scaling and rectifi cation, we
use a 1m × 1m frame with grid lines spaced by
10 cm as well as a ruler with millimeter marks.
For very small folds we counted pixels on
images using standard commercial image pro-
cessing software. Each measurement includes
the deformation amplitude A, from the base of
the lamina to the most upper part of its curved
wave structure. The half wavelength (λ/2) is
measured on the base of the lamina between
the two minima points (illustrated on inset in
Fig. 3). Although this measurement technique
is rather crude the power spectrum is strikingly
robust with a power law of 1.89 and R
2
= 0.98.
The robustness of the power law and its
agreement with the measured KHI power law
in other disciplines, together with the facts that
these hundreds of samples (with amplitudes and
associated wavelengths varying from scales of
centimeters to decimeters) are associated with
dozens of different earthquake events, and are
taken from two different sites, all suggest that
KHI is likely the governing mechanism of the
sediment deformation.
DIRECT NUMERICAL SIMULATIONS
OF KHI
Since the observed power spectra, and the
linear stability analysis both support the KHI
hypothesis, we proceed with direct numerical
simulations (DNS) examining the response of
stably stratifi ed saturated mud to an imposed
shear. This response depends on the material
properties of the mud, mostly on its density and
viscosity profi les. In order to obtain a reason-
able estimation of the paleo–Lake Lisan mud
properties we use the modern Dead Sea sedi-
ments as an analogue.
The purpose of these simulations is to verify
whether the deformations observed in the fi eld
can be generated by KHI, given typical earth-
quake properties (duration on the order of sec-
onds, ground acceleration ~0.1 g, where g is
gravity), typical layer thickness (from a few
centimeters up to 0.5 m), and typical density
and viscosity stratifi cations. As a best reason-
able estimation for the latter two properties, we
sampled mud from the Dead Sea lake bed at two
layers: at depths of 10 cm and 30 cm. The aver-
age densities are 1600 kg/m
3
for the upper layer
and 1750 kg/m
3
for the lower layer, where their
respective viscosities (measured with a Newto-
nian analog viscometer) are 0.3 PaS and 3 PaS.
We use the FLUENT commercial software
(http://www.ansys.com/products/fl uid-dynam-
ics/fl uent/) to solve the Navier-Stokes equations
numerically. The simulation setup is composed
of two stratifi ed fl uid layers, subject to shear. In
the simulations the layers are 2 m long and their
Figure 2. Comparison of fi eld observations in Lisan Formation sediments with numerical
simulations showing similar stages of Kelvin-Helmholtz instability evolution from linear wave
through asymmetric billows, coherent vortices, and fully turbulent breccia. Grid spacing on
photos is 10 cm.
Figure 3. The deformation amplitude (A) squared versus wavenumber k of 310 folds mea-
sured in Masada (solid triangles) and Peratzim (open circles). The dashed blue regression
line of A
2
= 0.26k
-1.89
, R
2
= 0.98, is compared with a reference curve of A
2
= 0.26k
-2
(solid). Inset
picture at top right illustrates how the amplitudes and wavelengths were measured.
on March 25, 2010geology.gsapubs.orgDownloaded from
GEOLOGY, April 2010 305
thickness varies between 4, 10, and 50 cm. The
model grid is built using the GAMBIT software,
with a fi xed horizontal resolution of 0.5 cm
and a vertical resolution of 0.1, 0.3, and 1 cm
respectively. The background hydrostatic pres-
sure is taken to be 600,000 Pa corresponding
to a 50 m lake depth, based on paleo lake level
record (Bartov et al., 2002). To study the two-
phase problem with the FLUENT simulations
we applied the option of fl uid volume conser-
vation, free boundary condition at the interface
between the layers, and no slip solid boundary
conditions for the upper and lower boundaries.
The upper layer is accelerated horizontally,
with respect to the lower layer, imposing a
range of accelerations of 0.1, 0.2, 0.3, and 0.6 g.
A localized sinusoidal perturbation with a fre-
quency of 1 Hz (representing a seismic wave) is
initiated at the interface with small amplitude of
5 mm. The time step of the simulation is 0.01 s
and the simulations are run up to 1.5 s.
Snapshots after 1 s of evolution of these 12
runs are presented in Figure 4A. The four types
of deformation found in the fi eld (linear waves,
asymmetric billows, coherent vortices, and fully
turbulent breccia layers) are produced by the
simulations. The resemblance of the simula-
tions to the observed deformations is apparent
in Figure 2. The larger the ground acceleration
and the thinner the layer, the more intense is the
deformation. While the former dependency is
quite obvious, the latter is not trivial, although
predicted by Heifetz et. al (2005) by the linear
analysis. On the one hand, the viscosity becomes
more effective for thin layers since the Reynolds
number (Re = UD/ν, where U is the characteris-
tic velocity, D is the layer thickness and ν is the
kinematic viscosity) becomes smaller. On the
other hand, the bulk Richardson number (Ri)
becomes smaller as well [Ri = (g∆ρ/ρ
m
∆U
2
)D,
where ∆ρ is the density difference between the
layers and ρ
m
is their mean value]. The Rich-
ardson number indicates the ratio between the
gravitational potential energy of the stably strat-
ifi ed sediments and the required shear energy,
exerted by the earthquake, to overcome the for-
mer. Because the sheared region is concentrated
at the interface between the layers but acts to
deform the full depth of the layers, the shear
energy density is larger for thin layers, making
the KHI mechanism more effi cient.
The deformation stages as a function of Rich-
ardson and Reynolds numbers are summarized
in Figure 4. As expected from the theory, no
instability is obtained when Ri > 0.25.
DISCUSSION
The ubiquitous appearance of deformed
coherent billows, together with the basic condi-
tions of stably stratifi ed sediments subjected to
earthquake-induced shear, strongly suggest that
KHI is indeed the governing mechanism of fold
evolution. Nonetheless, it is impossible to abso-
lutely determine that the seismites deformations
examined in this study resulted only from KHI
during paleo-earthquakes.
Among other plausible mechanisms is the
liquefaction of the underlying muddy layer and
passive collapse of the overlying cohesive mud
during the earthquake (Owen, 1987). Then,
even slopes with slight inclination can yield
asymmetrical morphologies. Evidence for simi-
lar KHI-induced deformations in other places
were observed after the tsunami generated by
the great Sumatra earthquake (Matsumoto et
al., 2008), where coherent billows were formed
at the sheared interface at the bottom of the tsu-
nami sand deposits. Simulations of the effects
of strong earthquakes in Lake Lisan also show
that seiches may form and cause destratifi ca-
tion in the water column associated with breccia
forming at the lake bottom (Begin et al., 2005).
Hence, the seiche-induced shear at the bottom
of the lake could have enhanced the turbulent
characteristics of the deformation. Another case
was observed in deformed clay sediments that
also show coherent billows in the Jharia Basin,
India. It was shown experimentally and numeri-
cally by Dasgupta (2008), that the waveform of
shear induced deformation is enhanced if the
two layers have different rheological properties.
A detailed analysis of the deformation
amplitude power spectrum of more than 300
samples (in varying sizes of few millimeters
to 1 m), taken from two different sites near
the Dead Sea, triggered by dozens of differ-
ent earthquakes, reveals a strikingly well-
constrained sharp power law of 1.89, a similar
value to the power law obtained for KHI in
other environments.
Although it is impossible to determine the
Ozmidov scale, from which the stratifi cation
shifts the power spectrum from the inertial Kol-
mogorov power law to the KH one, this fi nd-
ing strongly supports the KHI hypothesis (the
Ozmidov scale is defi ned as the square root of
the ratio between the dissipation rate of turbu-
lent kinetic energy and the third power of the
Figure 4. A: Simulation snapshots after 1 s from onset of earthquake fi rst shock for different ground accelerations and various layer thick-
ness. Basic simulation setup shown at bottom left. B: Values of Reynolds (Re; color coded) and Richardson numbers (Ri; dashed lines)
based on the same layer thickness and ground acceleration as the simulation snapshots on the left (curves are smoothed). Annotation
between gray lines indicates ranges with characteristic deformation patterns obtained for each run, after 1 s of model time.
on March 25, 2010geology.gsapubs.orgDownloaded from
306 GEOLOGY, April 2010
buoyancy frequency. While the buoyancy fre-
quency can be extracted from the density profi le
there is no reliable way to obtain the dissipation
rate from the fi eld data).
Our numerical simulations are somewhat
crude. They do not take directly into account
the two phase fl ow non-Newtonian behavior
of the consolidated mud, the buildup of pore
pressure that may lead to liquefaction, the pres-
ence of fi nite thick shear layer and other related
phenomena. Furthermore, the material proper-
ties of the sediments (see above) are taken from
measurements of the current lakebed sediments,
which may differ from the paleo–lake Lisan
sediments. Nevertheless, the simulations show
that within typical ranges of earthquake ground
acceleration, layer thickness, and perturbed
seismic frequency, all types of KH deforma-
tion phases (linear waves, asymmetric billows,
coherent vortices, and fully turbulent breccia
layers) are reconstructed. The robustness of the
results may therefore testify to the robustness of
the KH mechanism.
The numerical simulations indicate that the
larger the ground acceleration and the thin-
ner the layer, the more intense are the defor-
mations. The duration of the earthquake was
found to affect the geometry, rather than the
deformation amplitude. This is somewhat dif-
ferent from the earthquake duration effect on
asymmetric morphologies generated by gravity
currents above liquefi ed layers, (Moretti et al.,
1999; Owen, 2003).
Potentially, Figure 4 may serve as a sort of
“paleoseismogram”; identifi cation of the geom-
etry of the deformation and the layer thickness
provides an estimation of the peak ground accel-
eration. By assuming locations of paleo earth-
quakes and using known attenuation relations
(e.g., Boore et al., 1997) an indirect estimation
for the earthquake magnitude may be obtained
from the geometrical properties of the deformed
sediment layer.
CONCLUSIONS
We suggest that the various types of defor-
mation in the Lisan Formation can be explained
as the results of earthquake triggered KHI. The
instability caused a continuous development,
which culminated in turbulent breccias layers.
The deformation process was quenched at dif-
ferent stages depending on the sediment prop-
erties (layer thickness, density and viscosity
gradients) and induced acceleration. These rela-
tions may enable the estimation of paleo-earth-
quake magnitude.
ACKNOWLEDGMENTS
We thank Amotz Agnon for stimulating discus-
sions and good advice. We are also grateful to Mas-
simo Moretti and an anonymous journal referee for
thorough revisions and constructive comments. The
research was funded by the Binational U.S.-Israel Sci-
ence Foundation grant #2004087 to Heifetz and Israel
Science Foundation grant 1539/08 to Marco.
REFERENCES CITED
Agnon, A., Migowski, C., and Marco, S., 2006, In-
traclast breccia layers in laminated sequences:
Recorders of paleo-earthquakes, in Enzel, Y., et
al., eds., New frontiers in Dead Sea paleoen-
vironmental research: Geological Society of
America Special Paper 401, p. 195–214.
Bartov, Y., Stein, M., Enzel, Y., Agnon, A., and Re-
ches, Z., 2002, Lake levels and sequence stra-
tigraphy of Lake Lisan, the late Pleistocene pre-
cursor of the Dead Sea: Quaternary Research,
v. 57, p. 9–21, doi: 10.1006/qres.2001.2284.
Begin, B.Z., Steinberg, D.M., Ichinose, G.A., and
Marco, S., 2005, A 40,000 years unchanging of
the seismic regime in the Dead Sea rift: Geol-
ogy, v. 33, p. 257–260, doi: 10.1130/G21115.1.
Begin, Z.B., Ehrlich, A., and Nathan, Y., 1974, Lake
Lisan, the Pleistocene precursor of the Dead
Sea: Geological Survey of Israel Bulletin 63,
30 p.
Boore, D.M., Joyner, W.B., and Fumal, T.E., 1997,
Equations for estimating horizontal response
spectra and peak acceleration from western
North American earthquakes: A summary of
recent work: Seismological Research Letters,
v. 68, p. 127–153.
Dasgupta, P., 2008, Experimental decipherment of
the soft-sediment deformation observed in the
upper part of the Talchir Formation (Lower
Permian), Jharia Basin, India: Sedimentary
Geology, v. 205, p. 100–110, doi: 10.1016/
j.sedgeo.2008.01.006.
El-Isa, Z.H., and Mustafa, H., 1986, Earthquake de-
formations in the Lisan deposits and seismotec-
tonic implications: Royal Astronomical Soci-
ety Geophysical Journal, v. 86, p. 413–424.
Heifetz, E., Agnon, A., and Marco, S., 2005, Soft
sediment deformation by Kelvin Helmholtz
Instability: A case from Dead Sea earthquakes:
Earth and Planetary Science Letters, v. 236,
p. 497–504, doi: 10.1016/j.epsl.2005.04.019.
Ken-Tor, R., Agnon, A., Enzel, Y., Marco, S., Neg-
endank, J.F.W., and Stein, M., 2001, High-
resolution geological record of historic earth-
quakes in the Dead Sea basin: Journal of
Geophysical Research, v. 106, p. 2221–2234,
doi: 10.1029/2000JB900313.
Kundu, P.K., and Cohen, I.M., 2008, Fluid mechan-
ics (fourth edition): London, Academic Press,
872 p.
Li, H., and Yamazaki, H., 2001, Observations of a
Kelvin-Helmholtz billow in the ocean: Jour-
nal of Oceanography, v. 57, p. 709–721, doi:
10.1023/A:1021284409498.
Marco, S., and Agnon, A., 1995, Prehistoric earth-
quake deformations near Masada, Dead Sea gra-
ben: Geology, v. 23, p. 695–698, doi: 10.1130/
0091-7613(1995)023<0695:PEDNMD>2.3
.CO;2.
Marco, S., Stein, M., Agnon, A., and Ron, H., 1996,
Long term earthquake clustering: A 50,000
year paleoseismic record in the Dead Sea Gra-
ben: Journal of Geophysical Research, v. 101,
p. 6179–6192, doi: 10.1029/95JB01587.
Matsumoto, D., Naruse, H., Fujino, S., Surpha-
wajruksakul, A., Jarupongsakul, T., Sakakura,
N., and Murayama, M., 2008, Truncated fl ame
structures within a deposit of the Indian Ocean
tsunami: Evidence of syn-sedimentary defor-
mation: Sedimentology, v. 55, p. 1559–1570,
doi: 10.1111/j.1365-3091.2008.00957.x.
Migowski, C., Agnon, A., Bookman, R., Negendank,
J.F.W., and Stein, M., 2004, Recurrence pattern
of Holocene earthquakes along the Dead Sea
transform revealed by varve-counting and ra-
diocarbon dating of lacustrine sediments: Earth
and Planetary Science Letters, v. 222, p. 301–
314, doi: 10.1016/j.epsl.2004.02.015.
Moretti, M., Alfaro, P., Caselles, O., and Canas, J.A.,
1999, Modelling seismites with a digital shak-
ing table: Tectonophysics, v. 304, p. 369–383,
doi: 10.1016/S0040-1951(98)00289-3.
Owen, G., 1987, Deformation processes in uncon-
solidated sands, in Jones, M.E., and Preston,
R.M.F., eds., Deformation of sediments and
sedimentary rocks: Geological Society of Lon-
don Special Publication 29, p. 11–24.
Owen, G., 2003, Load structures: Gravity driven sed-
iment mobilization in the shallow subsurface,
in Rensbergen, P.V., et al., eds., Subsurface
sediment mobilization: Geological Society of
London Special Publication 216, p. 21–34.
Manuscript received 14 September 2009
Revised manuscript received 24 October 2009
Manuscript accepted 27 October 2009
Printed in USA
on March 25, 2010geology.gsapubs.orgDownloaded from
