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the Creative Commons Attribution 4.0 License.

# Calibrating a new attenuation curve for the Dead Sea region using surface wave dispersion surveys in sites damaged by the 1927 Jericho earthquake

### Yaniv Darvasi

### Amotz Agnon

Instrumental strong motion data are not common around the Dead Sea region. Therefore, calibrating a new attenuation equation is a considerable challenge. However, the Holy Land has a remarkable historical archive, attesting to numerous regional and local earthquakes. Combining the historical record with new seismic measurements will improve the regional equation.

On 11 July 1927, a rupture, in the crust in proximity to the northern Dead
Sea, generated a moderate 6.2 *M*_{L} earthquake. Up to 500 people
were killed, and extensive destruction was recorded, even as far as 150 km
from the focus. We consider local near-surface properties, in
particular, the shear-wave velocity, as an amplification factor. Where the
shear-wave velocity is low, the seismic intensity far from the focus would
likely be greater than expected from a standard attenuation curve. In this
work, we used the multichannel analysis of surface waves (MASW) method to
estimate seismic wave velocity at anomalous sites in Israel in order to
calibrate a new attenuation equation for the Dead Sea region.

Our new attenuation equation contains a term which quantifies only lithological effects, while factors such as building quality, foundation depth, topography, earthquake directivity, type of fault, etc. remain out of our scope. Nonetheless, about 60 % of the measured anomalous sites fit expectations; therefore, this new ground-motion prediction equation (GMPE) is statistically better than the old ones.

From our local point of view, this is the first time that integration of the 1927 historical data and modern shear-wave velocity profile measurements improved the attenuation equation (sometimes referred to as the attenuation relation) for the Dead Sea region. In the wider context, regions of low-to-moderate seismicity should use macroseismic earthquake data, together with modern measurements, in order to better estimate the peak ground acceleration or the seismic intensities to be caused by future earthquakes. This integration will conceivably lead to a better mitigation of damage from future earthquakes and should improve maps of seismic hazard.

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Generating a modern and applicable attenuation equation is one of applied seismologists' main interests. Considering the Dead Sea area, for which instrumental strong motion data are not available, this task is particularly challenging. Using the Holy Land's historically rich database, researchers had defined seismic intensities and estimated earthquake locations. Investigating anomalous sites, with seismic intensities higher or lower than predicted from the basic regional attenuation relation, may lead to a better attenuation equation. The local geological conditions can strongly influence the nature and severity of shaking at a given site. Assessing the local geological conditions by geophysical techniques at these anomalous sites, and adding a logarithmic term to a basic attenuation equation, should improve the equation.

This work focuses on the 1927 event, but it is part of wider research which extends to additional earthquakes. The 1927 event was chosen as it is the only devastating one recorded, albeit teleseismically, during the instrumented period.

Our main goal in this research is a tighter constraint on the attenuation equation derived from this event. This should allow us to examine whether this preliminary work coincides with our expectations of site amplification and de-amplification due to the local lithology.

## 1.1 Site response

Ground motion is controlled by a number of variables, including source characteristics, source distance, propagation directivity, near-surface geology, etc. The elastic properties of near-surface materials and their effect on seismic wave propagation are crucial to earthquake and civil engineering, and environmental and Earth science studies.

Seismic surface waves are initiated at the moment that the earthquake wave front impinges on the surface. These waves spread out, and the surface shakes as they pass. Surface wave amplitude at the surface is controlled by the mechanical properties of the rocks below. These often consist of low-velocity weathered rock over bedrock with much higher velocities. When seismic waves pass from a high-velocity layer to a low-velocity layer, their amplitudes and duration typically increase. The phenomena of site amplification, as a result of soft sediments overlying hard bedrock, is well known since the early days of seismology (Milne, 1898). Site effects are also well known and were investigated after several major earthquakes: Mexico City 1985 (Singh et al., 1988), Yerevan 1989 (Borcherdt et al., 1989), San Francisco 1989 (Hough et al., 1990), Los Angeles 1994 (Hall et al., 1994) and Kobe 1995 (Aguirre and Irikura, 1997). Therefore, local lithology is a crucial factor for estimating site amplification, defined as the amplitude ratio between the surface layer and the underlying bedrock. Site amplification at a specific site can be attributed to many factors, such as basin effects, focusing effects, topography and reverberation of the seismic waves in the upper layers due to acoustic impedance differences (Fig. 1).

The amplification, *A*, is proportional to the reciprocal square root of the
product of the shear-wave velocity, *V*_{s} (Eq. 1) (Aki and Richards, 2002):

where *ρ* is the density of the investigated soil. As shear-wave
velocity decreases by a given fraction, the amplification increases by half
that fraction (for a constant density). Since density plays a minor role
(Dal Moro, 2014; Xia et al., 1999), the *V*_{s} value can be used to represent
site conditions.

The most widely used index in the classification of the soil response is the average shear-wave velocity in the uppermost 30 m, the ${V}_{{\mathrm{s}}_{\mathrm{30}}}$. This index was accepted for site classification in the US National Earthquake Hazards Reduction Program (NEHRP) (Building Seismic Safety Council, 2001). In Europe, by the new provisions of Eurocode 8 (CEN, 2011), and in Israel, it is accepted by the design provisions for earthquake resistance of structures – SI 413 (The Standards Institution of Israel, 2013). The value of 30 m comes from the US and European building codes, where it was found empirically that this depth is directly proportional to deeper and shallower values (Boore et al., 2011). Zaslavsky et al. (2012) argued that the use of ${V}_{{\mathrm{s}}_{\mathrm{30}}}$ is a simplification that cannot be justified in the complex geological conditions in Israel, yet no alternatives have thus far been proposed. Therefore, in this scenario, the Standards Institution of Israel still adopts the ${V}_{{\mathrm{s}}_{\mathrm{30}}}$ index.

In modern attenuation equations, also known as ground-motion prediction equations (GMPEs), coefficients are derived from strong motion data, namely from ground acceleration measurements. In the past, and in areas lacking the technology to record earthquakes, it was impossible to measure the peak ground acceleration (PGA) directly. Therefore, it is common to categorize historical earthquakes with seismic intensity scales that describe the damage at each site or area (Ambraseys, 2009; Guidoboni and Comastri, 2005).

## 1.2 The 6.2 *M*_{L} 1927 Jericho earthquake

The left-lateral Dead Sea transform separates the Sinai–Levant Block from
the Arabian Plate (Fig. 2). The 6.2 *M*_{L} 11 July 1927 Jericho earthquake (Ben-Menahem et al., 1976; Shapira, 1979) was
the strongest and most destructive earthquake to hit the Holy Land during
that century. Furthermore, it was the first to be instrumentally recorded by
seismographs. The epicentral location was originally estimated to be a few
kilometers south of the Damia Bridge, which is 30 km north of
Jericho (International Seismological Summary – ISS Bulletin of 1927). In
the following decades, new estimates have been published: Shapira et al. (1993) calculated the epicenter to be near Mitzpe Shalem.
Zohar and Marco (2012) estimated the epicenter to be near the Almog settlement, about 30 km north of Shapira's epicenter, and Kagan et al. (2011) surmised
that the source was somewhere on the Kalia fault, located in the northern
part of the Dead Sea graben, perpendicular to the main Dead Sea fault
(Fig. 2).

The damage from the earthquake was heavy, especially in places near the source but not only there. In Nablus, located 70 km from the epicenter (Fig. 2), 60 people were killed, 474 were injured, and more than 700 structures were destroyed, most of which were built on soft sediments (Blanckenhorn, 1927; Willis, 1928). By comparison, Jerusalem is only about 30 km from the source and the damage there was much smaller, especially in property. However, at Mount Scopus and the Mount of Olives (eastern neighborhoods in Jerusalem), the damage exceeded that in other parts of Jerusalem (Abel, 1927; Brawer, 1928). Other cities also suffered from this earthquake. Tens of people were injured and even died, and hundreds of houses were ruined in Ramla and Lod (Brawer, 1928). Jericho in the Jordan Valley also suffered significant damage, especially in terms of buildings collapsing (Fig. 3). The total number of victims was about 350–500 (Ambraseys and Melville, 1988; Amiran, 1952; Arieh, 1967; Ben-Menahem, 1991). Beyond the casualties, several environmental effects were reported. The Jordan River flow ceased near the Damia Bridge for about 21.5 h (Willis, 1928) and a 1 m seiche wave was observed in the Dead Sea (Abel, 1927; Blanckenhorn, 1927). Some evidence suggests that the earthquake was felt up to 700 km from the epicenter (Ben-Menahem, 1991), although a different interpretation suggests this distance was only 300 km (Ambraseys and Melville, 1988).

Compiling historical evidence, Avni (1999), in his PhD thesis, estimated the
seismic intensities (MSK or the Medvedev–Sponheuer–Karnik scale) (Medvedev et
al., 1965) at 133 different locations around Israel, Palestine, Jordan,
Lebanon, Syria and Egypt (Fig. 4 for locations
and the Supplement). The curve that Avni (1999) fit to his
scattered MSK vs. *d* points represents his basic attenuation equation and had
an *R*^{2} of about 0.26. Based on the methodology proposed by Bakun and
Wentworth (1997), Hough and Avni (2011) published a new attenuation equation
for the Dead Sea region:

where MMI is the modified Mercalli intensity (assumed to be equivalent to MSK),
*M* is the magnitude, and *d* is the distance from the epicenter.

The multichannel analysis of surface waves (MASW) method is environmentally friendly, non-invasive, low cost, rapid and robust, and provides reliable ${V}_{{\mathrm{s}}_{\mathrm{30}}}$ data (Xia et al., 2002). Multichannel shallow seismic surveys make it possible to separate different wave fields in the frequency and velocity domains. Fundamental and higher modes can be analyzed simultaneously, but generally, only the fundamental mode is used because it has the highest energy (Park et al., 1998).

The MASW method consists of three main steps: (a) acquisition of experimental data, (b) signal processing to obtain the experimental dispersion curve and (c) inversion to estimate ${V}_{{\mathrm{s}}_{\mathrm{30}}}$ (Fig. 5). The inverse problem consists of estimating a set of parameters that describe the soil deposit, based on an experimental dispersion curve. Inversion problems based on wave propagation theory cannot be solved in a direct way due to their non-linearity. Thus, iterative methods must be used where a theoretical dispersion curve is determined for a given layer model and compared to the previously obtained experimental dispersion curve (Ryden et al., 2004). ${V}_{{\mathrm{s}}_{\mathrm{30}}}$ typically does not converge to a single stable value. In other words, for the same dispersion curve, one will get slightly different ${V}_{{\mathrm{s}}_{\mathrm{30}}}$ depending on the initial model.

We carried out the surveys with a linear array of 24 vertical geophones (R. T. Clark's geophones with a natural frequency of 4.5 Hz) at equal intervals of 2–3 m over a total length of 46–69 m. For the survey sound source, we used a 5 kg sledgehammer striking a 20 cm square aluminum plate at variable offsets of 5, 10, 15, 20, 25 and 30 m (both forward and reversed) (Fig. 6a). The seismic data were recorded on a Geometrics Geode seismograph at a sampling rate mostly of 8 kHz for 0.5–2 s (Table 1). For an acceptable signal-to-noise ratio, we used the so-called “vertical stacking” approach, which is a summation of multiple synchronized repetitions of the test (usually five times).

Rayleigh wave dispersion curves are obtained by the MASW module of the
RadExPro^{®} software, whose calculation procedure is based on a
paper by Park et al. (1998), and also by the WinMASW^{®}
software. From all the dispersion images that we calculated from each offset
shot (Fig. 6b), we chose the smoothest and
clearest one (Fig. 6c) to compute the site's
${V}_{{\mathrm{s}}_{\mathrm{30}}}$ profile. An inversion process then finds the shear-wave velocity
profile whose theoretical dispersion curve is as close as possible to the
experimental curve (Fig. 6d). The data and
coefficients are automatically inverted via genetic algorithms which
represent an optimization procedure belonging to the classification of
global-search methods. Genetic algorithms are commonly used to generate
high-quality solutions to optimization and search problems by relying on
bio-inspired operators such as mutation, crossover and selection compared to
traditional linear inversion methods based on gradient methods (Jacobian
matrix). These inversion techniques produce a very reliable result in terms
of precision and completeness (Dal Moro et al., 2007).

From 24 surveys, we succeeded in extracting ${V}_{{\mathrm{s}}_{\mathrm{30}}}$ for 19 of the 20 sites studied (the Hartuv data were too noisy for interpretation) (Table 2 and the Supplement). These would be used to recalibrate the attenuation equation arrived at by previous investigators at 19 of the 133 sites.

## 3.1 Velocity model

All ground models were considered to be a stack of horizontal homogeneous
elastic layers, neglecting lateral variations in soil properties. The number
of unknowns for a layered model, when considering only shear-wave velocity,
is three for each layer: density, thickness and one elastic constant.
Therefore, the number of unknowns is 3*n*−1 (where *n* represents the number of
layers). The change in density with depth is usually small in comparison to
the change in shear modulus and is normally neglected (Park et al., 1997).

## 3.2 Number of layers and layer thicknesses

The resolution of surface wave surveys decreases with depth. Thin layers are well resolved when they are close to the surface, whereas at great depth, the resolution is limited and only large changes can be detected (Foti et al., 2014). Regardless of the number of the layers at the site, ${V}_{{\mathrm{s}}_{\mathrm{30}}}$ is almost the same in each case (Fig. 7). For these reasons, as well as the lack of density information, we did not restrict each model to a specific number of layers. Without boreholes or other direct lithostratigraphic constraint, which is the case in our work, a useful rule of thumb is to assume layer thicknesses increasing with depth, to compensate for the decreased resolution with depth, an intrinsic shortcoming of surface wave testing (Foti et al., 2014).

## 3.3 Depth of investigation

We used a 5 kg sledgehammer and summed up five strikes. For some
sites, this type of source is insufficient to determinate a shear-wave
profile down to 30 m. In addition, at some sites, we were not able to spread
the geophones at intervals of more than 2 m, which limited the length
of the seismic line. This length probably excludes longer wavelengths which
limit the depth of investigation. Lastly, as the shear-wave velocity of the
lowest frequency is higher, more data are available for deeper layers.
Therefore, the penetration depth will decrease in areas with low shear-wave
velocity. For instance, if we can clearly detect a phase velocity of about
300 m s^{−1} at 5 Hz, we can roughly
estimate a depth of investigation of approximately 20–30 m according to
the following equation:

where *n* ranges between 2 and 3 (Foti et al., 2014; Dal Moro, 2014). In other
words, this equation emphasizes that the depth of investigation is about a
half to a third of the largest wavelength observed.

## 3.4 Recent improvement of the 1927 epicenter

Zohar and Marco (2012) relocated the 1927 epicenter to a point near the
Almog settlement. We used this most recently published epicenter to
calculate new epicentral distances for the 133 sites. Since Eq. (2) above
is dependent upon *d*, we checked the variable scatter in the points but found
that the changes in the best-fit coefficients were very minor, so we
assumed for all purposes to use the original.

Figure 8 shows a scatter plot of the original MMI
(assumed equivalent to MSK) vs. new *d* for their 133 sites. Hough and
Avni (2011) fit these data with a curve whose equation best describes the
attenuation equation for this event. Using the mathematical form of their
curve, we calculated upper and lower limits such that 60 % of the points
are enclosed. This we call the 60 % prediction boundary. We consider that
the lithological effects probably account for much of the scatter beyond
this boundary, due to amplification and de-amplification.

A number of researchers have studied the 1927 event. Avni (1999) tried to reduce the impact of local geology and attempted to generate basic attenuation curves for specific azimuths. Zohar and Marco (2012) relocated the source position, while Shani-Kadmiel et al. (2016) studied directivity of the source pattern. None of these publications address the ${V}_{{\mathrm{s}}_{\mathrm{30}}}$ measurements. An attenuation equation with a term that depends on the ${V}_{{\mathrm{s}}_{\mathrm{30}}}$ index should lead to a better understanding of past events and to more useful predictions of future earthquakes.

## 4.1 Survey locations and validation

The decision as to where exactly each survey should take place was based on Avni's thesis (1999). Where the location was not sufficiently known, we rechecked the reference given by Avni. In most cases, there was evidence of specific damaged buildings. We tried to locate these buildings on historical maps (1927–1945). Unfortunately, most sites were located inside urban areas, where we could not carry out the seismic surveys. Therefore, we surveyed in nearby open areas as close as possible to the referenced damage zones.

To validate our results, we compared them with a summary of thousands of
seismic evaluations around Israel carried out over the years by the
Geophysical Institute of Israel (GII) and compiled in a report by Aksinenko
and Hofstetter (2012). These evaluations were based upon refraction and
borehole velocity measurements yielding *V*_{s} and/or *V*_{p} values, as well as the
effects of topography and geology. The spacing of their data was such that
often a number of GII sites had to be averaged to provide a value within
several kilometers for comparison with our MASW values. However,
Fig. 9 shows that the GII-based values are in
consistent agreement with those of the MASW. However, this comparison is a
bit tricky because ${V}_{{\mathrm{s}}_{\mathrm{30}}}$ results for two sites 5 km or much less distant
could be significantly different, as shown in Fig. 10. Remembering that ${V}_{{\mathrm{s}}_{\mathrm{30}}}$ enters a logarithmic term, we find our
approach potentially useful.

Table 2 lists our 24 sites alphabetically, with their respective ${V}_{{\mathrm{s}}_{\mathrm{30}}}$
values, the computed errors and epicentral distances, *d*. The ${V}_{{\mathrm{s}}_{\mathrm{30}}}$ values
vary from a low of 232 m s^{−1} in Beit Alfa, −85 m a.s.l. (Fig. 11), in the
thick and active alluvial plain of the famous valley of Gilboa some 10 km
from the Dead Sea rift and a site of many millennia of agriculture. The
highest value is 1444 m s^{−1} in Peki'in, 680 m a.s.l. (Fig. 11), in an area
of ancient hillside orchards and massive carbonate bedrock. On the other
hand, the two Motza sites (Fig. 11) lie in Emek HaArazim (valley of the
cedars) on the western flank of Jerusalem within the massive anticlinorium
of the Judean Hills, at about 570 m a.s.l. Motza 1 (1065 m s^{−1}) is on a
compacted dirt parking lot above alluvium and the Soreq Fm., while Motza 2
(874 m s^{−1}) is farther up the valley on a gentle hillside above the Beit Meir
Fm. Both are of similar limestone and marl composition and Cretaceous age.

## 4.2 A new attenuation equation

In the present case of the 1927 earthquake, the sources of the data are mostly historical documents and not strong data measurements. This makes it difficult to quantify site response into a single equation. In the practical modern attenuation relationship, ${V}_{{\mathrm{s}}_{\mathrm{30}}}$ is a crucial index. A term that depends on ${V}_{{\mathrm{s}}_{\mathrm{30}}}$ has previously been constrained for several large data sets (Abrahamson et al., 2014; Boore et al., 1997; Campbell and Bozorgnia, 2008). We chose the Boore et al. (1997) attenuation equation (Eq. 4) in order to emphasize site response:

where *Y* is the ground-motion variable (peak horizontal acceleration or
pseudo-acceleration response in *g*), *M* is the moment magnitude, *r* is the
epicentral distance in kilometers, and *V*_{A} and all *b* terms are frequency-dependent
coefficients to be determined. By adding Boore et al.'s (1997)
*V*_{s} term to the Hough and Avni (2011) attenuation equation (Eq. 2), we suggest a
new equation for the region:

where *V*_{A} and *C*_{4} are adjustable coefficients. The first four
coefficients remain the same as we assert that the magnitude, attenuation,
geometrical spreading and site response are all independent. We adopt the
value of *V*_{A} from Boore et al.'s (1997) equation (Eq. 4), as it
represents a single value independent of the frequency. We took
formerly derived GMPE, with its coefficients, and added another term, by
regressing only for the new coefficient, then optimizing *C*_{4} and
*V*_{A} by least squares fitting (LSF), as shown in
Fig. 12; we get the final equation:

## 4.3 The performance of the new attenuation equation

With these coefficients, 58 %, or 11 of 19 sites, were amplified or
de-amplified as we expected. For the entire distance range (up to 250 km), the ${V}_{{\mathrm{s}}_{\mathrm{30}}}$ corrections leave 42 % of sites out of the prediction
boundary (8 of 19 sites). Seismic intensities at all eight
sites are overpredicted by the attenuation equation (Eq. 2)
(Fig. 13). We expect that ${V}_{{\mathrm{s}}_{\mathrm{30}}}$ at these sites
will be higher than 655 m s^{−1} in order to obtain de-amplification. However,
our results show the opposite effect – these eight sites are characterized
by lower ${V}_{{\mathrm{s}}_{\mathrm{30}}}$, which drives amplification. This can be caused by the fact
that measurements were taken over agricultural fields, of which the upper
layers (the first few meters) are characterized by low shear-wave velocity,
decreasing the average *V*_{s}. Another reasonable explanation is that we did not
succeed in extracting the average shear-wave velocity down to 30 m and
perhaps we missed some high-velocity shear-wave layers in deeper layers. In
such cases, we constrain the last layer to be thicker in order to estimate
${V}_{{\mathrm{s}}_{\mathrm{30}}}$ for all our surveys.

In this research, we investigate site amplification and de-amplification
around Israel. According to previous studies (Aki, 1988; Boore, 2003;
Borcherdt, 1994; Field and Jacob, 1995; Joyner and Boore, 1988), the local
lithology can amplify or de-amplify wave amplitude. The commonly used modern
seismic method – MASW – allowed the extraction of *V*_{s} profiles at 19 sites
reportedly damaged by the 1927 6.2 *M*_{L} earthquake. We use these profiles
to update the attenuation equation for the Dead Sea region by including the
${V}_{{\mathrm{s}}_{\mathrm{30}}}$ term.

According to this new equation, 11 sites, which constitute 58 % of our measured samples, move into the 60 % prediction boundary. This suggests that the prediction boundary actually encompasses over 80 % of the macroseismic observations. This fit is better than any available attenuation equation for the Dead Sea region. However, as we have used only 19 sites, we should consider further research and provide wider results. Although our final equation (Eq. 6) shows amplification and de-amplification depending on ${V}_{{\mathrm{s}}_{\mathrm{30}}}$, it does not take into consideration any other factor, such as building quality, foundation depth, topography, earthquake directivity, type of fault, etc. Obviously, for better results, we must use additional methods and jointly invert some other seismic data such as refraction (S and P waves), horizontal-to-vertical spectral ratio (HVSR), MASW of the transverse component of Love waves, MASW of the radial component of Rayleigh wave, extended spatial autocorrelation (ESAC), etc. Also, with these data in hand, a full inversion for the epicenter will be in order.

Despite the scarcity of data, this is the first time that an integration of historical data with shear-wave velocity profile measurements improved the attenuation relation. In order to better estimate the peak ground acceleration or the seismic intensities that will be caused by future earthquakes, attenuation relations are necessary for areas characterized by high seismicity. Some of the regions of low-to-moderate seismicity have rich sources of historical earthquake data. The integration of historical data with modern shear-wave velocity profile measurements will lead to a better understanding of future earthquakes.

The entire database of the *V*_{s} measurements can be found at https://doi.org/10.6084/m9.figshare.7775972.v1 (Davarsi and Agnon, 2019).

The supplement related to this article is available online at: https://doi.org/10.5194/se-10-379-2019-supplement.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Environmental changes and hazards in the Dead Sea region (NHESS/ACP/HESS/SE inter-journal SI)”. It is not associated with a conference.

We thank the Neev Center for Geoinfomatics's facilities and its students. We
are especially grateful to John K. Hall, founder of the Center, for his
ongoing support. We are grateful to the Helmholtz Association of German
Research Centers for funding this research. We thank Moshe Reshef for
comments and suggestions on an earlier draft and Ran Bachrach for
valuable advice. We acknowledge the contribution of Michael Weber and
the geophysical deep sounding section at GFZ. Finally, we thank Amit Ronen
for his assistance.

Edited by: Charlotte
Krawczyk

Reviewed by: two anonymous referees

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