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Supplementary Information to
Evidence for boundary-layer mantle flow beneath the
Dead Sea Transform from seismic anisotropy
Georg Rümpker*, Trond Ryberg, Günter Bock & Desert Group
GeoForschungsZentrum Potsdam, Telegrafenberg, 14473 Potsdam, Germany
*corresponding author (rumpker@gfz-potsdam.de)
On the observation of dominant transverse displacement components.
Dominant transverse (vs. radial) displacement components can occur even in simple 1layer anisotropic structures. Figures 2 and S1 show that the finite-difference waveforms
obtained for our preferred model (Figure 4) exhibit the same effect. Mathematically, the
effect can be explained by considering the frequency-domain expressions for the radial
and transverse displacement components due to a single anisotropic layer1
ur ~ cos( t / 2)  i sin(  t / 2) cos[ 2(  i )]
ut ~ i sin(  t / 2) sin[ 2(  i )]
with splitting parameters t and , initial polarization i, and frequency . Assuming a
plane harmonic wave of period T, the radial component ur vanishes under the conditions
that
t  T / 2
  i  45.
For our observations, with a dominant period T = 3.2 s and a backazimuth i = 61, this
corresponds to splitting parameters  =16 and t = 1.6 s. Such values are obtained in
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our splitting analysis at stations that exhibit the largest transverse amplitudes for periods
between 2 and 5 s (see e.g. Figure S1).
Thus, whenever above conditions are met (in an approximate sense), even a single
anisotropic layer can cause dominant transverse displacement components. A further
prerequisite for this is a waveform of more-or-less sinusoidal shape (harmonic wave). A
simple pulse shape (-function) does not result in a vanishing radial component. In our
case, the observation of this effect is facilitated by the application of the band-pass filter
for periods between 2-5 seconds. At longer periods, between 5-7s, the amplitudes of the
transverse components are more similar to those of the radial components (Figures 2
and S1). This is in agreement with the long-period limit, in which case the radial
component is expected to dominate. The frequency-dependence of the relative
amplitudes can occur even for a single anisotropic layer. However, the frequencydependence of the observed splitting parameters (see below) requires a more complex
anisotropic structure. The analysis is corroborated by the comparison between observed
and calculated waveforms along the entire profile (Figure 2) using the model given in
Figure 4. For each trace, the amplitude scale used for radial and transverse components
is identical, allowing their direct comparison.
Splitting parameters from observed and calculated SKS waveforms. The
splitting analysis for a station in the region of the large transverse amplitudes (at a
station about –15 km distance along the profile) is detailed in Figure S1 for the two
period bands (2-5s and 5-7s). In the usual manner, horizontal waveform components
and particle motions are shown before and after application of an inverse splitting
operator that best minimizes the energy of the transverse component. In both cases
(period bands) the transverse energy is almost completely removed and the particle
motion is linearised parallel to the theoretical backazimuth direction of the event. Figure
S1 also describes the splitting analysis applied to the calculated waveforms obtained for
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our preferred model (see Figure 4). In both period ranges, the forward modelling and
the splitting analysis yield amplitudes and splitting parameters in agreement with the
observations.
Some care must be taken for the splitting analysis at shorter periods. As shown in
Figures S1a (data) and S1c (model), two distinct regions of low T-component energy
may occur (separated by about 90 degrees). Depending on the noise level, it can thus be
difficult to obtain a set of unique splitting parameters, if only the short period range is
considered. This could pose a problem to the analysis, if the measured fast polarization
is directly interpreted in terms of a symmetry-axis direction in the medium. However,
we only use the measured splitting parameters as a means to parameterise the
waveforms and to facilitate the comparison between observations and modelling. To
resolve possible ambiguities at shorter periods, we consistently choose the parameter
combination (the T-energy minimum) that is closer to the (unique) minimum at longer
periods (5-7s). It turns out this choice does not affect the inversion, as long as the
minima at different stations are chosen in a consistent manner. The validity of this
approach is further supported by the fact that the agreement between observations and
modelling is not only limited to amplitudes and splitting parameters but extents to the
topological details of the T-energy variation as function of delay time and fast axis.
Through comparison between FD modelling and observations, we avoid a direct
interpretation of the observed splitting parameters in terms of medium properties. The
direct interpretation, strictly, is only possible if the medium can truly be characterized
by a single anisotropic layer. This inherent limitation of the 1-layer splitting analysis
has been overcome for 2-layered and purely depth-dependent media2. However, for
laterally varying and depth-dependent anisotropic structures, the inversion seems to
require the full waveform-modelling approach that is used here.
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Waveform inversion method. We use a local optimisation technique based on a
Simplex algorithm3 to iteratively improve the fit between splitting parameters that are
obtained from synthetic and observed waveforms. The inversion involves forward
calculations of the SKS wavefield using a complete finite-difference method to solve the
anisotropic wave equation. For the forward modelling the oblique incidence of the
incoming SKS wavefront with respect to the Arava Fault is accounted for by an
appropriate projection of the coordinate system. The definition of the misfit function
used in the inversion employs the comparison (by RMS differences) between splitting
parameters obtained from the synthetic and observed waveforms. During the inversion
process we allow for changes of the horizontal symmetry (a) axis over the complete
range of 180 degrees and for variations in the strength of anisotropy between 0 and
10%. For the comparison between data and model we used smoothed curves of
observed splitting parameters to suppress effects of non-systematic (random)
fluctuations due to e.g. sensor misorientations and site effects. The errors assigned to
the data are relatively uniform along the profile (Figure 1). Tests showed that the
smoothing of data points did not affect the model estimation. The main reason for
showing the smoothed curves in the Figures is to aid the visual comparison between
data and model results.
Complexity of the model and number of anisotropic domains. The observed
waveform variations clearly suggest a three-parted lateral structure beneath the profile,
while smaller-scale or smooth variations of elastic properties cannot be excluded.
However, models consisting of more than three lateral blocks are not required to explain
the basic features that we observe (frequency dependence and lateral variations).
Introducing a larger number of anisotropic blocks (laterally) may allow a further
reduction of the misfit. However, we think that it is prudent to fit the data with a model
of minimal complexity.
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Initially, we tested whether a three-block structure in the crust or in the mantle alone
can explain the observations (see Figures S2). Estimates of Fresnel-zone size4, which
give an indication for the lateral resolution of splitting measurements, suggest that the
observed short-scale lateral variations in splitting are caused to a significant amount by
variations of crustal anisotropy. For this type of model (Fig. S2c) the best-fitting
anisotropic parameters in the mantle are given by an a-axis orientation of 13 and 3.8%
anisotropy. In the crust we obtain orientations of -20 (western stations) and -11
(eastern highlands). Within the central 25-km wide block the symmetry axis is oriented
at 4. However, the differences between observed and calculated splitting parameters
remain relatively large.
For a model with lateral variations of anisotropy confined to the mantle (Fig. S2d)
we obtain values of -15 and 5.8% for the crustal layer. The anisotropy in the mantle is
characterised by a narrow, 20 km wide, central region, where the a-axis orientation is
25 i.e. it differs by 14-20 compared to the surrounding mantle. Within this zone the
anisotropy is increased by up to 1.5%.
The modelling shows that variations of anisotropy in the mantle are better suited
to reduce the relative variance between model and observations. We also considered
another four-block structure with two anisotropic domains in the crust and in the
mantle, respectively (see Figure S3b). This model gives a better fit to the data than the
model with laterally varying crust, but the model with three anisotropic domains in the
mantle still performs better. Increasing the total number of blocks to five (Figure S4)
further reduces the misfit. However, the 5-block structure with two domains in the
mantle (Figure S4a) exhibits a larger relative variance than the (less complex) 4-block
structure with three mantle domains (Figure S3c). This supports our interpretation in
terms of a relatively complex anisotropic structure in the mantle. These results are
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summarized in the Figure 3, where the relative variance is shown as function of the total
number of anisotropic blocks in the crust and mantle.
References
1.Rümpker, G., & Silver, P. G. Apparent shear-wave splitting parameters in the
presence of vertically varying anisotropy, Geophys. J. Int., 135, 790-800 (1998).
2.Silver, P. G., & Savage, M. K. The interpretation of shear-wave splitting parameters
in the presence of two anisotropic layers, Geophys. J. Int., 119, 949-963 (1994).
3.Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. Numerical
Recipes in Fortran 77 : The Art of Scientific Computing, Cambridge University Press
(1996).
4.Rümpker, G., & Ryberg, T. New “Fresnel-zone” estimates for shear-wave splitting
observations from finite-difference modeling, Geophys. Res. Lett., 27, 2005-2008
(2000).
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Supplementary information: Figure captions
Figure S1 Shear-wave splitting analysis for observed and calculated
seismograms for a station at –15 km distance along the profile with dominant
transverse amplitudes. Horizontal waveform components and particle motions
are shown before and after application of an inverse splitting operator that best
minimizes the energy on the transverse component. The resulting splitting
parameters are indicated by the solid red dot in the T-component energy
distribution. The red arrow (E-N corrected) points in the direction of the
backazimuth for the event (61). The splitting analysis is performed for period
bands a, 2-5 s and b, 5-7 s. c, d, The same analysis performed for the
calculated waveforms obtained from the best-fitting model given in Figure 4.
Figure S2 Models of anisotropy in the crust and mantle beneath the Dead Sea
Transform (DST). a, Best fitting model with anisotropy confined to a single
homogeneous (135km thick) layer occupying the crust and upper mantle. The
synthetic parameters are independent of frequency in this case. Lines represent
(smoothed) splitting parameters obtained from the observed waveforms. Dots
indicate corresponding splitting parameters (delay times and fast polarisation
directions) obtained from synthetic waveform modelling using a complete finitedifference method. For comparison the variance  between observed and
calculated splitting parameters for this model has been set to 1. b, Best-fitting
laterally homogeneous 2-layer model of the crust and mantle. c, Best-fitting
model with a laterally homogeneous anisotropic mantle layer. The crust is
divided into three distinct anisotropic domains; their lateral extent is also
determined during the inversion. d, Best-fitting model with a laterally
homogeneous anisotropic crustal layer and three distinct anisotropic domains in
the mantle.
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Figure S3 Models of crustal and upper-mantle structure consisting of four
distinct anisotropic domains. The anisotropic parameters and the lateral extent
of the domains are determined during the inversion. a, Best-fitting model with a
laterally homogeneous mantle layer. The crust is divided into three domains
(same as in Fig. 2c). b, Best-fitting model with two domains in the crust and in
the mantle. c, Best-fitting model with a laterally homogeneous crustal layer and
three domains in the mantle (same as in Fig. 2d). This model exhibits the
smallest value of the relative variance (=0.56) of the three models considered
here.
Figure S4 Models of crustal and upper-mantle structure consisting of five
distinct anisotropic domains. The anisotropic parameters and the lateral extent
of the domains are determined during the inversion. a, Best-fitting model with
two anisotropic domains in the mantle layer. The crust is divided into three
domains. b, Best-fitting model with two domains in the crust and three in the
mantle.
Figure S5 Effects of alternative anisotropic and isotropic variations on the
inversion. a, Best-fitting two-dimensional model with lateral variations of crustal
and mantle anisotropy beneath the Dead Sea Transform (DST) obtained from
the simultaneous inversion of the observed splitting parameters. The relative
variance between observed and calculated splitting parameters lies at =0.39
(see Fig. 4). b, Best-fitting model with uniformly anisotropic asthenospheric
layer included. The parameters for this layer are kept fixed during the inversion.
c, Best-fitting model with laterally varying isotropic crustal layer.