• from Eisenberg and Kowalewska (2024)

Antiochia Hippos (Sussita in Aramaic), one of the poleis of the Decapolis, is located 2 km east of the shores of the Sea of Galilee, in modern Israel. Situated on Mt. Sussita, which rises to a height of about 350 m above the lake, the city was cut off from its surroundings by three streams and could only be accessed through a topographic formation of a saddle (fig. 1) in the south-east and a winding path in the west¹. The city’s main construction materials were the two local stones: basalt and a soft calcrete/caliche (nari)².

Antiochia Hippos was founded after the Battle of Paneion (ca. 199 BC), either by Antiochus IV Epiphanes (175–164 BC), or most probably by Antiochus III the Great (222–187 BC)³. After Pompey’s conquest in 64 BC, the city was incorporated into Provincia Syria. It flourished throughout the Roman period, being the only polis directly next to the Sea of Galilee from the east with a territorium expanding to all the southern Golan⁴. As early as mid-4th century AD, Hippos became the seat of a bishopric, and during the Byzantine period at least seven churches were built in the city. During the Early Islamic period, Hippos was replaced as a regional capital by Tiberias, situated on the opposite side of the Sea of Galilee. In AD 749, just at the end of the Umayyad rule, Hippos was destroyed by an earthquake and never resettled.⁵

• from Claire Epstein in Stern et. al. (1993 v.2)

Hippos, a Greek city, known in Arabic as Qal'at el-Husn, is situated some 2 km (1 mi.) east of the Sea of Galilee on a promontory rising 350 m above the sea (map reference 212.242). It was founded by the Seleucids in the Hellenistic period, possibly on the site of an earlier settlement. The town, known by its Greek name, Antiochia Hippos (hippos, "horse"), continued to exist until the Arab conquest. In Aramaic it was known as Sussita. It was conquered in one of the campaigns of Alexander Jannaeus (Syncellus, ed. Dindorf, I, 559). Pompey took it from the Jews (Josephus, Antiq. XIV, 75); according to Pliny (NHV, 74), it was one of the cities of the Decapolis (League of Ten Greek Cities). Augustus gave the city to Herod, much to the dissatisfaction of the inhabitants. After Herod's death it became part of the Province of Syria (Josephus, Antiq. XV, 217; XVII, 320; War I, 396; II, 97). During the First Revolt against Rome, the Jews attacked Hippos (War II, 459, 4 78). Jews from the city were among the defenders of Taricheae (Magdala) (War III, 542). The territory of Hippos extended down to the Sea of Galilee (Josephus, Life 31, 153), and the city was the sworn enemy of Jewish Tiberias on the opposite shore of the lake (Lam. Rab. 19), despite the trade connection between them (J.T., Shevi'it 8, 38a). Jewish villages east of the lake were included in the territory of Hippos and were exempt from tithes in the time of the patriarch Judah I, being considered beyond the frontiers of the land of Israel proper (Tosefta, Shevi'it 4:10; Tosefta, Ohal. 18:4). Remains of ancient synagogues have been found at Fiq (Aphek) and at Umm el-Qanatir, both of which lay within the territory of Hippos. In the Byzantine period, Hippos was the seat of a bishop, being one of the sees of Palaestina Secunda. Like many other towns in the Byzantine period, it enjoyed great prosperity, and many churches and public buildings were erected. The city was probably abandoned after the Arab conquest at the beginning of the seventh century. Isolated buildings were erected on its ruins in later times.

In the nineteenth century Hippos was identified with the neighboring village of Sussiya, which preserved the city's ancient name (Sussita), while Qal'at el-Husn, whose natural shape resembles a camel's hump, was considered to be the site of ancient Gamala. However, following recent surveys of the ruins at Qal'at el-Husn, its identification with Hippos is now generally accepted.

• from Claire Epstein in Stern et. al. (1993 v.2)

With the settlement at 'En Gev in 1937, surface surveys were again carried out at Hippos by members of the kibbutz. These owed much to the earlier, thorough studies made by G. Schumacher during the latter part of the nineteenth century. However, the new information from observation on the spot, as well as from aerial photographs, made possible a reliable reconstruction of the city plan, on which the positions of its chief public buildings were correctly plotted.

Although Hippos is known to have been founded in the Hellenistic period, few remains from that time have been found, probably because of the comparatively small size of the Hellenistic town. The inhabitants were entirely dependent on a natural water supply, which was inadequate for a large population. After its conquest by Pompey in 63 BCE, Hippos, as one of the cities of the Decapolis, was rebuilt in accordance with standard contemporary town planning. The town plan, which had been preserved, is essentially that of the Roman period, although many buildings were erected later The streets of the city ran at right angles to one another over the length and breadth of the town, forming the characteristic insulae. The public buildings stood at the intersections of the important streets. Of these, the main street is easily distinguishable. It is paved with large basalt flagstones and runs from north-northeast to south-southwest through the center of the town. It is still in use today as a path. Halfway along the main street was the nymphaeum. Close to it was a large subterranean cistern with a vaulted roof and plastered walls and a flight of steps leading down to the water level. After the water had been brought to the nymphaeum and used in its ornamental fountains, it was collected in the cistern for further use. In Hippos, water was a valuable commodity; the main water supply was brought from some distance by a specially constructed aqueduct (see below). Not far from the cistern are Byzantine baths that also required a considerable amount of water.

Evidence that this town of the Decapolis had imposing buildings in Roman times can be seen in the many architectural remains strewn over the surface: massive red-granite column shafts, numerous capitals (Corinthian and Ionic), decorated pilasters, molded lintels, and carved cornices, many of which were reused in the Byzantine period. Most of these lie along the main street or in the center of the city.

The town wall has also been well preserved. It is provided with a number of towers at strategic points. The wall follows the contours of the hill and makes use of the natural cliff wherever possible. On the south side, sectors of the wall still stand to a considerable height, providing an excellent view of the Roman road that ascends from the lakeside through Wadi Jamusiyeh (Nahal Sussita). It is very likely that there was a harbor of some kind at the point where this valley opens upon the lake and where the Roman road coming from the city turned south to continue along the eastern shore of the Sea of Galilee. Evidence of such a harbor may be seen in the heaps of stones extending for some distance into the water at this spot.

At the eastern end of Wadi Jamusiyeh is a small promontory or bluff in which there are caves containing niches, stone sarcophagi, ornamented tomb doors, and other evidence of burials. This was doubtless one of the places the people of Hippos used as a cemetery, other graves having been found in the west, also outside the city walls.

• from Claire Epstein in Stern et. al. (1993 v.2)

Excavations were carried out at Hippos by C. Epstein (1950-1955), M. Avi-Yonah (195l), A. Shulman(1951), and E. Anati (l952), on behalf of the lsrael Department of Antiquities.

• from Arthur Segal in Stern et. al. (2008)

Following an urban survey of the site in 1999, a large-scale archaeological project, planned to include at least ten seasons of excavation, was inaugurated at Hippos (Sussita). The project is directed by A. Segal, under the auspices of the Zinman Institute of Archaeology, University of Haifa. Assisting in the direction of the expedition during the seasons reported were J. Mlynarczyk of the Polish Academy of Sciences and M. Burdajewicz of the National Museum in Warsaw. In the summer of 2002, the third season of excavation, the expedition was joined by a group from Concordia University, St. Paul, Minnesota, headed by M. Schuler.

• Hippos-Sussita in Google Earth
  Hippos-Sussita
  
  click on image to explore this site on a new tab in Google Earth
• Hippos-Sussita on govmap.gov.il
  Hippos-Sussita
  
  click on image to explore this site on a new tab in govmap.gov.il

• Fig. 4 - Column drums
  Figure 4
  
  The southeastern side of the Basilica at Hippos. Some of the columns are partly reconstructed, while the drums in the eastern aisle rest in their original position following the 363 CE earthquake. Looking south.
  
  (M. Eisenberg)
  
  Eisenberg and Osband (2022)
  in Basilica in original position after 363 CE Quake from Eisenberg and Osband (2022)
• Fig. 6 - Southern part
  Figure 6
  
  Hippos, the southern part of the Southern Bathhouse. On the left is the cold room (frigidarium) and a pool, and to its right a furnace room (praefurnium) that was covered by several meters high refuse dump that does not postdate the late 3rd century CE.
  
  (M. Eisenberg)
  
  Eisenberg and Osband (2022)
  of southern bathhouse from Eisenberg and Osband (2022)
• Fig. 7 - Saddle Propylaeum
  Figure 7
  
  Hippos, the Saddle Propylaeum looking northwest. The staircase and the reused pavement (0.51 m above the original gate pavement) were built after the 363 CE earthquake.
  
  (M. Eisenberg)
  
  Eisenberg and Osband (2022)
  from Eisenberg and Osband (2022)
• Fig. 5 - architectural fragments
  Figure 5
  
  The Flowers Mausoleum northern wall and architectural fragments at its foot during excavations; view towards east (photo M. Eisenberg)
  
  Eisenberg and Kowalewska (2024)
  of the Flowers Mausoleum from Eisenberg and Kowalewska (2024)

• from Eisenberg (2021:157-162)

Phase	Date	Comments
Pre-basilica Building Phases		Hippos’ Roman basilica stood on naturally almost flat basalt bedrock that extended east of the rectangular temenos of the HLC (Figs. 2 – 6). This area was occupied by other structures before the erection of the basilica in the 1st century CE (Figs. 4 – 5).
A	late 4th – early 2nd century BCE	Scattered pottery sherds of the late 4th century and mainly 3rd century BCE were found in numerous loci above the bedrock, particularly abundant in the northern part of the area, in the west, adjacent to the eastern HLC wall 10, and in the south inside a cavity (L2347) covered by a Phase-D wall (W2232, Figs. 5 – 6). The cavity also produced four out of nine of the coins dated to the 3rd–2nd century BCE from the area of the basilica (Table 1). Phase A represents the earliest remains of settlement at Hippos11. Similar Ptolemaic-period pottery types and coins were recovered in the neighboring HLC probes.12 Footnotes 11 Excluding the traces of Chalcolithic activity in various areas around the site and the one instance of Iron Age (11th century BCE) pottery discovered in the above mentioned cavity L2347. 12 Eisenberg 2017a, 59 – 64.
B	ca. mid-2nd century BCE	Probes all over the basilica area revealed pottery and a few coins dated to ca. mid-2nd century BCE (Table 1)13. Also part of this phase are several plaster installations for liquids, located in the northern side of the area, and probably also two cisterns and three silos (Figs. 4 – 7). The silos and cisterns adapted natural cavities in the basalt bedrock and they were plastered with a thick layer of high-quality white hydraulic plaster. Their function was recognized based on their shape, depth and the analysis of pollen from the plaster. The silos’ plastersamples contained 65% and 54% of cerealis (grain) pollen14. Some installations were rendered out of use when the eastern HLC wall (W1151) was constructed on top of them. Other installations were blocked not later than Phase D – the Early Roman period15. Footnotes 13 Kapitaikin 2018, 91 – 92. 14 The data was reported by P. S. Geyer, who took and analyzed the samples in 2015 (not published). 15 Eisenberg 2017a, 63.
C	late 2nd – mid-1st century BCE	This phase represents the activity from the time of construction and use of the HLC temenos walls16: plaster floors exposed to the east of the HLC that clearly adjoin the eastern temenos wall (W1151), patched plaster floors exposed in the northeast and southern parts of the area, and a tower-like structure (W3054, W3095, W3065)17 in the northwest corner of the area, on the edge of the cliff, built against the HLC eastern wall (W1151, Figs. 4 – 6). Some of the Phase B silos and cistern continued in use. The important finds that most probably should be assigned to this phase (although they could also be of an earlier date) are three Doric capitals and four engaged drums found reused in buttresses, constructed on the northern cliff edge for support of the basilica (W2278 and W3204, Fig. 8). Additional eroded architectural elements, apparently from the same structure, were salvaged in the same area too. All the ashlars are made of local soft caliche (nari) and bear remnants of stucco. These elements were part of one of the first public buildings at Hippos18. Footnotes 16 Kapitaikin 2018, 91 – 93. 17 The tower-like structure has an inner nari frame of walls (W3053, W3080, W3063) adjacent to the basalt walls. The function of the structure is unclear, but its dating is suggested by the use of bossed corner ashlars identical to the ones of the HLC walls. 18 Eisenberg 2016, 5; Peleg-Barkat 2017, 150 – 51.
D	last third of the 1st century BCE – early 1st century CE	Several wall foundations in nari and basalt are attributed to this phase. The walls are concentrated in the central southern part of the area and in the west, along the HLC eastern wall (W1151). Some of the walls are cut by the western stylobate of the basilica (W2358, Figs. 5 – 7, 9). Only two or three coins are assigned to this phase (Table 1), but the pottery is abundant, found in almost all the fills inside the cavities in the bedrock, sealed by the basilica’s plaster floors19. The nature of the structure/s to which these walls belonged is unclear. The most curious is W2227 – a ca. 20 m long basalt wall foundation, which runs parallel to the basilica’s western stylobate (W2358), and at the same time almost parallel to the eastern HLC wall, 2.70 m (in the north) to 3.0 m (in the south) away from it (Figs. 5 – 7). W2227 is ca. 1.0 m wide, built of partially dressed basalt ashlars on the outer faces, with medium-sized basalt stones in the core. This building technique is similar to that used for some other walls in the central southern part of the area. Five rectangular foundations (EPW1–5, some ca. 1.5 x 1.3 m and some ca. 1.7 x 1.4 m) were built adjacent to W2227 at intervals of 1.7 – 2.0 m (Fig. 5). The intervals were filled with reinforcing walls 0.6 m wide. Each of the foundations almost adjoints its corresponding basilica pedestal. The sixth foundation (EPW6) was located 6.5 m north of EPW1, above W3095. These pre-basilica walls and rectangular foundations must have been part of a public building. All efforts to locate additional walls of this structure to the east were in vain. It is tempting to interpret the rectangular foundations as podia of the colonnade of an earlier basilica. Since the foundations abut W2227, this wall could not have been part of the superstructure of the earlier basilica – the earlier basilica western wall would have to be located further west, within the HLC (no such wall was located) or directly on top of the remains of the eastern HLC wall (W1151, ca. 2.9 m away from the speculative podia; but this wall has only three securely identified layers – the original Hellenistic, late-1st-century CE connected to the basilica, and Byzantine). The existence of a pre-basilica public structure is supported by the find of seven fragments of large basalt Ionic capitals, recovered from fills and reused in the foundations of the basilica (B7411; Fig. 10). Based on the diameter of the fully preserved volute, the capital belonged to a column 0.78 m in diameter (for comparison, the basilica columns were 0.80 m in diameter). Footnotes 19 Kapitaikin 2018, 91 – 94. 18 Eisenberg 2016, 5; Peleg-Barkat 2017, 150 – 51.

• Fig. 1 - Plan of Hippos-Sussita
  Figure 1
  
  Plan of the site showing the main excavated areas.
  
  Kowalewska and Eisenberg (2021)
  with excavation areas from Kowalewska and Eisenberg (2021)
• Fig. 5 - Plan of the
  Figure 5
  
  THE BASILICA
  
  

  1. A PLAN WITH BUILDING PHASES
  2. A SCHEMATIC PLAN

  
  
  (Y. NAKAS AND M. EISENBERG)
  
  Eisenberg (2021)
  Basilica and environs from Eisenberg (2021)
• Fig. 5 - Plan of the
  Figure 5
  
  THE BASILICA
  
  

  1. A PLAN WITH BUILDING PHASES
  2. A SCHEMATIC PLAN

  
  
  (Y. NAKAS AND M. EISENBERG)
  
  Eisenberg (2021)
  Basilica and environs from Eisenberg (2021) - magnified
• Fig. 6 - Aerial Photo
  Figure 6
  
  THE BASILICA, AN AERIAL PHOTOGRAPH TOWARDS SOUTHWEST. THE ARROW IS MARKING THE CAVITY IN THE BASALT BEDROCK
  
  (M. EISENBERG)
  
  Eisenberg (2021)
  of the Basilica towards the SW from Eisenberg (2021)
• Fig. 7 - Southern part
  Figure 7
  
  THE SOUTHERN PART OF THE BASILICA. NOTE THE PREBASILICA STYLOBATE FOUNDATION ON THE BOTTOM AND NARI AND BASALT WALLS IN THE CENTER. A VERTICAL AERIAL PHOTOGRAPH
  
  (M. EISENBERG)
  
  Eisenberg (2021)
  of the Basilica from Eisenberg (2021)
• Fig. 18 - Suggested Reconstruction
  Figure 18
  
  HIPPOS’ BASILICA SUGGESTED RECONSTRUCTIONS:
  
  

  1. SECTION OF THE NORTHERN SIDE
  2. LENGTH SECTION
  3. SIDE VIEW OF THE SOUTHERN FACADE

  
  
  (Y. NAKAS)
  
  Eisenberg (2021)
  of the Basilica from Eisenberg (2021)
• Fig. 19 - Suggested Reconstruction
  Figure 19
  
  HIPPOS’ BASILICA, A SUGGESTED RECONSTRUCTION. VIEW TOWARDS NORTHEAST
  
  (Y. NAKAS)
  
  Eisenberg (2021)
  of the Basilica from Eisenberg (2021)
• Fig. 20 - Suggested Reconstruction
  Figure 20
  
  HIPPOS’ BASILICA, A SUGGESTED RECONSTRUCTION OF THE INTERIOR. VIEW TOWARDS NORTH
  
  (Y. NAKAS)
  
  Eisenberg (2021)
  of the interior of the Basilica from Eisenberg (2021)

Figures

Discussion

• Plan of Hippos-Sussita
  Plan of Hippos Sussita
  
  Used with permission from BibleWalks.com
  from BibleWalks.com
• Fig. 16 - Plan of the northwest Church
  Figure 16
  
  plan of of the North-West Church (2000-2004)
  
  Segal et al (2004)
  from Segal et al (2004)
• Fig. 9 - Aerial View of the Cathedral
  Figure 9
  
  The Cathedral at the end of the 2021 excavation, aerial view from 3D model.
  
  Kowalewska and Eisenberg (2021)
  from Kowalewska and Eisenberg (2021)

Plans, Photos, and Figures Discussion

Nine columns of the northern row of the cathedral are oriented N220°E ± 10° and two remaining columns of the southern row are oriented N295°E ± 10° (Wechsler et al, 2018).

Yagoda-Biran and Hatzor (2010) utilized a two-dimensional formulation of the discontinuous deformation analysis (DDA) method (Shi, 1993) to produce a lower bound of 0.2 - 0.4 g for Peak Horizontal Ground Acceleration (PGA) required to topple the columns. The model for their columns was free standing as shown in Figure 2c of their paper and does not include a superstructure such as an architrave or a roof indicating it is likely to produce a conservative (i.e. low) value of minimum PGA required to topple the columns. Input material values for the columns, consisting of red and gray granite possibly imported from Aswan¹, were

• E = 40 GPa
• ν =0.18
• ρ = 2700 kg/m³

The friction angle (Φ) between column base and pedestal was assumed to be 45°. Optimal contact spring stiffness (2 x 10⁸ N/m) was determined numerically. Simulations were performed for both one and three sinusoidal loading cycles at a variety of frequencies up to 5 Hz. (shown in Figure 3 of their paper). At frequencies of 1.5 Hz. and below, minimum PGA to topple the columns was about 0.2 g for both 1 and 3 loading cycles. Above 1.5 Hz., the single loading cycle simulations were more sensitive to frequency and required a higher PGA to topple the columns. The authors suggested that if only sinusoidal inputs are considered, 3 cycle simulations were more likely be representative of PGA thresholds required to topple the columns. Thus they used the three cycle simulations to produce a range of frequency dependent threshold PGA's required to topple the column that varied from 0.2 g below 1.5 Hz. up to 1 g at 5 Hz..

Recognizing the fairly wide range of threshold PGA's resulting from this analysis, Yagoda-Biran and Hatzor (2010) performed a subsequent set of simulations using strong motion records applied to the centroid of the column and base. The strong motion records came from instrumentally recorded earthquakes thought to be representative of the Dead Sea Transform². The predominant frequencies of these strong motion records varied from 0.45 - 2.2 Hz. and produced threshold PGA's between 0.2 and 0.4 g. Although Yagoda-Biran and Hatzor (2010) did not conclude that their column analysis resulted in an estimated threshold PGA of 0.2 - 0.4 g to topple the columns, it can be reasonably assumed that this is result. However, as mentioned previously, these threshold PGA's are likely underestimated as they modeled free standing columns without a superstructure. Wechsler et al (2018) commented on modeling the column falls as follows:

The Cathedral is, so far, the only structure that has been at the center of quantitative archaeoseimsic studies. Yagoda-Biran and Hatzor (2010) tried to estimate minimum levels of peak ground acceleration (PGA) during the earthquake ground motion which was necessary to topple the Cathedral columns. However, they used the model of a freestanding column of the same size as the ones found in the Cathedral, but with no capital, architrave or other superstructure. Since 2D models were used and forces were applied to the center of gravity of the columns and pedestals, the reported 0.2 - 0.4 m/s² PGA threshold at frequencies between 0.2 and 4.4 Hz can only be regarded as a rough estimate and are not necessarily representative for the complete structure of the Cathedral which has a significantly different response to earthquake ground motions than a solitary column. Hinzen (2010) used 3D discrete element models conforming to the size of the toppled columns of the Cathedral and showed that the toppling direction during a realistic earthquake ground motion in three dimensions is a matter of chance. A column that is being rocked by earthquake ground motions is in a nonlinear dynamic system and its behavior tends to be of a chaotic character. Small changes to the initial conditions can have a strong influence on the general dynamic reaction and significantly alter the toppling direction. The same paper shows that the parallel orientation is probably an effect of the superstructure connecting the columns mechanically and not a consequence of the ground motion character. This interpretation is also strongly supported by the fact that the two remaining columns of the southern row rest at angles of ~90° compared with the columns from the northern row, as shown in a 3D laser scan model of the site (Fig. 2.4). A similar analysis of the Hippos columns was performed by Hinzen (2010)

Variable	Input	Units	Notes
PGA		g	Peak Horizontal Ground Acceleration
R		km.	Distance to earthquake producing fault
Seismic Amplification		unitless	Site Effect due to Topographic or Ridge Effect (set to 1 to assume no site effect)
Variable	Output - Site Effect not considered	Units	Notes
I		unitless	Conversion from PGA to Intensity using Wald et al (1999)
M		unitless	Attenuation relationship of Hough and Avni (2009) used to calculate Magnitude
Variable	Output - Site Effect removed	Units	Notes
I		unitless	Conversion from PGA to Intensity using Wald et al (1999)
M		unitless	Attenuation relationship of Hough and Avni (2009) used to calculate Magnitude

Calculate   

Magnitude is calculated from Intensity (I) and Fault Distance (R) based on Hough and Avni (2009) who did not specify the type of Magnitude scale they were using.

Figures

Discussion

Output with site effect removed assumes that PGA is higher than it would be if there was no site effect. In this situation, Intensity (I) with site effect removed is calculated pre-amplification (i.e. it will be lower). This is because an Intensity estimate with the site effect removed is helpful in producing an Intensity Map that will do a better job of "triangulating" the epicentral area. Site Effect is based on Figure 13a and Equation 2 of Massa et al (2010)

Equation 2

log₁₀(Y) = a + b*M+ c*log₁₀(R) + S_t + σ

where

Y = PGA
M = Magnitude
R = Hypocentral Distance (km.)
S_t = additional PGA from Topographic Effect
σ = standard deviation of PGA
a,b,c = coefficients relating to attenuation of source energy away from the source

In their study, they estimated a frequency dependent additional PGA (S_t in Eqn. 2) which is added by a topographic site effect. The additional topographic site effect PGA varied from ~0.1 g to 0.5 g for dominant frequencies of approximately 1 - 5 Hz.. Higher PGA's were shown to be present for higher frequencies which are more likely to occur when the earthquake producing fault is closer to the site. They also noted that a greater topographic effect was observed when the seismic energy arrived orthogonal (perpendicular in their words) to the ridge. Both of these considerations suggest that a topographic ridge effect should be considered at Hippos Sussita when other evidence suggests that one of the Sea of Galilee faults broke during the earthquake. The additional Site Effect PGA is linearly scaled from 0 - 0.5 g for site effects where amplitude increases from 1x to 10x. It's not the greatest transform to remove site effect from the Intensity estimate but may be useful for crude estimates.

Source : Kramer (1996:92-93)

Seismic Moment and Moment Magnitude

Variable	Input	Units	Notes
μ		GPa	Shear Modulus
D		m	Displacement
w		km.	Fault width
l		km.	Fault length
Variable	Output	Units	Notes
Mo		N-m	Seismic Moment
Mo		dynes-cm.	Seismic Moment
Mw		unitless	Moment Magnitude

Calculate   

Variable	Input	Units	Notes
RθΦ		unitless	Radiation Patttern
F		unitless	Free surface effect
vs		km./s	Shear Wave velocity of the rock
ρ		g/cc	Density of the rock
Mw			Moment Magntidue
fmax		Hz.	cutoff frequency - 15 Hz. typical for W N Am.
Δσ		bars	50 bars typical for W N Am.
f		Hz.	frequency
R		km.	Fault Distance
Variable	Output	Units	Notes
C			constant
Mo		dyne-cm.	Seismic Moment
fc		Hz.	Corner frequency
A(f)			Amplitude (UNDER CONSTRUCTION)

Calculate    Plot

|A(f)| = [C*M_o*(f²/{1-(f/f_c)²})*(1/sqrt{1 + (f/f_max)⁸})]e^{-{π*f*R/Q(f)*v_s}}/R         (3.30 - Kramer, 1996:92)

|A(f)| = fourier amplitudes
C = constant
M_o = Seismic Moment (dyne-cm.)
f = frequency (Hz.)
f_c = corner frequency (Hz.)
f_max = cutoff frequency (Hz.)
Q(f) = frequency dependent quality factor, inversely proportional to the damping ratio of the rock
π = Pi
R = distance from circular rupture surface
v_s = shear wave velocity of the rock

C = R_θΦ*F*V / 4*π*ρ*v_s³         (3.31 - Kramer, 1996:92)

R_θΦ = Radiation Pattern ≈ 0.55
F = Free-surface effect =2
V = √2/2 - accounts for partitioning of energy into two horizontal components
π = Pi
ρ = density of the rock
v_s = shear wave velocity of the rock

f_c = 4.9 x 10⁶*v_s*(Δσ/M_o)^1/3         (3.32 - Kramer, 1996:93)

f_c = corner frequency (Hz.)
v_s = shear wave velocity of the rock (km/sec.)
Δσ = stress drop (bars) - 50 and 100 are typically used for western and eastern North America
M_o = Seismic Moment (dyne-cm.)

M_w = (2/3)*log₁₀M_o-10.7         (2.5 - Kramer, 1996:49)

M_w = Moment Magnitude
M_o = Seismic Moment (dyne-cm.)

fxsolver

M_o = μ*A*D         (2.1 - Kramer, 1996:42)

μ = Shear Modulus (Pa)
A = Area of rupture (m2)
D = displacement (m)

fxsolver

Units

1 Pa = 1 N/m2
1 dyne is the force required to accelerate 1 gram 1 cm/s2
1 N = 100,000 dynes
1 bar = 10^6 dynes/cm2

Eisenberg, M. (2021) The Basilica of Hippos of the Decapolis and a Corpus of the Regional Basilicae in The Basilica in Roman Palestine, Adoption and Adaptation Processes, in Light of Comparanda in Italy and North Africa, A. Dell’acqua and O. Peleg-Barkat (eds)

Eisenberg, M. and Osband, M. (2022) Evidence for Settlement Decline in Late 3rd–mid-4th Centuries CE in the Hippos Region and Beyond, Aram v. 34:1 & 2, 153-184

Eisenberg, M. and Kowalewska, A.(2024) The Flowers Mausoleum at Hippos of the Decapolis: A first glance into one of the finest Roman provincial architectural decorations in basalt, Zeit(en) des Umbruchs, Nr. 7

Hinzen, K. G. (2010). Sensitivity of earthquake-toppled columns to small changes in ground motion and geometry, Isr. J Earth Sci. 58, nos. 3-4, 309-326, doi: 10.1560/IJES.58.3-4.309.

Karcz, I. and U. Kafri (1978). "Evaluation of supposed archaeoseismic damage in Israel." Journal of Archaeological Science 5(3): 237-253.

Kelany, a., Negem, m., tohami, a. and Heldal, t. (2009) Granite quarry survey in the aswan region, egypt: shedding new light on ancient quarrying. In abu-Jaber, N., bloxam, e.G., Degryse, p. and Heldal, t. (eds.) QuarryScapes: ancient stone quarry landscapes in the Eastern Mediterranean, Geological Survey of Norway Special publication,12, pp. 87–98.

Kowalewska, Arleta and Eisenberg, Michael (2021) Horbat Sussita (Hippos) – Preliminary Report Hadashot Arkheologiyot Volume 135 Year 2023

Massa et al. (2010) An Experimental Approach for Estimating Seismic Amplification Effects at the Top of a Ridge, and the Implication for Ground-Motion Predictions: The Case of Narni, Central Italy Bulletin of the Seismological Society of America Mlynarczyk, J. (2008). Churches and the Society in Byzantine-period Hippos. Decapolis, ARAM Society,, Oxford, ARAM.

Wechsler, N., Marco, S., Hinzen, K.G., and Hinojosa-Prieto, H. (2018) Chapter 2 - Historical Earthquakes around the Sea of Galilee in Hippos-Sussita of the Decapolis: The First Twelve Seasons of Excavations, Vol. II

Yagoda-Biran and Hatzor (2010) Constraining paleo PGA values by numerical analysis of overturned columns Earthquake Engineering & Structural Dynamics 39(4):463 - 472

Hippos-Sussita of the Decapolis: The First Twelve Seasons of Excavations, Vol. I

Hippos-Sussita of the Decapolis: The First Twelve Seasons of Excavations, Vol. II

Digital Hippos

Publications List from Digital Hippos

Hippos (Sussita) Excavations Project at OCHRE

OCHRE homepage

Hippos-Sussita at biblewalks.com

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Schiirer, GJV 2, 155ff.

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A. Ovadiah, PEQ ll3 (1981), 101-104

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M. Nun, The Sea of Galilee: Water Levels Past and Present, Ein Gev 1991, II.