paper 3 3d gravity modeling of buyuk menderes basin in western anatolia using parabolic density...

8/10/2019 PAPER 3 3D gravity modeling of Buyuk Menderes basin in Western Anatolia using parabolic density function [LEDI

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3D gravity modeling of Byk Menderes basin in Western Anatolia using

parabolic density function

Mahir Isk a,*, Hakk Senel b

a Department of Geophysical Engineering, Sakarya University, 54187 Sakarya, Turkeyb Department of Geophysical Surveying, General Directorate of Mineral Research and Exploration, 06520 Ankara, Turkey

a r t i c l e i n f o

Article history:Received 29 January 2008Received in revised form 30 April 2008Accepted 28 May 2008

Keywords:

Sedimentary basinJuxtaposed vertical prismsParabolic density contrast3D gravity modeling

a b s t r a c t

A method to model 3D sedimentary basins with parabolic density contrast is applied to Byk Menderesbasin in Western Anatolia. The measured gravity fields, reduced to a horizontal plane, are assumed to beavailable at grid nodes of a rectangular/square mesh. Juxtaposed 3D vertical prisms with their geometri-cal epicenters on top coincide with grid nodes of a mesh to approximate a sedimentary basin. The algo-rithm based on Newtons forward difference formula automatically calculates the initial depth estimatesof a sedimentary basin assuming that 2D infinite horizontal slabs can generate the measured gravityfields and among these slabs thedensity contrast varies with depth. The lower boundary of a sedimentarybasin is formulated by estimating the depth values of the 3D prisms with in predetermined limits. Mea-sured gravity fields pertaining to the Byk Menderes basin, Turkey, where the density contrast varieswith depth, are interpreted to show the applicability of the method.

2008 Elsevier Ltd. All rights reserved.

1. Introduction

An anomaly cannot be easily related to the target structuresince gravity anomalies are formed by density differences inunderground geology. Therefore, the reliable interpretation de-pends on the fact that the underground geology and density con-trasts are well known. The densities of sedimentary rocks varywith some factors that are pressure, compaction, porosity, age,depth, etc. (Athy, 1930). For example, the density increases expo-nentially with depth. Thus, Cordell (1973), Chai and Hinze(1988), and Rao et al. (1993) modeled the sedimentary basins byusing the exponential density function.

Murthy and Rao (1979) derived the anomaly equation of apolygonal model for linear variation in density contrast. They ap-plied this equation to the case of exponential variation by dividing

each side of the polygon into several segments over each of whichthe density contrast can be assumed to decrease linearly. Rao(1986)used a quadratic density function for modeling the gravityanomalies of a sedimentary basin. Litinsky (1989) investigated sed-imentary basins by using the concept of effective hyperbolic den-sity contrast. Rao (1990) used a quadratic density function andan asymmetric trapezium model for modeling the gravity anoma-lies of a sedimentary basin.Rao et al. (1990)also investigated theLos Angeles basin by using the quadratic density functionwith 2 12D and 3D prismatic models. Mickus and Peeples (1992)

benefited from the BackusGilbert inversion method for gravityand magnetic interpretation of sedimentary basins. Sevin andAtes (1996) interpreted AydnGermencik gravity anomalies byusing the Levenberg-Marquardt inversion method. Ates et al.(1997) modeled Byk Menderes graben by using AydnMilasgravity anomalies.Senel (1997)investigated Byk Menderes gra-benusingthefault model.Isk (1997) interpreted sedimentarybasinanomalies with variable density contrast using inversion methods.

In this paper, a method based on Newtons forward differenceformula coupled with an algorithm (Chakravarthi and Sundarara-jan, 2004) is presented, assuming that the density contrast varieswith depth. This method also enables to obtain depth estimatesof a sedimentary basin from measured gravity fields. The applica-bility and efficiency of the method is demonstrated on a syntheticmodel and a selected sedimentary basin namely the Byk Mende-

res basin, Turkey.

2. Parabolic density function

The density of sedimentary rocks is particularly related withporosity and depth (Athy, 1930). The density of the sediments insedimentary basins increases with depth. The density contrast de-creases between the sediments and surrounding rocks because ofcompaction due to increase of depth and pressure together in thesediments (Cordell, 1973). The decrease of the density contrast,in principle, does not obey a deterministic mathematical formula-tion due to effects of stratigraphic layering, facies variations, dia-genesis, tectonic history, cementation and compaction due to

1367-9120/$ - see front matter 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.jseaes.2008.05.013

* Corresponding author. Tel.: +90 264 2955699; fax: +90 264 2955601.E-mail address:[email protected](M. Isk).

Journal of Asian Earth Sciences 34 (2009) 317325

Contents lists available at ScienceDirect

Journal of Asian Earth Sciences

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / j a e s
mailto:[email protected]://www.sciencedirect.com/science/journal/13679120http://www.elsevier.com/locate/jaeshttp://www.elsevier.com/locate/jaeshttp://www.sciencedirect.com/science/journal/13679120mailto:[email protected]


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geostatic pressure. However, the density contrast-depth relation-ship can be approximated by various density functions.

The densitydepth relationship in the sedimentary basins canbe approximated by a parabolic function (Visweswara Rao et al.,1994):

Dqz Dq30

Dq0kz2

1

In the equation, Dq(z) is density contrast at depthz, Dqois thedensity contrast at the surface and k is a constant which explainthe decrement of density contrast with increasing depth.

In Eq.(1), the values ofk and Dqo are unknown and are esti-mated by a least-squares fitting to the density contrast-depth datawhich can be determined by well or seismic or borehole data ininvestigation field.

3. Gravity anomaly of sedimentary basin

Gravity anomaly expression for any 3D body is given by ( Blak-ely, 1995):

g GDqZx

Zy

Zz

zdxdydz

x2 y2 z23=2

2

where G is the gravitational constant and Dq is constant densitycontrast.

In Eq.(2), if parabolic density function (Eq.(1)) is using insteadofDq, it can be written:

g GDq30

Zx

Zy

Zz

zdxdydz

Dq0kz2x2 y2 z23=2

3

After that integral is solved, gravity equation (gprism) of a verticalprism (Fig. 1) with the parabolic density contrast whose top depth(z1) is on surface is obtained forz1= 0(Chakravarthi et al., 2002).

Analytical gravity expression of a sedimentary basin at any gridnode (i,j) of a rectangular/square mesh will be seen as the sum ofgravity effects of the juxtaposed prisms inFig. 2:

gbasini;j XNY1m2

XNX1n2

gprismm;n 4

whereNXandNYare the number of grid nodes alongx- andy-axesof the Cartesian coordinate system. The top of all of the prisms is onsurface and the gravity data is at the center of each prism.

4. Inversion of sedimentary basin anomalies

If the values of density contrast of sediments at several depthsare noted, k and Dqocan be determined by fitting this data to Eq.(1).

The basin is viewed as a series of juxtaposed 3D vertical prisms.The width of the prism is equivalent to the station spacing. The topdepths of all prisms coincide with the ground surface for the out-cropping basin. Ultimately, the problem of modeling becomes thedetermination of the bottom depths of the prisms.

Initially, sum of the gravity values of these prisms at every sta-tion are calculated using Eq.(4). The objective function defined bythe differences between the observed anomalies gobs(i, j) and thecalculated anomalies gbasin(i,j) are used to modify the depths ofthe prisms as follows:

Fig. 1. 3D vertical prism model (B(0, 0, 0) is the origin, P(x, 0, 0) is the calculationpoint, z1andz2are the top and bottom depths, respectively).

Fig. 2. Juxtaposed 3D prisms model.

318 M. Isk, H. Senel / Journal of Asian Earth Sciences 34 (2009) 317325


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XNYi1

XNXj1

e2ij XNYi1

XNXj1

gobsi;j gbasini;j2

min 5

The necessary condition for Eq.(5)to be minimum is to equate thepartial derivatives with respect to the prism depths to zero. There-fore, the error equation in the objective function can be written as:

eij gobsi;j XNYi1

XNXj1

gbasini;j

ogbasini;j

ozij dzij

o2gbasini;j

2oz2ijdz2ij

# 6

If Eq.(6)is rearranged by omitting second and higher degree deriv-ative terms, it can be written as:

eij gobsi;j gbasini;j 7

where,

gbasini;j XNY

i1XNX

j1

gbasini;j ogbasini;j

ozijdzij 8

The initial depths of the prisms are obtained by using the gravity ef-fect of an infinite horizontal slab, which is given as follow (Chakra-varthi and Sundararajan, 2004):

Fig. 3. Plan view (a) and 3D view (b) of synthetic model along with computed (c) and inverted (d) gravity fields.

M. Isk, H. Senel / Journal of Asian Earth Sciences 34 (2009) 317325 319


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zsmn gobsm;nDq0

2pGDq20kgobsm;n 9

wherem= 2,. . .,NY 1,n= 2,. . .,NX 1 andsis iteration number.In addition,z(m, n) = 0, for m= 1 and NYand n= 1 and NX. Thus, tak-ing into consideration the objective function (Eq. (5)), the prismdepths are improved at each iteration by using Eq. (10).

zs1

mn zs

mn dzmn 10where dzmn is the increments or decrements in the prism depths.

This modification of the prism depths is carried out a specifiednumber of iterations or until the sum of the squares of the anom-alies becomes negligible.

5. Synthetic example

Plan and 3D view of the synthetic model of a basin with3 km as depth are shown in Fig. 3a and b, respectively. The

model consists of 60 grid nodes at an interval of 2 km alongthe x-axis and y-axis. Dqo=0.68 gr/cm

3 and k= 0.12 gr/cm3/km were determined by the density contrast-depth data as-sumed as Dq(0.5 km) =0.6 gr/cm3, Dq(1 km) =0.45 gr/cm3

and Dq(3 km) =0.3 gr/cm3. Computed gravity field of themodel is shown in Fig. 3c and the inverted field is shown inFig. 3d. At the end of 15th iteration, the similarity can be

obviously seen between the computed field and the invertedfield.Moreover, the gravity data added random noise in the range of

1 to +1 mgal was used to know how sensitive of the method. Ifthe error range (0.01 mgal) of modern gravimeters is taken intoconsideration, the noise is exaggerated. In this case, at the endof 15th iteration, the maximum depth of the basin of 3.1 kmwas obtained. Noisy gravity field of the model is shown inFig. 4a and the inverted field is shown in Fig. 4b. 3D view ofthe assumed and calculated models are shown in Fig. 4c and d,respectively.

Fig. 4. Computed (a) and inverted (b) gravity fields with adding random noise (1 mgal), and 3D view of assumed (c) and calculated (d) models.



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6. Field example

6.1. Structural geology

Neogene extensional basins of the Aegean region have been thefocus of considerable research. Extension in this region has beenvariously attributed to (i) westward escape of the Anatolian block

along the North Anatolian Transform Fault (Dewey and S

engr,1979), (ii) Neogene to recent subduction in the Hellenic trench(Le Pichon and Angelier, 1979) and (iii) gravitational collapse ofthickened crust following Palaeogene Alpine-Himalayan compres-sion (Seyitoglu and Scott, 1991).

The Byk Menderes graben of western Turkey is a part of theWestern Anatolian extensional province (McKenzie, 1978; Deweyand Sengr, 1979). The main east-west trending part of theByk Menderes graben (Fig. 5) extends from Ortaklar in the westto Sarayky in the east, a distance about 125 km, with a width of812 km (Seyitoglu and Scott, 1992). Along most of this length

its north side is bounded by a steeply dipping major fault whichseparates the Neogene sediments of the graben from the metamor-phic sequences of the Menderes massif to the north. This fault oc-curs along the base of the main topographic escarpment of thearea, which forms a prominent east-west trending (Akg, 1985;Paton, 1992; Cohen et al., 1995). Faulting on the south side ofthe graben is considered to be of lesser significance and displace-

ment and the overall structure appears to be that of half-grabenfacing south (Sengr, 1987).

6.2. Gravity modeling

The Bouguer anomaly map with 2.4 gr/cm3 terrain density wasused for interpretation. The observed gravity field of the basin wasdigitized at a grid of 2 km alongx- andy-axes of the mesh in orderto obtain 540 grid nodes.Isk (1997)determined the density con-trast-depth data by interpreting the detail geological informationand the geoelectrical sections of the investigation field. The basin

Fig. 5. Geological map and studied area (modified fromSeyitoglu and Scott, 1992).



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was modeled by using Dqo= 0.8 gr/cm3 andk= 0.05 gr/cm3/km

that were derived from this data. The maximum thickness of thebasin of 3.9 km was obtained at the end of 3rd iteration. The ob-

served and calculated gravity field maps of the basin are shown

in Fig. 6a and b and the plan view, 3D viewof basement relief mod-els of the basin are shown in Fig. 6c and d, respectively.

Fig. 6. Observed (a) and calculated (b) gravity fields, and inferred plan view (c) and 3D view (d) of basement relief of Byk Menderes basin, Turkey (with the parabolicdensity function).



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Moreover, the basin was modeled by using the constant density

contrast to be compared with the basin model derived from thevariable density function. Thus, the values of k in the parabolic

density function was assumed as zero and the maximum thickness

of the basin of 3.1 km was obtained at the end of 3rd iteration. Theobserved and calculated gravity field maps of the basin are shown

Fig. 7. Observed (a) and calculated (b) gravity fields, and inferred plan view (c) and 3D view (d) of basement relief of Byk Menderes basin, Turkey (with the constantdensity contrast).



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in Fig. 7a and b and the plan view, 3D view of basement relief mod-els of the basin are shown inFig. 7c and d, respectively.

The density of the sediments in sedimentary basins increaseswith depth. The density contrast decreases between the sedimentsand surrounding rocks because of compaction due to increase ofdepth and pressure together in the sediments. Therefore, the vari-able density model (3.9 km) is more fitting with the true depth,comparison with the constant density model (3.1 km).

7. Conclusions

Modeling of 3D sedimentary basins from the gridded gravitydata is presented. The density contrast along a sedimentary basinis assumed to be varying parabolically with depth. Results of thatapproach are well-matched on the synthetic and field examples.In order to obtain correctly the density function unknowns, thedensity contrast-depth information is needed and this can bedetermined by well or seismic or borehole data in investigationfield.

The maximum depth of the sedimentary basin is 3.9 km in thisstudy. Cohen et al. (1995) obtained the depth of the basin as 1.5 kmat Aydn.Isk (1997)determined 2.02.2 km depth between Aydnand Sultanhisar and 2.22.3 km depth between Sultanhisar andNazilli. Also Senel (1997) obtained the depth of the basin as2.5 km between Sultanhisar and Nazilli. Recently, Sar and Salk(2006)determined 2.0 km depth between Aydn and Sultanhisarand 3.5 km depth between Nazilli and Sarayky. If the results(Fig. 8) and depth maps are taken into consideration, it may be saidthat the graben structure in the region is getting deeper from Northto South and from West to East.

References

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Ates, A., Sevin, A., Kadoglu, Y.K., Kearey, P., 1997. Geophysical investigations of thedeep structure of the AydnMilas region, southwest Turkey: evidence for thepossible extension of the Hellenic Arc. Israel Journal of Earth Sciences 46, 2940.

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Fig. 8. Comparative results of the field example.



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Senel, H., 1997. Inversion of gravity anomaly of Byk Menderes faults. Journal ofKocaeli University 4, 6672.

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Visweswara Rao, C., Chakravarthi, V., Raju, M.L., 1994. Forward modelling: gravityanomalies of two-dimensional bodies of arbitrary shape with hyperbolic andparabolic density functions. Computer and Geosciences 20, 873880.


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