Bulletin of the Seismological Society of America, Vol. 106, No. 1, pp. 93–103, February 2016, doi: 10.1785/0120150102
Ⓔ
Distributed Slip Model for Forward Modeling Strong Earthquakes by Shahar Shani-Kadmiel,* Michael Tsesarsky,† and Zohar Gvirtzman
Abstract
We develop a generic finite-fault source model for simulation of large earthquakes: the distributed slip model (DSM). Six geometric and seven kinematic parameters are used to describe a smooth pseudo-Gaussian slip distribution, such that slip decays from peak slip within an elliptical rupture patch to zero at the borders of the patch. The DSM is implemented to initiate seismic-wave propagation in a finitedifference code. Radiation pattern and spectral characteristics of the DSM are compared with those of commonly used finite-fault models, that is, the classical Haskell’s model (HM) and the modified HM with radial rupture propagation (HM-RRP). The DSM accounts for directivity effects in the fault-parallel direction, as well as fault-normal ground motions, and overcomes the unrealistic uniform slip and stress singularities of the Haskell-type models. We show the potential of the DSM to estimate the ground motions of strong earthquakes. We use this model to initiate seismic-wave propagation during the 1927 M L 6.25 Jericho earthquake and compare calculated macroseismic intensities to reported intensities at 122 localities. The root mean square of intensity residuals is 0.68, with 56% of the calculated intensities matching the reported intensities and 98% of the calculated intensities within a single unit from the reported intensities. The DSM is an essential step toward robust ground-motion prediction in earthquake-prone regions with a long return period and limited instrumental coverage. Online Material: Animation of rupture and wave propagation.
Introduction wave propagation effects, such as amplification in sedimentary basins. Moreover, GMPEs are mainly valid for regions where there are sufficient strong-motion data, for example, Next Generation Attenuation (NGA)-West (Power et al., 2008) and NGA-West 2 (Gregor et al., 2014) and cannot be readily exported to other regions without validation of the models with available data. Numerical simulations of seismic-wave propagation have the potential to overcome this lack of data and can properly model wave propagation through complex geometries such as sedimentary basins and alluvial valleys (Frankel, 1993; Olsen et al., 1995; Graves et al., 1998; Davis et al., 2000; Luzón et al., 2004; Stupazzini et al., 2009; Gvirtzman and Louie, 2010; Shani-Kadmiel et al., 2012, 2014). Furthermore, simulations allow us to explore the range of possible ground motions that we might expect for earthquake ruptures that are evident in the geologic record but not the historic or instrumental records (Allen, 2007). Three sources of uncertainty need to be addressed in earthquake ground-motion prediction: near-surface nonlinear effects, seismic-wave propagation in complex 3D earth, and the earthquake rupture process. In contrast to the first two sources of uncertainty, which remain constant in time for
Prediction of earthquake ground motion at a site of interest is crucial for mitigating seismic hazard. In many regions, the occurrence of strong earthquakes is proven from paleoseismic, archeological, and historic records, yet instrumentally recorded data are limited. For example, the Dead Sea Transform (DST) is an ∼1000-km-long active tectonic plate boundary between the African and Arabian plates, which is estimated from noninstrumental data to be capable of producing large earthquakes (Mw > 6) with a recurrence interval of 100 years (Agnon, 2014). Seismic-hazard estimation in such regions is either based on ground-motion prediction equations (GMPEs) (Ambraseys et al., 2005; Boore and Atkinson, 2008; Atkinson and Boore, 2011) or on forward numerical modeling of seismic-wave propagation (Graves et al., 1998; Olsen et al., 2006; Day et al., 2008; Roten et al., 2011). GMPEs suffer from a shortage of data for large earthquakes at short distances and only approximately account for *Also at Geological Survey of Israel, 30 Malkhe Israel Street, Jerusalem 95501, Israel,
[email protected]. † Also at Department of Geological and Environmental Sciences, BenGurion University of the Negev, P.O.B 653, Beer-Sheva, 84105, Israel,
[email protected].
93
94
(a)
2
4
6
Fault parallel cross section
Depth, km
2
3.0 2.4 1.8 1.2 0.6 0.0
4 6 8 10
Rupture patch
Slip, m
0
12 0
10
15
20 25 Distance, km
2.8
26
28
30
DSM 2 .0
0 .8 0 .4
1 .6 1 .2
2 .4 2 .0
1 .6 1 .2
Depth, km
40
3.2
2.0
24
2.4
1.2
22
1.6
(e)
HM-RRP 4 5 6 7 8 9
20
35
HM
0.8
16.5 18.5 20.5 22.5 24.5 26.5
(d)
30
(c)
PSM 4 5 6 7 8 9
0.4
Depth, km
(b)
5
0 .8 0 .4
a given area of interest and for which accuracy can be gradually improved, the earthquake rupture process remains a significant obstacle. First, source inversions based on geodetic and seismic methods are nonunique (Vallée and Bouchon, 2004). Second, source inversions are earthquake specific and should not be simply applied to model past or future earthquakes (Goulet et al., 2015). Hence the challenge is how should the seismic source be represented in numerical simulations of unrecorded or future earthquakes. A common and widely used representation of a seismic source is the double-couple point-source model (PSM, Fig. 1b) (Maruyama, 1963). This model is good as a far-field approximation of large earthquakes but is less successful at estimating ground motions in the near field because it does not account for the rupture process (Ben-Menahem, 1961; Madariaga, 2007). To account for the rupture process, Haskell (1964) developed a finite-source model (Haskell’s model [HM], Fig. 1c), consisting of a rectangular finite fault where a line of dislocations suddenly appears at one edge of the rupture patch, propagates with constant velocity V r and constant slip D along the length of the fault, and sharply drops to zero at the opposite edge. A slight modification of the HM is a model in which rupture initiates at a point and propagates radially (HM with radial rupture propagation [HM-RRP], Fig. 1d) (Savage, 1966; Hartzell and Heaton, 1983). However, the sharp drop from constant slip D within the rupture patch to zero at the borders in both the HM and the HM-RRP introduces stress singularities and is physically not realistic. Several stochastic approaches have also been used to prescribe finite-source kinematics. Examples include the composite-source model, a superposition of overlapping circular subevents of random sizes, located randomly on the fault (Zeng et al., 1994) and the Motazedian and Atkinson (2005) EXSIM finite-source stochastic model, among others. The purpose of this article is to develop a generic, kinematic finite-fault source model that reproduces the largescale characteristics of the earthquake while balancing between simple robust concepts and complex details of the rupture. We build on an idea originally proposed by Vallée and Bouchon (2004) that an earthquake source can be reliably described as an ensemble of elliptical slip patches with uniform slip distribution within each of the patches. This approach was successfully applied for the source inversions of the 1999 Mw 7.4 Izmit earthquake in Turkey and the 1995 Mw 8.0 Jalisco earthquake in Mexico (Vallée and Bouchon, 2004), the 2000 Mw 6.7 Tottori earthquake in Honshu, Japan (Di Carli et al., 2010), the 2007 M w 7.6 Tocopilla earthquake in Chile (Peyrat et al., 2010), and the 2007 M w 6.7 Michilla earthquake in Chile (Ruiz and Madariaga, 2011), among others. In what follows, we first set the basis for implementation of the distributed slip model (DSM) for numerical forward modeling of seismic-wave propagation. We then compare the radiation pattern of the DSM with the PSM, HM, and HM-RRP, by implementing these models in a node-based second-order finite-difference code for the solution of the seismic-wave equation. Finally, we simulate ground motions
S. Shani-Kadmiel, M. Tsesarsky, and Z. Gvirtzman
16.5 18.5 20.5 22.5 24.5 26.5 Distance, km
16.5 18.5 20.5 22.5 24.5 26.5 Distance, km
Figure 1.
(a) Fault-parallel section across the computational domain, with rupture patch location denoted by a solid rectangle for the Haskell’s model with radial rupture propagation (HM-RRP) and the distributed slip model (DSM) and a dotted rectangle for the HM, which is offset in the x direction to match the epicenter location of the other models. Velocity and density profiles of the computational domain are plotted on the left: V P and V S are P- and S-wave velocity in kilometers per second, ρ is density in grams per cubic centimeters. The shaded bar plotted on the right corresponds to the slip distribution of the rupture models below. (b) Point-source model (PSM): location of the nucleation point (denoted by a star) relative to the rupture patch. (c) HM, unilateral rupture initiating at the left edge of the rupture patch, denoted by the thick, dashed line. Uniform color represents uniform slip Davg of 0.97 m. Rupture time isochrones (in seconds) are plotted in white. (d) HM-RRP: radial rupture initiating at the nucleation point, same location as (b). Uniform shaded fill represents uniform slip Davg of 0.97 m. Rupture time isochrones (in seconds) are plotted in white. (e) DSM: radial rupture initiating at the nucleation point, same location as (b). The shaded gradient represents nonuniform slip according to the shaded bar in (a); white lines mark rupture time isochrones in seconds. The color version of this figure is available only in the electronic edition.
during the 1927 M L 6.25 Jericho earthquake (Blankenhorn, 1927; Brawer, 1928; Ben-Menahem et al., 1976) by implementing the DSM to initiate seismic-wave propagation. We compare synthetic macroseismic intensities with reported intensities first compiled following this earthquake by Brawer (1928). This earthquake was the most destructive earthquake to occur in the vicinity of Israel since the 1834 Mw ∼ 6 Southern Dead Sea earthquake (Ben Menahem, 1991), with between 250–500 deaths and 400–700 injuries. Many buildings were damaged, landslides and rockfalls were observed, and the flow of the Jordan River had stopped for 21.5 hrs (Amiran et al., 1994). The Brawer (1928) reports
Distributed Slip Model for Forward Modeling Strong Earthquakes were re-evaluated by Avni et al. (2002), who paid close attention to the quality of the sources and testimonies, and were integrated with macroseismic data. This procedure resulted in 133 settlements and sites for which seismic intensity was assessed by the Medvedev–Sponheuer–Karnik (MSK64) scale (Medvedev et al., 1965) and later corrected to account for construction quality, topographic slope, groundwater level, and surface geology by Zohar and Marco (2012). We compare the calculated intensities with the mean site intensity at 122 localities that fall within the computational domain used.
The Distributed Slip Model We assume an elliptical rupture patch with a nonuniform slip distribution of width W and length L at orientation α, measured between the ellipse major axis and the x axis. The elliptical perimeter is defined by a collection of points Pe;i (i 1; 2; 3; …; m), and the nucleation point Pn (xn ; yn ) is given in fault-plane coordinates with origin at the center of the rupture patch. Slip distribution Dr along a line i from Pn to each point Pe;i xe;i ; ye;i on the perimeter of the ellipse is defined as
95 2
EQ-TARGET;temp:intralink-;;313;733
e−ki Ri Dmin ;
EQ-TARGET;temp:intralink-;;313;700
EQ-TARGET;temp:intralink-;;313;682
Dp ≠0 1 − Dmin
− ki R2i lnDmin ki −R−2 i lnDmin :
This formulation results in a continuous, spatially smooth pseudo-Gaussian slip distribution on the elliptical rupture patch. Rupture initiates at Pn and propagates radially at rupture velocity V r, which we take as 0.9 the shear-wave velocity of the ruptured rocks. This yields seven parameters: W, L, α, xn , yn , Dp , and V r . In order to implement the DSM on the finite-difference grid, it is spatially discretized to the spacing dh of the grid and mapped onto a fault plane in the geological model at location Pf (longitude, latitude, depth), corresponding to the center of the patch. Each point on the fault is then prescribed a focal mechanism (strike, dip, rake) and a seismic moment M 0 μDrdh2 , in which μ is the shear modulus. This yields another six parameters (longitude, latitude, depth, strike, dip, and rake), for a total of 13 parameters.
Model Setup and Simulations EQ-TARGET;temp:intralink-;;55;461
Dp 2 Dr e−ki r − Dmin ; 1 − Dmin
0 ≤ r ≤ Ri ;
in which Dp is the peak slip and Dmin is a correction coefficient related to the normalization of D between Dp and 0 as 2 the term e−ki r ≠ 0. In this article Dp occurs at Pn but may be prescribed anywhere on the rupture patch, and we set Dmin equal to 0:1Dp . ki is the exponential decay coefficient, and Ri is the distance from Pn (in which r 0) to Pe;i (in which r Ri ). Two boundary conditions (BCs) must be satisfied: BC1: Dr 0 Dp and dDr 0=dr 0, BC2: Dr Ri 0. From BC1:
EQ-TARGET;temp:intralink-;;55;265
Dp 2 e−ki r − Dmin 1 − Dmin Dp 1 − Dmin Dp 1 − Dmin
Dr 0
EQ-TARGET;temp:intralink-;;55;195
2ki rDp −k r2 d Dr 0 e i 0: 1 − Dmin dr
From BC2:
EQ-TARGET;temp:intralink-;;55;137
Dr Ri
Dp 2 e−ki r − Dmin 0 1 − Dmin
We adopt the relations presented by Wells and Coppersmith (1994) for Mw, rupture patch size (W; L), peak slip Dp , and average slip Davg to scale our slip distribution and prescribe the correct M 0 to each point on the rupture patch. In order to compare the earthquake source representations discussed above, we set up a computational domain, 40 km × 40 km × 12 km, discretized into 2:81 × 108 grid points spaced at dh 41 m. We use gradient velocity and density above the rupture patch to avoid unwanted resonance effects and constant velocity and density along the depth of the rupture patch as presented in Figure 1a. The DSM, HM, HM-RRP, and PSM are each in turn implemented on the finite-difference grid for the initiation of seismicwave propagation. Figure 1a illustrates the location of the rupture patch on a fault-parallel cross section of the 3D computational domain, and Figure 1b–e presents slip distribution and rupture time isochrones in seconds. Table 1 summarizes the parameters used for each model. Each of the preceding earthquake sources simulates an M w 5.96 (M 0 1:087 × 1018 N·m) sinistral strike-slip earthquake. The location of the nucleation point for the DSM, HM-RRP, and PSM models is identical and is denoted by a star in Figure 1. In the case of the HM, the rupture nucleates along the entire edge of the patch, denoted by a thick dashed line, and propagates unilaterally. Hence, the rupture patch, denoted by a dotted rectangle in Figure 1a, is translated in the x direction so that the location of the epicenter is identical in all models. The source time function or the moment rate time function of each point source assigned to each grid point on the fault is a Gaussian pulse with a central frequency of 1.2 Hz and maximum frequency of 3 Hz and is scaled accordingly by M0
96
S. Shani-Kadmiel, M. Tsesarsky, and Z. Gvirtzman PGV, m/s
(c)
HM-RRP
1.50 0.75 0.00
PSM
0.00
(a)
1.50 0.75
PGV, m/s
to satisfy the slip distribution Dr on the rupture patch. Point sources are initiated with a time offset to mimic rupture propagation. In order to keep the duration of the PSM similar to the other models, we collapsed all the point sources of the DSM to a single point at the hypocenter but kept the time offset between source initiations. We study peak ground velocity (PGV) to quantify symmetry and directivity (Fig. 2). Ground-motion synthetics computed on the fault and auxiliary planes at an epicentral distance of 10 km are used for time- and frequency-domain analysis (Fig. 3). Ⓔ Seismic-wave propagation is visualized in Animation S1 in the electronic supplement available to this article. Seismic waves initiated by the source are propagated through the computational domain using the Wave Propagation Project (WPP) code from Lawrence Livermore National Laboratories (LLNL). WPP solves the governing equations in second-order formulation using a node-based finite-difference approach. It accounts for surface topography by discretizing the viscoelastic wave equation and the free-surface boundary conditions on a curvilinear grid to a certain depth related to the elevation extremums and below that depth on a Cartesian grid, which leads to a computationally efficient algorithm. A freesurface condition is imposed on the top boundary and absorbing super-grid conditions on all other boundaries to mimic a much larger physical domain and prevent energy from being reflected back into the computational domain (Petersson and Sjögreen, 2014). The underlying numerical method for solving the viscoelastic wave equation is described in detail in Petersson and Sjögreen (2012).
(b)
HM
(d)
DSM
40 35 30 x, km
25 20 15 10 PGV, m/s
5 1.50 0.75 0.00
40 35 30 x, km
25 20 15 10 PGV, m/s
5 1.50 0.75 0.00 0
5 10 15 20 25 30 35 40 y, km
0
5 10 15 20 25 30 35 40 y, km
0.00 0.15 0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50 PGV, m/s
Figure 2. Peak ground velocity (PGV) at the free surface calculated for the four different source models: (a) PSM, (b) HM, (c) HMRRP, and (d) DSM. Curves in the right and bottom panels of each map are row- and column-wise maxima, respectively. The epicenter location is denoted by a star, and the locations of synthetic ground motions (as discussed in the text and presented in Fig. 3) are denoted by inverted triangles. Contours labels are in meters per second. The color version of this figure is available only in the electronic edition.
Results Comparison of Seismic Radiation The PGV at the free surface of each model is presented in Figure 2. The right and bottom panels for each of the four images present PGV maxima in each row (y direction) and each column (x direction) of the grid, respectively. The PGV of the PSM is plotted for reference (Fig. 2a). The radiation pattern of the HM shows a strong directivity effect where most of the energy is radiated in the direction
of rupture propagation, and almost no energy is radiated in the fault-normal direction (Fig. 2b). This is naturally due to the unilateral, and unrealistic, rupture process that initiates along the edge of the rupture patch and propagates to the opposite edge, finally arresting after 3.36 s. The right panel displays a decreasing PGV curve from a maximum of
Table 1 Parameters Used for the Four Slip Models Geometry Model*
DSM HM HM-RRP PSM
W(km)
L(km)
α(°)
5.0 5.0 5.0
10.0 10.0 10.0
0 0 0
x(km)
21.5 25.0 21.5 20.0‡
Nucleation †
y(km)
20.0 20.0 20.0 20.0‡
†
z(km)
6.5 6.5 6.5 8.5‡
†
Slip
xn (km)
yn (km)
Dp (m)
Davg (m)
−1.5 −5.0 −1.5
2.0 2.0
3.0 0.76 0.76 -
0.97 0.76 0.76 -
W, width; L, length; α, orientation measured between the ellipse major axis and the x axis; xn and yn , nucleation point in fault-plane coordinates; Dp , peak slip; Davg , average slip. *DSM, distributed slip model; HM, Haskell’s model; HM-RRP, HM with radial rupture propagation; PSM, point-source model. † Instead of a geographical coordinate system in longitude, latitude, depth, we used a right-hand Cartesian coordinate system x, y, z, in which x is positive north, y is positive east, and z is positive down. ‡ Coordinates for the location of the PSM.
97
(a) 1e−4
Ground velocity, m/s
3.6 1.8 0.0 −1.8 −3.6
fp+ Vx
10
–3
10
–4
10
–5
10
–6
10
–1
10
–2
10
–3
10
–4
10
–4
10
–5
10
–6
10
–7
10
–4
10
–5
10
–6
10
–7
10
–1
10
–2
10
–3
10
–4
10
–4
10
–5
10
–6
10
–7
10
–1
10
–2
10
–3
10
–4
(b) 1.32 0.88 0.44 0.00 −0.44
fp+ Vy
(c) 1e−4 2.6 0.0 −2.6 −5.2 −7.8
fp+ Vz
Spectral displacement, m·s
Distributed Slip Model for Forward Modeling Strong Earthquakes
fp- Vx
(e) 1.32 0.88 0.44 0.00 −0.44
fp- Vy
(f) 1e−4
Ground velocity, m/s
2.6 0.0 −2.6 −5.2 −7.8
fp- Vz PSM HM
HM-RRP DSM
(g) 1e−1 ap+ Vx
3.6 1.8 0.0 −1.8 −3.6
HM-RRP
4
5
6
7 8 Time, s
DSM
9
10
11
0.2 0.5
0 2
5
10 Frequency, Hz
Spectral displacement, m·s
Ground velocity, m/s
3.6 1.8 0.0 −1.8 −3.6
Spectral displacement, m·s
(d) 1e−4
Figure 3. Synthetic ground motions computed at locations indicated by the triangles in Figure 2. The left panels are velocity time histories of the x, y, and z components, corresponding to radial, transverse, and vertical components, respectively. The right panels are the corresponding Fourier spectra, with the ω−2 slope plotted for reference as a thick dashed line. The color version of this figure is available only in the electronic edition.
98
S. Shani-Kadmiel, M. Tsesarsky, and Z. Gvirtzman
∼0:88 m=s in the rupture direction to zero with no distinguishable local maxima. In the fault-normal direction shown in the bottom panel of Figure 2b, the PGV curve monotonically decreases from the maximum on the fault plane to zero. Hence, the radiation pattern of the HM is strongly nonsymmetric, with only one pronounced lobe in the main rupture direction. The rupture of the HM-RRP nucleates at a point within the rupture patch rather than along the edge and propagates radially, reaching the bottom edge after 0.17 s and the left edge after 1.18 s, and finally arrests at the top right corner after 2.61 s (Fig. 1d). PGV in the main rupture direction is 1.24 and 0:83 m=s in the opposite direction (Fig. 2c, right panel), and PGV in the fault-normal direction is 0:59 m=s (Fig. 2c, right panel, center bulge). Hence, PGV in the main rupture direction is amplified by a factor of 1.5 relative to the opposite direction and by a factor of 2.1 relative to the fault-normal direction. The rupture of the DSM nucleates at a point within the elliptical rupture patch and propagates radially, reaching the nearest edge after 0.13 s and arresting after 2.3 s at the farthest edge (Fig. 1d). PGV in the main rupture direction is 1:49 m=s, 0:86 m=s in the opposite direction (Fig. 2d, right panel), and 0:87 m=s in the fault-normal direction (Fig. 2d, right panel, center bulge). Hence, PGV in the main rupture direction is amplified by a factor of 1.7 relative to the opposite direction and fault-normal direction. Thus, the directivity effect of the DSM is more pronounced than that of the HM-RRP and yet more symmetric with regard to the fault-normal radiation. Time and Frequency Domain Analysis Ground-motion synthetics are computed along the fault plane, fp and fp−, and along the auxiliary plane, ap and ap−, at a distance of 10 km from the epicenter (location denoted by inverted triangles in Fig. 2). Figure 3 presents velocity time histories (on the left) for the x, y, and z components, corresponding to radial, transverse, and vertical components, respectively, and displacement Fourier spectra (on the right). The PSM ground-motion synthetics and the ω−2 slope are plotted for reference. Polarity and phase arrivals are consistent among the four models although slight phase shifts are evident due to the varying rupture propagation in the different models. For instance, P and S waves are slightly faster to arrive in the HM (Fig. 3a–c) because rupture nucleates along the edge of the patch, from a depth of 4 km to a depth of 9 km (Fig. 1c), placing many sources closer to the surface as opposed to the other fault models that nucleate toward the bottom of the patch, at a depth of 8.5 km. Directivity effects are evident in the time domain, because amplitudes at fp in the main rupture direction are larger than amplitudes at fp− in the opposite direction. Furthermore, directivity effects are visible in the frequency domain because amplitude spectra at fp are systematically higher for the propagating rupture models relative to the PSM. Because of the short rupture propagation
of the HM-RRP and the DSM in the direction of fp−, opposite the main rupture direction, only amplitudes at frequencies higher than 0.5 Hz are amplified relative to the PSM (Fig. 3e). The HM, which ruptures unilaterally, produces a significantly lower amplitude spectrum relative to the PSM at fp− (Fig. 3e). At high frequencies, a typical ω−2 spectral decay is evident, particularly so in the radial and vertical components, which include P-wave data as well. For clarity, we show only synthetics of the x component (transverse) of the HM-RRP and the DSM at ap (Fig. 3g), keeping in mind that at ap− the polarity of the time history is simply reversed. It is evident that the DSM produces significantly higher amplitudes, by a factor of ∼2:7, in the faultnormal direction. The 1927 M L 6.25 Jericho Earthquake We simulate earthquake ground motions during the 1927 M L 6.25 Jericho earthquake by implementing the DSM (Fig. 4a, Table 2) with epicenter location and magnitude according to Shapira et al. (1993) and Avni et al. (2002). A pure sinistral strike-slip focal mechanism is assumed, following Ben-Menahem et al. (1976). Rupture patch size and average slip are prescribed according to relations presented by Wells and Coppersmith (1994). Rupture is set to propagate mainly in the northward direction. The computational domain, rotated 6.45° clockwise relative to north to conveniently match the strike of the fault plane, extends 280 km in the x direction (6.45° clockwise from north), 120 km in the y direction (96.45° clockwise from north), and 13 km in the z direction (down). The computation accounts for realistic surface topography from Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Global Digital Elevation Model (GDEM) v.2 by discretizing the free-surface boundary condition on a curvilinear grid. Grid spacing at the surface is dh 85 m, doubling to 170 m at a depth of 10.4 km and yielding a total of 6:3 × 108 grid points. A laterally homogeneous velocity model starting at the surface topography and extending downward was used for the computational domain (Fig. 4b,c). Although rather simplistic, this essentially 1D velocity model introduces lateral variations because it is shifted in the vertical axis by surface topography. Note, for example, that the prominent topographic depression of the Dead Sea Rift Valley (Fig. 4c), de-elevated relative to its surrounding by almost 1500 m in places, creates a lateral gradient to lower seismic velocities in the valley, which is filled with sediments. Ground-motion synthetics are used for computing seismic intensity based on PGV at localities of reported intensities (Avni et al., 2002; Zohar and Marco, 2012). PGV values are translated to seismic intensity on the European Macroseismic Scale 1998 (EMS98; Grünthal, 1998), the successor of the MSK64 (Medvedev et al., 1965), using the Kästli and Fäh (2006) equation, I 2:263 log10 PGV 9:498, in which PGV is in meters per second. Spatial distribution
99
(a) (c)
4.0 5.5 7.0 8.5 10.0
0.0
(b)
0
0.5
1
2
1.0 1.5 Slip, m
3
4
5
6
2.0
Ri ft
107
Se a
91 95 99 103 Distance along strike, km
De ad
87
Va lle y
4 .0 3 .5 3 .0 2 .5 2 .0 1 .5 1 .0 0 .5
Depth along dip, km
Distributed Slip Model for Forward Modeling Strong Earthquakes
2.5
7
0
Depth, km
2 4 6 8 10
P-wave velocity, km/s
12 3.5 4.2 4.9 5.6 6.3 7.0
Figure 4.
Rupture and velocity models used for simulating seismic-wave propagation during the 1927 ML 6.25 Jericho earthquake. (a) DSM: radial rupture initiating at the nucleation point denoted by a star, white lines mark the rupture time isochrones in seconds, and shading represents the amount of slip. (b) 1D profiles of velocity and density used for the computational domain. (c) 3D volume showing P-wave velocity and Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Global Digital Elevation Model (GDEM) v.2 surface topography. The rupture extent and epicenter are marked by a solid white line and a star, respectively. The color version of this figure is available only in the electronic edition.
of PGV and reported-minus-calculated seismic intensity residuals are outlined in Figure 5, and the overall level of agreement is detailed in Figure 6. A dashed black line in Figure 5 marks the boundaries of the computational domain. The extent of the DSM rupture, which was set to propagate mainly northward, is marked by a short solid white line, with a star marking the location of the epicenter. The seismic radiation pattern as depicted by the PGV distribution is composed of four lobes: a large lobe in the front of the rupture and three smaller lobes in the back and fault-normal directions. Scattered spots of larger values of PGV are visible, especially further away from the epicenter as topographic effects become more significant than source effects. Macroseismic intensity residuals (reported–calculated) are denoted by shaded triangles, circles, and inverted triangles for seismic intensities that are overestimated, matching, and underestimated by our computation, respectively. The inset figure at the top-left corner
of Figure 5 shows that there is no clear azimuthal discrepancy between over- and underestimated localities. Reported and calculated seismic intensities as a function of epicentral distance are presented in Figure 6a. The dashed lines are curve fitted (see fit parameters in Table 3) using the attenuation relations of macroseismic intensities presented in Stromeyer and Grünthal (2009): EQ-TARGET;temp:intralink-;;313;299
q II ; a; b; R; h I − a log10 R2 h2 =h2 p −b R2 h 2 − h ;
in which I , a, and b are the reference intensity at the epicenter (R 0) and two coefficients, respectively, determined simultaneously in the regression process, and R and h are epicentral distance and hypocenter depth, respectively.
Table 2 Distributed Slip Model (DSM) Parameters Used for the 1927 ML 6.25 Jericho Earthquake Geometry
Nucleation
Slip
W (km)
L (km)
α (°)
Longitude (° E)
Latitude (° N)
z (km)
xn (km)
yn (km)
Dp (m)
Davg (m)
7
20.0
0
35.44
31.56
9.8
−3.0
−2.8
2.5
0.81
W, width; L, length; α, orientation measured between the ellipse major axis and the x axis; xn and yn , nucleation point in fault-plane coordinates; Dp , peak slip; Davg , average slip.
100
S. Shani-Kadmiel, M. Tsesarsky, and Z. Gvirtzman
1e−1
180°
32.0
–2 –1 0 1 Residuals
7.0
6.0
5.0
2 4.0
PGV, m/s
5°
13
22
5°
120
32.5
o m a in 90°
60
a tio n a l d
0
8.0
Com put
270°
33.0
°
31
45
5°
0°
3.0 31.5 2.0 31.0 1.0 0.5 0.0 34.0
34.5
35.0
35.5
36.0
Figure 5. Map view of the PGV distribution layered on top of the ASTER GDEM v.2 shaded relief. Selected contours of PGV are plotted and marked on the shaded bar, and contour labels in meters per second. Boundaries of the computational domain are marked by a dashed black rectangle. The rupture extent and epicenter are marked by a solid white line and a star, respectively. Macroseismic intensity residuals (reported–calculated) are marked by shaded triangles for underestimates, circles for matching, and inverted triangles for overestimates. The shading intensity is correlated with residual value. The inset at the top-left corner plots the same residuals as a function of azimuth and distance from the epicenter. The color version of this figure is available only in the electronic edition. The overlapping parts of the two curves suggest a high level of agreement between reported and calculated intensities. Macroseismic intensity residuals plotted as a function of epicentral distance (Fig. 6b) indicate that, for the simulated epicentral location, residuals are not distance dependent. Distribution of residuals (Fig. 6c) shows that 56% of the calculated intensities match the reported intensities and that 98% of the calculated intensities are within a single unit from the reported intensities. The root mean square (rms) of intensity residuals for the 122 points is 0.68.
Discussion The DSM was implemented into a finite-difference code to simulate the large-scale characteristics of strong earthquakes, specifically macroseismic intensity, for regions where seismic hazard is proven but seismicity is low and instrumental coverage is limited. Based on a generalized slip function,
ensuing from numerous source inversions, the DSM presents a necessary modification of Haskell-type models with constant slip. We developed the DSM as a robust and efficient method to study the large-scale characteristics of ground motions and their variations as a function of source geometry, location, and directivity effects. The ever-increasing seismic risk in developing countries (Bilham, 2004) and the improbable deployment of seismic networks in those areas accentuate the need for forward modeling of strong earthquakes as a measure for mitigation of seismic hazard and risk by understanding the effects associated with the seismic source. HM prescribes a nonphysical, constant slip distribution with unilateral propagation of the rupture, which results in unrealistic directivity where most of the seismic energy is radiated in the direction of rupture and practically no seismic energy is radiated in the opposite direction or the fault-normal direction. The HM-RRP depicts a more realistic radiation pattern known from many seismic observations with four
Distributed Slip Model for Forward Modeling Strong Earthquakes
101
40
(a)
3.0 Reported
8
30
7
2.5
6
4 0
30
60 90 120 Epicentral distance, km
(b)
150
180
20
2.0
15 10
(c)
3
PGV ratio
25
5
Reported - Calculated
35
Calculated
x, km
Intensity
9
1.5
5
2 0
1
1.0 0
0 −1 −2 −3 0
60 120 180 0 10 20 30 40 50 60 70 Frequency Epicentral distance, km
Figure 6. Reported and calculated macroseismic intensities. (a) Intensities as a function of epicentral distance, with curves fitted by regression according to the Stromeyer and Grünthal (2009) equation for attenuation relations for macroseismic data. (b) Intensity residuals (reported–calculated) as a function of epicentral distance. (c) Histogram of the residuals in (b). The color version of this figure is available only in the electronic edition. pronounced lobes of shaking (Wald et al., 1991; Pollitz et al., 2012). However, as shown by Wald et al. (1991), it does not adequately fit the ground motions in the fault-normal lobes, where it yields smaller amplitudes relative to observations. In this context, our DSM model may result in a better estimation of ground motions in the fault-normal lobes because it produces larger amplitudes relative to the HM-RRP at locations of equal distance from the epicenter. At the location of the peak ground motion of the fault-normal lobes, which does not occur at the same place for the DSM and HM-RRP, these estimates are ∼30% stronger for the DSM as illustrated in Figure 2c and 2d but may be larger by up to a factor of ∼2:7 for locations at equal epicentral distances as illustrated in Figure 3g, showing velocity synthetics at ap. In order to further emphasize the difference in radiation patterns, we
Table 3 Fit Parameters for the Stromeyer and Grünthal (2009) Equation
Reported Calculated
I
a
b
9.35 9.32
4.076 4.456
−0.0111 −0.015
I , reference intensity at the epicenter; a and b are coefficients.
5
10
15
20 25 y, km
30
35
40
Figure 7. PGV ratio computed as the PGV of the DSM divided by that of the HM-RRP. Contours of the selected PGV values are plotted as a location reference. Dotted contour lines represent values from the DSM, and dashed contour lines represent values from the HMRRP. Epicenter and rupture extent are marked by a star and the dashed white line, respectively. The color version of this figure is available only in the electronic edition.
divide the PGV of the DSM by that of the HM-RRP (Fig. 7). In the fault-parallel direction, the PGV ratio is on the order of unity; however, in the fault-normal direction, the ratio may reach values larger than 3. The calculated macroseismic intensities based on simulated ground motions of the 1927 Jericho earthquake, initiated by the DSM, are in good agreement with reported intensities. The rms of residuals (reported–calculated) is 0.68, with 56% of the calculated intensities matching the reported intensities and 98% of the calculated intensities within a single unit from the reported intensities. The exact location of the Jericho earthquake, its depth, and the rupture direction are the subject of considerable controversy as arises from the recent review by Aldersons and Ben-Avraham (2014). Ben-Menahem et al. (1976) placed the epicenter near the Damia bridge (32.0° N, 35.5° E), 30 km north of the city of Jericho, and assumed that the rupture propagated south. Later studies relocate the epicenter 60 km south along the DST to achieve better arrival-time residuals at stations up to a distance of 40° (Shapira et al., 1993). We simulate this earthquake with the epicenter relocated by Shapira et al. (1993) and assume northward rupture propagation. The reported macroseismic intensities are well explained by the epicentral location, because residuals are not distance dependent (Fig. 6b). Furthermore, had the rupture propagated southward as originally suggested by Ben-Menahem et al. (1976), the radiation pattern in Figure 5 would have been mirrored in the north–south direction, rendering reported intensities north of the epicenter unexplained.
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Conclusions
References
We developed the DSM, a generic, kinematic earthquake source representation that accounts for fault geometry, propagation of the rupture, and slip distribution. Slip distribution within an elliptical rupture patch smoothly decays from the point of maximum slip Dp to zero at the borders, avoiding singularities in the rupture process. The DSM was found to capture the essential pattern of seismic radiation around a finite fault: directivity and faultnormal seismic radiation. The DSM and the HM-RRP exhibit similar ground motions in the fault-parallel direction. However, relative to the HM-RRP, the DSM produces significantly larger ground-motion amplitudes, by up to a factor of ∼3 in the fault-normal direction. For the purpose of seismic-hazard mitigation neither the HM nor the PSM gives a reliable estimation of ground-motion patterns expected during a large earthquake, especially in the near field. Moreover, using these source models to initiate seismic-wave propagation in forward models might result in erroneous representation of ground motions: overestimating ground motions in certain areas of interest while underestimating in other areas. We use the DSM to initiate seismic-wave propagation during the 1927 M L 6.25 Jericho earthquake and compare calculated macroseismic intensities to reported intensities at 122 localities. The rms of macroseismic intensity residuals (reported–calculated) is 0.68, with 56% of the calculated intensities matching the reported intensities and 98% of the calculated intensities within a single unit from the reported intensities. We showed that the DSM has the potential to predict the large-scale ground motions during strong earthquakes, specifically macroseismic intensities. The DSM is capturing the salient features of seismic radiation pattern: directivity and fault-normal radiation symmetry. This is an essential step toward more realistic simulation of large earthquakes, which is essential for robust ground-motion prediction for regions with limited recorded data due to low seismicity and limited instrumental coverage.
Agnon, A. (2014). Pre-instrumental earthquakes along the Dead Sea rift, in Dead Sea Transform Fault System: Reviews, Z. Garfunkel, Z. Ben-Avraham, and E. Kagan (Editors), Springer, The Netherlands, 207–261, doi: 10.1007/978-94-017-8872-4_8 Aldersons, F., and Z. Ben-Avraham (2014). The seismogenic thickness in the Dead Sea area, in Dead Sea Transform Fault System: Reviews, Springer, The Netherlands, 53–89. Allen, R. M. (2007). Earthquake hazard mitigation: New directions and opportunities, in Treatise on Geophysics, G. Schubert (Editor), Vol. 4, H. Kanamori (Series Editor), Elsevier Science, 607–648. Ambraseys, N. N., J. Douglas, S. K. Sarma, and P. M. Smit (2005). Equations for the estimation of strong ground motions from shallow crustal earthquakes using data from Europe and the Middle East: Horizontal peak ground acceleration and spectral acceleration, Bull. Earthq. Eng. 3, no. 1, 1–53. Amiran, D. H. K., E. Arieh, and T. Turcotte (1994). Earthquakes in Israel and adjacent areas: Macroseismic observations since 100 BCE, Isr. Explor. J. 44, nos. 3/4, 260–305. Atkinson, G. M., and D. M. Boore (2011). Modifications to existing groundmotion prediction equations in light of new data, Bull. Seismol. Soc. Am. 101, no. 3, 1121–1135. Avni, R., D. Bowman, A. Shapira, and A. Nur (2002). Erroneous interpretation of historical documents related to the epicenter of the 1927 Jericho earthquake in the Holy Land, J. Seismol. 6, no. 4, 469–476. Ben-Menahem, A. (1961). Radiation of seismic surface-waves from finite moving sources, Bull. Seismol. Soc. Am. 51, no. 3, 401–435. Ben-Menahem, A. (1991). Four thousand years of seismicity along the Dead Sea rift, J. Geophys. Res. 96, no. B12, 20,195, doi: 10.1029/91JB01936. Ben-Menahem, A., A. Nur, and M. Vered (1976). Tectonics, seismicity and structure of the Afro-Eurasian junction—The breaking of an incoherent plate, Phys. Earth Planet. In. 12, no. 1, 1–50, doi: 10.1016/00319201(76)90005-4. Bilham, R. (2004). Urban earthquake fatalities: A safer world, or worse to come? Seismol. Res. Lett. 75, no. 6, 706–712. Blankenhorn, M. (1927). Das Erdbeben in Juli 1927 in Palastina, Z. Dtsch. Palast. Ver 50, 288–296 (in German). Boore, D. M., and G. M. Atkinson (2008). Ground-motion prediction equations for the average horizontal component of PGA, PGV, and 5%-damped PSA at spectral periods between 0.01 s and 10.0 s, Earthq. Spectra 24, no. 1, 99–138. Brawer, A. J. (1928). Earthquake shocks in Palestine from July, 1927, to August, 1928, Jew. Pal. Expl. Soc. 316–325 (in Hebrew). Davis, P. M., J. L. Rubinstein, K. H. Liu, S. S. Gao, and L. Knopoff (2000). Northridge earthquake damage caused by geologic focusing of seismic waves, Sci. Sci. 289, no. 5485, 1746–1750. Day, S. M., R. Graves, J. Bielak, D. Dreger, S. Larsen, K. B. Olsen, A. Pitarka, and L. Ramirez-Guzman (2008). Model for basin effects on long-period response spectra in southern California, Earthq. Spectra 24, no. 1, 257–277, doi: 10.1193/1.2857545. Di Carli, S., C. François-Holden, S. Peyrat, and R. Madariaga (2010). Dynamic inversion of the 2000 Tottori earthquake based on elliptical subfault approximations, J. Geophys. Res. 115, no. B12, doi: 10.1029/ 2009JB006358. Frankel, A. (1993). Three-dimensional simulations of ground motions in the San Bernardino Valley, California, for hypothetical earthquakes on the San Andreas fault, Bull. Seismol. Soc. Am. 83, no. 4, 1020–1041. Goulet, C. A., N. A. Abrahamson, P. G. Somerville, and K. E. Wooddell (2015). The SCEC Broadband Platform Validation Exercise: Methodology for code validation in the context of seismic-hazard analyses, Seismol. Res. Lett. 86, no. 1, 17–26, doi: 10.1785/0220140104. Graves, R. W., A. Pitarka, and P. G. Somerville (1998). Ground-motion amplification in the Santa Monica area: Effects of shallow basin-edge structure, Bull. Seismol. Soc. Am. 88, no. 5, 1224–1242. Gregor, N., N. A. Abrahamson, G. M. Atkinson, D. M. Boore, Y. Bozorgnia, K. W. Campbell, B. S.-J. Chiou, I. M. Idriss, R. Kamai, E. Seyhan,
Data and Resources Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Global Digital Elevation Model (GDEM) v.2 (Tachikawa et al., 2011) grids are taken from http://gdem.ersdac.jspacesystems.or.jp/ (last accessed August 2015). The Wave Propagation Project (WPP) code for finite-difference simulations is available at the Lawrence Livermore National Laboratory website (https:// computation-rnd.llnl.gov/serpentine/software.html, last accessed March 2015). Reported intensities are taken from appendix A in Zohar and Marco (2012).
Acknowledgments This work was partially supported by the Ministry of Energy and Water, Israel, Grant Reference Number 211-14-002.
Distributed Slip Model for Forward Modeling Strong Earthquakes et al. (2014). Comparison of NGA-West2 GMPEs, Earthq. Spectra 30, no. 3, 1179–1197. Grünthal, G. (1998). European Macroseismic Scale. Cahiers du Centre Européen de Géodynamique et de Séismologie, Luxembourg, Vol. 15, Centre Européen de Géodynamique et de Séismologie, Luxembourg, 101 pp. Gvirtzman, Z., and J. N. Louie (2010). 2D Analysis of earthquake ground motion in Haifa Bay, Israel, Bull. Seismol. Soc. Am. 100, no. 2, 733–750. Hartzell, S. H., and T. H. Heaton (1983). Inversion of strong ground motion and teleseismic waveform data for the fault rupture history of the 1979 Imperial Valley, California, earthquake, Bull. Seismol. Soc. Am. 73, no. 6A, 1553–1583. Haskell, N. A. (1964). Total energy and energy spectral density of elastic wave radiation from propagating faults, Bull. Seismol. Soc. Am. 54, no. 6A, 1811–1841. Kästli, P., and D. Fäh (2006). Rapid estimation of macroseismic effects and shake maps combining macroseismic and instrumental data, Proc. of the First European Conference on Earthquake Engineering and Seismology (ECEES), Geneva, Switzerland, 3–8 September 2006. Luzón, F., L. Ramírez, F. J. Sánchez-Sesma, and A. Posadas (2004). Simulation of the seismic response of sedimentary basins with vertical constant-gradient velocity for incident SH waves, Pure Appl. Geophys. 161, no. 7, 1533–1547, doi: 10.1007/s00024-004-2519-0. Madariaga, R. (2007). Seismic source theory, in Treatise on Geophysics, G. Schubert (Editor), Vol. 4, H. Kanamori (Series Editor), Elsevier Science. Maruyama, T. (1963). On the force equivalents of dynamical elastic dislocations with reference to the earthquake mechanism, Bull. Earthq. Res. Inst. 41, 467–486. Medvedev, S. W., W. Sponheuer, and V. Karnik (1965). Seismic Intensity Scale, version MSK 1964, United nation educational, scientific and cultural organization, Paris, 7 pp. Motazedian, D., and G. M. Atkinson (2005). Stochastic finite-fault modeling based on a dynamic corner frequency, Bull. Seismol. Soc. Am. 95, no. 3, 995–1010. Olsen, K. B., S. M. Day, J. B. Minster, Y. Cui, A. Chourasia, M. Faerman, R. Moore, P. Maechling, and T. Jordan (2006). Strong shaking in Los Angeles expected from southern San Andreas earthquake, Geophys. Res. Lett. 33, no. 7, 1–4, doi: 10.1029/2005GL025472. Olsen, K. B., J. C. Pechmann, and G. T. Schuster (1995). Simulation of 3D elastic wave propagation in the Salt Lake basin, Bull. Seismol. Soc. Am. 85, no. 6, 1688. Petersson, N. A., and B. Sjögreen (2012). Stable and efficient modeling of anelastic attenuation in seismic wave propagation, Comm. Comput. Phys. 12, 193–225. Petersson, N. A., and B. Sjögreen (2014). Super-grid modeling of the elastic wave equation in semi-bounded domains, Comm. Comput. Phys. 16, no. 4, 913–955. Peyrat, S., R. Madariaga, E. Buforn, J. Campos, G. Asch, and J. P. Vilotte (2010). Kinematic rupture process of the 2007 Tocopilla earthquake and its main aftershocks from teleseismic and strong-motion data, Geophys. J. Int. 182, no. 3, 1411–1430, doi: 10.1111/j.1365-246X.2010.04685.x. Pollitz, F. F., R. S. Stein, V. Sevilgen, and R. Burgmann (2012). The 11 April 2012 east Indian Ocean earthquake triggered large aftershocks worldwide, Nature 490, no. 7419, 250–253, doi: 10.1038/nature11504. Power, M., B. Chiou, N. Abrahamson, Y. Bozorgnia, T. Shantz, and C. Roblee (2008). An overview of the NGA project, Earthq. Spectra 24, no. 1, 3–21. Roten, D., K. B. Olsen, J. C. Pechmann, V. M. Cruz-Atienza, and H. Magistrale (2011). 3D simulations of M 7 earthquakes on the Wasatch fault, Utah, Part I: Long-period (0-1 Hz) ground motion, Bull. Seismol. Soc. Am. 101, no. 5, 2045–2063, doi: 10.1785/0120110031. Ruiz, S., and R. Madariaga (2011). Determination of the friction law parameters of the M w 6.7 Michilla earthquake in northern Chile by dynamic inversion, Geophys. Res. Lett. 38, no. 9, doi: 10.1029/2011GL047147.
103
Savage, J. C. (1966). Radiation from a realistic model of faulting, Bull. Seismol. Soc. Am. 56, no. 2, 577–592. Shani-Kadmiel, S., M. Tsesarsky, J. N. Louie, and Z. Gvirtzman (2012). Simulation of seismic-wave propagation through geometrically complex basins: The Dead Sea basin, Bull. Seismol. Soc. Am. 102, no. 4, 1729–1739, doi: 10.1785/0120110254. Shani-Kadmiel, S., M. Tsesarsky, J. N. Louie, and Z. Gvirtzman (2014). Geometrical focusing as a mechanism for significant amplification of ground motion in sedimentary basins: Analytical and numerical study, Bull. Earthq. Eng. 12, no. 2, 607–625, doi: 10.1007/s10518-013-9526-4. Shapira, A., R. Avni, and A. Nur (1993). A new estimate for the epicenter of the Jericho earthquake of 11 July 1927, Isr. J. Earth Sci. 42, no. 2, 93–96. Stromeyer, D., and G. Grünthal (2009). Attenuation relationship of macroseismic intensities in central Europe, Bull. Seismol. Soc. Am. 99, no. 2A, 554–565. Stupazzini, M., R. Paolucci, and H. Igel (2009). Near-fault earthquake groundmotion simulation in the Grenoble Valley by a high-performance spectral element code, Bull. Seismol. Soc. Am. 99, no. 1, 286, doi: 10.1785/ 0120080274. Tachikawa, T., M. Hato, M. Kaku, and A. Iwasaki (2011). Characteristics of ASTER GDEM version 2, Proc. of Geoscience and Remote Sensing Symposium (IGARSS), IEEE International, Vancouver, Canada, 24–29 July 2011. Vallée, M., and M. Bouchon (2004). Imaging coseismic rupture in far field by slip patches, Geophys. J. Int. 156, no. 3, 615–630. Wald, D. J., D. V. Helmberger, and T. H. Heaton (1991). Rupture model of the 1989 Loma Prieta earthquake from the inversion of strong-motion and broadband teleseismic data, Bull. Seismol. Soc. Am. 81, no. 5, 1540–1572. Wells, D. L., and K. J. Coppersmith (1994). New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement, Bull. Seismol. Soc. Am. 84, no. 4, 974–1002. Zeng, Y., J. G. Anderson, and G. Yu (1994). A composite source model for computing realistic synthetic strong ground motions, Geophys. Res. Lett. 21, no. 8, 725–728, doi: 10.1029/94GL00367. Zohar, M., and S. Marco (2012). Re-estimating the epicenter of the 1927 Jericho earthquake using spatial distribution of intensity data, J. Appl. Geophys. 82, 19–29, doi: 10.1016/j.jappgeo.2012.03.004.
Department of Geological and Environmental Sciences Ben-Gurion University of the Negev P.O.B: 653 Beer-Sheva 84105, Israel
[email protected] (S.S.-K.)
Department of Structural Engineering Ben-Gurion University of the Negev P.O.B: 653 Beer-Sheva 84105, Israel
[email protected] (M.T.)
Geological Survey of Israel 30 Malkhe Israel Street Jerusalem 95501, Israel
[email protected] (Z.G.) Manuscript received 11 November 2015; Published Online 05 January 2016
