3D Imaging of Dead Sea Area Using Weighted Multipath

Hindawi Publishing CorporationInternational Journal of GeophysicsVolume 2013 Article ID 692452 7 pageshttpdxdoiorg1011552013692452

Research Article3D Imaging of Dead Sea Area Using Weighted MultipathSummation A Case Study

Shemer Keydar1 Benjamin Medvedev12 Abdallah Al-Zoubi3

Michael Ezersky1 and Emad Akkawi3

1 Project Department The Geophysical Institute of Israel Lod 71100 Israel2 Schlumberger Via dellrsquoUnione Europea 4 San Donato Milanese Milan Italy3 Engineering Faculty Al-Balqarsquo Applied University Salt 19117 Jordan

Correspondence should be addressed to Shemer Keydar shemergiicoil

Received 4 November 2012 Revised 27 January 2013 Accepted 28 January 2013

Academic Editor Umberta Tinivella

Copyright copy 2013 Shemer Keydar et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The formation of sinkholes along the Dead Sea is caused by the rapid decline of the Dead Sea level as a possible result of humanextensive activity According to one of the geological models the sinkholes in several sites are clustered along a narrow coastal stripdeveloping along lineaments representing faults in NNW direction In order to understand the relationship between a developingsinkhole and its tectonic environment a high-resolution (HR) three-dimensional (3D) seismic reflection survey was carried outat the western shoreline of the Dead Sea A recently developed 3D imaging approach was applied to this 3D dataset Imaging ofsubsurface is performed by a spatial summation of seismic waves along time surfaces using recently proposedmultipath summationwith proper weights The multipath summation is performed by stacking the target waves along all possible time surfaces havinga common apex at the given point This approach does not require any explicit information on parameters since the involvedmultipath summation is performed for all possible parameters values within a wide specified range The results from processed3D time volume show subhorizontal coherent reflectors at approximate depth of 50ndash80m which incline on closer location to theexposed sinkhole and suggest a possible linkage between revealed fault and the sinkholes

1 Introduction

During the last thirty years hundreds of sinkholes haveappeared along theDead Sea (DS) shoreline in both Israel andJordan (Figure 1) [1ndash3] The process began in the southernpart of the DS coast and slowly spread northward along thewestern coast The eastern coast which is usually steeper hasbeen less affected at the flat-lying region close to the LisanPeninsula The sinkholes have already caused considerabledamage to infrastructure and there is obvious potential forfurther collapses beneath main highways and other infras-tructure

In order to understand the relationship between a devel-oping sinkhole and its tectonic environment a numerousnumber of high resolution seismic reflection surveys werecarried out using common midpoint (CMP) technique [35 6] The high-resolution seismic reflection method is

intended for the study faults and conduits in the shallowsubsurface (down to 100ndash200m deep) which could bringthe fresh water to the salt layer presumably from below Theconventional processing technique the so-called commonmidpoint (CMP) method essentially consists of a ldquostackrdquo(summation) of properly corrected traces thus increasing thesignal-to-noise ratio However in the shallow subsurfacethe conventional CMP method causes a loss of informationbecause of the problem of ldquostretchingrdquo of data caused byNMO time correction formulaThat is why a new 2D and 3Dfree stretch imaging approach had been applied in the frame-work of the MERC project M27-050 in order to examinetectonic hypothesis connecting the sinkholes with tectonicfaults [7ndash9]This approach involves zero-offset common shotpoint (CSP) stacking and diffraction imaging method [9]On the basis of those methods in combination with a newweighted multipath summation technique [10 11] a package

2 International Journal of Geophysics

19

20

630

620

610

600

590

580

570

560

550

230

240

250

12

3

45

678910

1112

13

1415

16 17

18

Dea

d Se

a

Evaporation

Ponds

Jord

an

Jordan

Isra

el

Nahal

Zeelim

Mount Sedom

Lisa

n Pe

nins

ula

0 10km

35∘30998400

31∘

30998400

31∘

JordanRiver

N

MineralBeach

Dead Sea areaSurvey area and its number

TownsSinkhole site13

800

700

600

500

40050 150 250

Mediterran

ean Sea

Haifa

Tel Aviv

Ashdod Jerusalem

Bersquoer Sheva

Israel

Jordan

Figure 1 Sinkhole sites along the Dead Sea shore (1) Palms (2) Samar Spring (3) Mineral Beach (4) Ein Gedi and Nahal Arugot (5) Yesha(6) Zeruya (7) Nahal Hever northern (8) Nahal Hever southern (9) Asarsquoel (10) Nahal Zeelim (11) Mezada (12) Rahaf (13) Mor (14) EinBoqeq (15) Newe Zohar (16) Lisan Peninsula (17) Ghor Al-Haditha (18) Dam-2 IndashIII sites under investigation (coordinates are in km newIsrael Mercator grid)

120573

119874

k

n

j

e2

i

e1

sum

Figure 2 Scheme of wavefront arriving at a Common Shot Point

of programs was written The CSP stack and diffractionmethod are complementary to each other and reveal usefulinformation about the subsurface The diffraction methodserves as a tool for detection of faults and voids while theCSP stacking contains information about the structure of thesubsurfaceThese methods were applied along the Dead Searsquos

120573

119874

sum

k

n

j

e2ie1

Figure 3The same as Figure 2 in case of one direction is normal tovector k

shorelines We have carried out several new seismic surveysalong line crossing the sinkhole lineaments and reinterpreteda number of previous reflection sections The 2D imagingtechnique has been presented in [7]This paper examines thenew 3D imaging approach and its application to 3D data thatwas acquired at the western shoreline of the Dead Sea Theresults of the imaging allow better understanding between

International Journal of Geophysics 3

N

Mediterranean

Haifa

Tel Aviv

Jerusalem

Israel-Sinaisubplate

Arabian PlateEilat 0 50 km

30∘

31∘

32∘

33∘

1

2

Sea

(a)

Dea

d Se

a1 3

24

3

65 8

910

6

12

Lisan

Mt Sedom

JordanValley

Diapirs(A) Visible(B) Radial fault system(C) Submerged(D) Suspected

Sinkholes

(1) Iddan fault(2) Khunazira or Amaziahu fault(3) Araba fault(4) Sedom fault

(7) Ein Gedi fault(8) Ghor Safii fault(9) West Dhira fault(10) East Dhira fault(11) West intrabasinalfault system (WIF)(12) East intrabasinalfault system (EIF)

EGD

Masada graben

Dhira basin

-400 m on 1980

(5) Ein Boqeq fault(6) West Margin fault network

3510000

3500000

3490000

3480000

3470000

3460000

3450000

3440000

3430000

3420000

3410000

3400000

720000 730000 740000

(b)

Figure 4 Dead Sea tectonic setting (a) Dead Sea transform (b) faults through the DS area [4]

ReceiverShot (every second)Salt western edge

Sinkhole clusterDyke2D reflection line

606750

606700

606650

237800 237850 237900 237950 238000 238050 238100

20 m

10 m 1

35

7 13

57

1 8 16 24 32 40 48

Figure 5 The geometry of 3D seismic survey

a developing sinkhole and its tectonic environment Wegive here a short description of 3D zero-offset stacking andmultipath weighted summation For amore comprehensivelydiscussion of the methods one can read in the relevantpapers

2 The 3D Zero Offset Stacking Method

The basis of the 3D zero-offset stacking method is a newnormal moveout (NMO) time correction formula for three-dimensional media as function on wavefront parameters [1112] One of these parameters on which the proposed timecorrection formula is based is the emergence angle 120573 definedas the acute angle between the wavefront normal and thenormal to the acquisition plane at the CSP Let us consider acentral ray and its associated wavefront arriving at a commonshot point (CSP) (Figure 2)

An ellipsoidal wavefront emerges at the CSP location119874 It has two independent vectors e

1and e

2tangent to

the wavefront and the normal n The emergence angle 120573is the angle between n and the normal to the acquisitionplane k Additional fundamental parameters on which thetime correction formula is based are the curvatures of thewavefront It is well known from the differential geometryof surfaces that at each point of the wavefront two principalcurvatures can be defined being the eigenvalues of the 2 times 2matrix of second derivatives These curvatures are the mini-mal and maximal curvatures and are related to the mean andGaussian curvatures The principal curvatures are associated


23211917151311

97531

Fold

(a)

100

50

0

minus50

minus100

minus80 minus60minus40minus20 0 20 40 60 80

Offs

et

Offset

0 2040

60

80

100

120

140160180200

220

240

260

280

300

320340

(b)

Figure 6 Fold scheme (a) The shots locations are marked by ldquo+rdquo and receivers locations are marked by squares (b) fold as function ofazimuth

to two perpendicular principal directions which togetherwith the wavefront normal form a rectangular system ofaxes The curvature of the wavefront is completely describedby the two principal curvatures and the angle the principaldirections make with the general coordinate system This isdenoted in Figure 2 as i j and k The principal curvaturescan be expressed in terms of principal radii of curvaturewhich play an important role in the traveltime correctionexpressions derived in this paper Figure 3 illustrates the casewhere one of the principal directions is normal to k Basedon those principles and eikonal equation only the following3D travel-time correction formula for an arbitrary system ofcoordinates was obtained

119905 =1

119881(11988631119909 + 11988632119910) +1

21198811198771

(11988611119909 + 11988612119910)2

+1

21198811198772

(11988621119909 + 11988622119910)2

+ sdot sdot sdot

11988631= sin120573 sin120601 119886

32= minus sin120573 cos120601

11988611= cos120601 119886

12= sin120601

11988621= minus cos120573 sin120601 119886

22= cos120573 cos120601

(1)

where 120573 is the emergence angle of the wavefront at point 119874120601 azimuth angle defined as the angle between the axis 119874119883and the principal direction of the wavefront at point 119874 119909and 119910 are the offsets along the axis 119874119883 and 119874 For a givensource receiver gather themoveout equations that express themoveout correction with respect to a zero-offset trace by fiveparameters measured at the central pointThe parameters areprincipal radii of the wavefront 119877

1 1198772 the azimuth angle 120601

the emergence angle 120573 and the reference velocity 119881In the following we give a short description of the

weighted multipath summation

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96

010

020

030

Station number50 m

Two-

way

tim

e (s)

Figure 7 Typical common shot gathering including 96 channels

3 Multipath Summation

The summation of 3D stacking is performed along timesurfaces defined by (1) The summation can be implementedusing either of the two approaches In the first conventionalapproach the target waves are stacked along the time surfacesdefined by wavefront parameters and velocity These optimalparameters usually are estimated using optimization prob-lem which consists of finding parameters which maximizesome correlation functional We use an alternative moreformal recently proposedmultipath summationwith a properweighting [10 13ndash15] The weighted multipath summationallows us to replace the complex optimization problem ofestimating the optimal parameters by summation alongall possible surfaces that are created from small variations


000

010

020

1 10 20 30 40 1 10 20 30 40

Two-

way

tim

e (s)

2

Station number1 10 20 30 40

Station number

000

010

020Two-

way

tim

e (s)

000

010

020Two-

way

tim

e (s)

Station number

5 7

Reflector surface

Faults

25 m 25 m 25 m

minus2535119890 minus 06 2535119890 minus 06 minus5059119890 minus 07 5059119890 minus 07 minus521119890 minus 07 521119890 minus 07

Number of reflection sections

(a)

Fault

Fault

W

E

Two-

way

tim

e

Lines from 1 to 7

(b)

Fault expressed in the time surfaceBuried salt layer

N

E

W

minus20minus30minus40minus50

606720

606700

606680

606660

606640237820 237840 237860 237880 237900 237920

minus56 minus50minus44 minus38

minus32 minus26minus20

Two-way reflection time (ms)

2WT

(ms)

(c)

Figure 8 Typical two-way time sections (a) constructed from 3D time cube obtained using 3D imaging approach (b) two-way time map ofreflector in the 3D presentation (c)

of those parameters The weighted multipath summation(WMPS) can be described by the following expressions

119868WMPS =sum119875119868119875119882(119868119875)

sum119875119882(119868119875)

119868119875= sum119875

sum119878

sum119877

119880119878119877(119879119878119877(119875))

(2)

where119882(119868119875) = exp(120582119868

119875) is an ldquooptimalrdquo weighting function

and 120582 is an undimensional large number 119868119875is the image

obtained for fixed parameters 119875 namely for radii of curva-tures azimuth and emergence angles 119880

119878119877(119879119878119877) is a seismic

trace for a given source-receiver pair 119879119878119877

is travel time fromshot 119878 to receiver 119877 The summation (2) with the properweight119882(119868

119875) is performed for all possible parameter values

within a specified range The image defined by 119868119875means that

for every point to be imaged seismic amplitudes are stacked

together along all possible time surfaces defined by (1) Theconstructive and destructive interference of the amplitudescontributed by each time surface produces an image closeto that obtained by stacking with the ldquocorrectrdquo parameter[16]

4 Case Study

41 Dead Sea AreamdashBrief Tectonic Setting Dead Sea (DS)is a pull apart basin or strike-slip one undergone to NW-SE compression and NE-SW tensile stress (Figure 4(a)) DSconsists of two basins the northern one (deeper) (denoted by1 in Figure 4(a)) and the southern one (shallower) (denotedby 2 in Figure 4(a)) And it is extended in approximately N-Sdirection

Numerous faults have been detected through DS area(Figure 4(b)) and havemainly extended in the same direction


[4 17 18] The Dead Sea is located nowadays at elevation ofminus426m below the sea level (bsl)

42 Study Site Mineral beach study site (Figure 1) is locatedbetween the Dead Sea shoreline at the east and route number90 (the main road along the western DS shore) at the westThe area is characterized by N-S normal faults [6] AroundMineral Beach sinkholes develop in both mudflat (southernboreholes Mn-2 Mn-5) and alluvial fan (northern boreholeMn-4) areas Boreholes show that salt layer at the northernpart of the area is located at 10m deeper (minus434m elevation)than that at the southern one (minus424m) At the northern partof the area salt is overlain by sandy-gravel sediments whereasthe southern part is composed of DS mud (clay) overlayingthe salt

The field acquisition covers 120m by 60m and consists ofseven receiver lines in a 10m interval between them Shootingwas carried out using six shot lines (288 shots in total) andeach shot includes 96 channels in 25m interval betweenthem The distance between shot lines is 10m (Figure 5)

We used truckmounted accelerated weight (Digipulse) asan energy source and single 10Hz geophone per station Inorder to image the new developing fault in details the surveywas designed with a full azimuth cover for offsets less than30m (Figure 6)

The data was recorded using 05msec sample rate and05 sec record length Typical common shot gathers are seenon Figure 7

The data was processed using the new 3D stackingalgorithm The range of variation of parameters in (2) was asfollows radii of curvature from 3 to 600 meter emergenceangle from minus5 to +5 degree and velocity from 300ms to1000ms The value of 120582 was 900 The results from processed3D imaging are presented in Figure 8(a) as a time sectionsalong reflection lines and in Figure 8(b) as a 3D cube timesection

A time map of the first reflector is presented inFigure 8(c) On all the figures are clearly seen subhorizon-tal coherent reflectors at approximate depth of 50ndash80mwhich incline on closer location to the exposed sinkhole Inaddition faults are seen on all sections (Figure 8(a) sectionsdenoted by 2 5 and 7) These faults are clearly seen onreflector presented in Figure 8(c) The results are consistentwith the results that were obtained from a previous 2D study[3] at the same site This work provides the first 3D HRimaging on the edge of a sinkhole and nearby fault Theresults of the seismic interpretation of 3D image suggest apossible linkage between revealed fault sinkholes and fieldobservation

5 Conclusions

In order to understand the relationship between a developingsinkhole and its tectonic environment a high-resolution(HR) three-dimensional (3D) seismic reflection survey wascarried out at the western shoreline of the Dead Sea The 3Dimage of the subsurface was obtained by the use of a recentlydeveloped 3D imaging approachThe core of this approach isa new 3D NMO time correction surface formula Imaging of

subsurface is performed by a spatial summation of seismicwaves along these time surfaces using recently proposedmultipath summation with proper weights The multipathsummation is performed by stacking the target waves alongall possible time surfaces having a common apex at the givenpoint This approach does not require any explicit informa-tion on parameters since the involved multipath summationis performed for all possible parameters values within a widespecified range The results from processed 3D time volumeshow subhorizontal coherent reflectors at approximate depthof 50ndash80m which incline on closer location to the exposedsinkhole and suggest a possible linkage between revealed faultand the sinkholes

Acknowledgments

This study has been performed within the framework ofMERC project M27-050 fund sponsored by the USAIDThanks are due to the support of the Israel Ministry of Infras-tructure The authors are also grateful to the GeophysicalInstitute of Israel for permission to publish this paper

References

[1] Y Arkin and A Gilat ldquoDead Sea sinkholes an ever-developinghazardrdquo Environmental Geology vol 39 no 7 pp 711ndash722 2000

[2] A Frumkin and E Raz ldquoCollapse and subsidence associatedwith salt karstification along the Dead Seardquo Carbonates andEvaporites vol 16 no 2 pp 117ndash130 2001

[3] Y Yechieli M Abelson A Bein O Crouvi and V ShtivelmanldquoSinkhole ldquoswarmsrdquo along the Dead Sea cost reflection ofdisturbance of lake and adjacent groundwater systemsrdquo Bulletinof the Geological Society of America vol 118 no 9-10 pp 1075ndash1087 2006

[4] Z Ben-Avraham ldquoGeophysical framework of the Dead Seastructure and Tectonicsrdquo in The Dead Sea the Lake and ItsSetting T M Niemi Z Ben-Avraham and J Gat Eds pp 22ndash35 Oxford University Press Oxford UK 1997

[5] M Abelson G Baer V Shtivelman et al ldquoCollapse-sinkholesand radar interferometry reveal neotectonics concealed withintheDead Sea basinrdquoGeophysical Research Letters vol 30 no 10pp 52ndash1 2003

[6] M Abelson Y Yechieli O Crouvi et al ldquoEvolution of the DeadSea sinkholesrdquo Special Paper of theGeological Society of Americano 401 pp 241ndash253 2006

[7] S Keydar BMedvedevM Ezerky and L Sobolevsky ldquoImagingshallow subsurface of Dead Sea area by Common Shot Pointstacking and diffraction method using weighted multipathsummationrdquo Journal of Civil Engineering and Science vol 1 no2 pp 75ndash79 2012

[8] S Keydar L Bodet C Camerlynck et al ldquoA new approach forshallow subsurface imaging and its application to the Dead Seasinkhole problemrdquo in Proceedings of the 73rd EAGE Conferenceand Exhibition pp 1ndash4 Vienna Austria April 2011

[9] S Keydar B Medvedev A Al-Zoubi andM Ezersky ldquoAnotherlook of imaging of shallow subsurface real examples fromthe Dead Sea sinkhole development areasrdquo in EGU GeneralAssembly vol 14 of Geophysical Research Abstracts vol 14 p1432 Vienna Austria April 2012


[10] S Keydar ldquoHomeomorphic imaging using path integralsrdquo inProceedings of the 66th EAGE Conference amp Exhibition pp 7ndash10 Paris France June 2004

[11] S Keydar and M Mikenberg ldquoPrestack time migration usingthe Kirchhoff sum along a new approximation of the reflectiontravel time curverdquo in Proceedings of the 72nd European Associ-ation of Geoscientists and Engineers Conference and Exhibition(EUROPEC rsquo10) pp 4916ndash4920 Barcelona Spain June 2010

[12] S Keydar andMMikenberg ldquoAnew time correction formula inthree-dimensional media as a function of wavefront attributesrdquoJournal of Seismic Exploration vol 17 no 4 pp 349ndash369 2008

[13] S Keydar and V Shtivelman ldquoImaging zero-offset sectionsusing multipath summationrdquo First Break vol 23 pp 21ndash242005

[14] E Landa S Fomel and T J Moser ldquoPath-integral seismicimagingrdquo Geophysical Prospecting vol 54 no 5 pp 491ndash5032006

[15] J Schleicher and J C Costa ldquoMigration velocity analysis bydouble path-integral migrationrdquo Geophysics vol 74 no 6 ppWCA225ndashWCA231 2009

[16] V Shtivelman S Keydar and M Mikenberg ldquoImaging near-surface inhomogeneities using weighted multipath summa-tionrdquo Near Surface Geophysics vol 7 no 3 pp 171ndash177 2009

[17] A Al-Zoubi and U S Ten Brink ldquoSalt diapirs in the DeadSea basin and their relationship to Quaternary extensionaltectonicsrdquoMarine and PetroleumGeology vol 18 no 7 pp 779ndash797 2001

[18] A Frumkin M Ezersky A Al-Zoubi E Akkawi and A-RAbueladas ldquoThe Dead Sea hazard geophysical assessment ofsalt dissolution and collapserdquo Geomorphology vol 134 pp 102ndash117 2011


19

20

630

620

610

600

590

580

570

560

550

230

240

250

12

3

45

678910

1112

13

1415

16 17

18

Dea

d Se

a

Evaporation

Ponds

Jord

an

Jordan

Isra

el

Nahal

Zeelim

Mount Sedom

Lisa

n Pe

nins

ula

0 10km

35∘30998400

31∘

30998400

31∘

JordanRiver

N

MineralBeach

Dead Sea areaSurvey area and its number

TownsSinkhole site13

800

700

600

500

40050 150 250

Mediterran

ean Sea

Haifa

Tel Aviv

Ashdod Jerusalem

Bersquoer Sheva

Israel

Jordan

Figure 1 Sinkhole sites along the Dead Sea shore (1) Palms (2) Samar Spring (3) Mineral Beach (4) Ein Gedi and Nahal Arugot (5) Yesha(6) Zeruya (7) Nahal Hever northern (8) Nahal Hever southern (9) Asarsquoel (10) Nahal Zeelim (11) Mezada (12) Rahaf (13) Mor (14) EinBoqeq (15) Newe Zohar (16) Lisan Peninsula (17) Ghor Al-Haditha (18) Dam-2 IndashIII sites under investigation (coordinates are in km newIsrael Mercator grid)

120573

119874

k

n

j

e2

i

e1

sum

Figure 2 Scheme of wavefront arriving at a Common Shot Point

of programs was written The CSP stack and diffractionmethod are complementary to each other and reveal usefulinformation about the subsurface The diffraction methodserves as a tool for detection of faults and voids while theCSP stacking contains information about the structure of thesubsurfaceThese methods were applied along the Dead Searsquos

120573

119874

sum

k

n

j

e2ie1

Figure 3The same as Figure 2 in case of one direction is normal tovector k

shorelines We have carried out several new seismic surveysalong line crossing the sinkhole lineaments and reinterpreteda number of previous reflection sections The 2D imagingtechnique has been presented in [7]This paper examines thenew 3D imaging approach and its application to 3D data thatwas acquired at the western shoreline of the Dead Sea Theresults of the imaging allow better understanding between


N

Mediterranean

Haifa

Tel Aviv

Jerusalem



30∘

31∘

32∘

33∘

1

2

Sea

(a)

Dea

d Se

a1 3

24

3

65 8

910

6

12

Lisan

Mt Sedom

JordanValley


Sinkholes



EGD

Masada graben

Dhira basin

-400 m on 1980


3510000

3500000

3490000

3480000

3470000

3460000

3450000

3440000

3430000

3420000

3410000

3400000

720000 730000 740000

(b)




606750

606700

606650

237800 237850 237900 237950 238000 238050 238100

20 m

10 m 1

35

7 13

57

1 8 16 24 32 40 48






1and e

2tangent to



23211917151311

97531

Fold

(a)

100

50

0

minus50

minus100


Offs

et

Offset

0 2040

60

80

100

120

140160180200

220

240

260

280

300

320340

(b)



119905 =1

119881(11988631119909 + 11988632119910) +1

21198811198771

(11988611119909 + 11988612119910)2

+1

21198811198772

(11988621119909 + 11988622119910)2

+ sdot sdot sdot

11988631= sin120573 sin120601 119886

32= minus sin120573 cos120601

11988611= cos120601 119886

12= sin120601

11988621= minus cos120573 sin120601 119886

22= cos120573 cos120601

(1)





1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96

010

020

030

Station number50 m

Two-

way

tim

e (s)





000

010

020

1 10 20 30 40 1 10 20 30 40

Two-

way

tim

e (s)

2


Station number

000

010

020Two-

way

tim

e (s)

000

010

020Two-

way

tim

e (s)

Station number

5 7

Reflector surface

Faults

25 m 25 m 25 m



(a)

Fault

Fault

W

E

Two-

way

tim

e

Lines from 1 to 7

(b)


N

E

W


606720

606700

606680

606660

606640237820 237840 237860 237880 237900 237920




2WT

(ms)

(c)



119868WMPS =sum119875119868119875119882(119868119875)

sum119875119882(119868119875)

119868119875= sum119875

sum119878

sum119877

119880119878119877(119879119878119877(119875))

(2)

where119882(119868119875) = exp(120582119868




119878119877(119879119878119877) is a seismic







4 Case Study











5 Conclusions



Acknowledgments


References





















N

Mediterranean

Haifa

Tel Aviv

Jerusalem



30∘

31∘

32∘

33∘

1

2

Sea

(a)

Dea

d Se

a1 3

24

3

65 8

910

6

12

Lisan

Mt Sedom

JordanValley


Sinkholes



EGD

Masada graben

Dhira basin

-400 m on 1980


3510000

3500000

3490000

3480000

3470000

3460000

3450000

3440000

3430000

3420000

3410000

3400000

720000 730000 740000

(b)




606750

606700

606650

237800 237850 237900 237950 238000 238050 238100

20 m

10 m 1

35

7 13

57

1 8 16 24 32 40 48






1and e

2tangent to



23211917151311

97531

Fold

(a)

100

50

0

minus50

minus100


Offs

et

Offset

0 2040

60

80

100

120

140160180200

220

240

260

280

300

320340

(b)



119905 =1

119881(11988631119909 + 11988632119910) +1

21198811198771

(11988611119909 + 11988612119910)2

+1

21198811198772

(11988621119909 + 11988622119910)2

+ sdot sdot sdot

11988631= sin120573 sin120601 119886

32= minus sin120573 cos120601

11988611= cos120601 119886

12= sin120601

11988621= minus cos120573 sin120601 119886

22= cos120573 cos120601

(1)





1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96

010

020

030

Station number50 m

Two-

way

tim

e (s)





000

010

020

1 10 20 30 40 1 10 20 30 40

Two-

way

tim

e (s)

2


Station number

000

010

020Two-

way

tim

e (s)

000

010

020Two-

way

tim

e (s)

Station number

5 7

Reflector surface

Faults

25 m 25 m 25 m



(a)

Fault

Fault

W

E

Two-

way

tim

e

Lines from 1 to 7

(b)


N

E

W


606720

606700

606680

606660

606640237820 237840 237860 237880 237900 237920




2WT

(ms)

(c)



119868WMPS =sum119875119868119875119882(119868119875)

sum119875119882(119868119875)

119868119875= sum119875

sum119878

sum119877

119880119878119877(119879119878119877(119875))

(2)

where119882(119868119875) = exp(120582119868




119878119877(119879119878119877) is a seismic







4 Case Study











5 Conclusions



Acknowledgments


References





















23211917151311

97531

Fold

(a)

100

50

0

minus50

minus100


Offs

et

Offset

0 2040

60

80

100

120

140160180200

220

240

260

280

300

320340

(b)



119905 =1

119881(11988631119909 + 11988632119910) +1

21198811198771

(11988611119909 + 11988612119910)2

+1

21198811198772

(11988621119909 + 11988622119910)2

+ sdot sdot sdot

11988631= sin120573 sin120601 119886

32= minus sin120573 cos120601

11988611= cos120601 119886

12= sin120601

11988621= minus cos120573 sin120601 119886

22= cos120573 cos120601

(1)





1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96

010

020

030

Station number50 m

Two-

way

tim

e (s)





000

010

020

1 10 20 30 40 1 10 20 30 40

Two-

way

tim

e (s)

2


Station number

000

010

020Two-

way

tim

e (s)

000

010

020Two-

way

tim

e (s)

Station number

5 7

Reflector surface

Faults

25 m 25 m 25 m



(a)

Fault

Fault

W

E

Two-

way

tim

e

Lines from 1 to 7

(b)


N

E

W


606720

606700

606680

606660

606640237820 237840 237860 237880 237900 237920




2WT

(ms)

(c)



119868WMPS =sum119875119868119875119882(119868119875)

sum119875119882(119868119875)

119868119875= sum119875

sum119878

sum119877

119880119878119877(119879119878119877(119875))

(2)

where119882(119868119875) = exp(120582119868




119878119877(119879119878119877) is a seismic







4 Case Study











5 Conclusions



Acknowledgments


References





















000

010

020

1 10 20 30 40 1 10 20 30 40

Two-

way

tim

e (s)

2


Station number

000

010

020Two-

way

tim

e (s)

000

010

020Two-

way

tim

e (s)

Station number

5 7

Reflector surface

Faults

25 m 25 m 25 m



(a)

Fault

Fault

W

E

Two-

way

tim

e

Lines from 1 to 7

(b)


N

E

W


606720

606700

606680

606660

606640237820 237840 237860 237880 237900 237920




2WT

(ms)

(c)



119868WMPS =sum119875119868119875119882(119868119875)

sum119875119882(119868119875)

119868119875= sum119875

sum119878

sum119877

119880119878119877(119879119878119877(119875))

(2)

where119882(119868119875) = exp(120582119868




119878119877(119879119878119877) is a seismic







4 Case Study











5 Conclusions



Acknowledgments


References




























5 Conclusions



Acknowledgments


References




















3D Imaging of Dead Sea Area Using Weighted Multipath

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Transcript of 3D Imaging of Dead Sea Area Using Weighted Multipath