Pure and Applied Geophysics. B. ORUÇ 1 and A. KESKINSEZER Introduction

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1 Pure appl. geophys. 165 (2008) Ó Birkhäuser Verlag, Basel, /08/ DOI /s Pure and Applied Geophysics Structural Setting of the Northeastern Biga Peninsula (Turkey) from Tilt Derivatives of Gravity Gradient Tensors and Magnitude of Horizontal Gravity Components B. ORUÇ 1 and A. KESKINSEZER 2 Abstract The tilt derivatives (or angles) are determined using the gravity gradient tensors (GGT) from two horizontal components (Gx, Gy) and vertical component (Gz), and the magnitude of the horizontal components (MHC). We show that the tilt derivatives from GGT and MHC are highly suitable for mapping linear geological structures or edges of target geology. The results obtained from theoretical data, with and without random noise, have been analyzed in this study. The tilt derivatives from GGT and MHC allow imaging the horizontal boundaries of gravity sources with a high resolution and show an improvement performance as edge detectors since they are ultra sensitive for detecting source boundaries. The tilt derivatives from GGT and MHC over the northeast of the Biga Peninsula in northwestern, Turkey are interpreted to image the edges of geological structures. Tilt derivatives provide a quick method which works well to obtain a detailed structural image of the complex area, with the most precision. The results indicate that the most predominant structural trends are in a NE-SW direction. Therefore, a good correspondence is recognized between structures well known by surface geology and many other lineaments which are unknown or only partially known. Key words: Gravity anomalies, gravity gradient tensor components, tilt derivatives, northwestern Turkey. 1. Introduction Gravity maps contain signals with a wide range of amplitudes, reflecting the varying depth, geometry and density contrasts of sources. Such maps are often dominated by large amplitude anomalies which can obscure more subtle anomalies. The purpose of data enhancement is to map subtle anomalies masked in the dynamic range due to the presence of high amplitude gravity anomalies. Steep, straight faults are commonly expressed as subtle potential-field lineaments, which can be gradient zones, 1 Engineering Faculty, Department of Geophysical Engineering, Kocaeli University, Umuttepe Campus, _Izmit/Kocaeli, Turkey. bulor@kou.edu.tr 2 Engineering Faculty, Department of Geophysical Engineering, Sakarya University, Esentepe Campus, Adapazarı//Sakarya, Turkey. ayhank@sakarya.edu.tr

2 1914 B. Oruç and A. Keskinsezer Pure appl. geophys., aligned breaks or discontinuities in the anomaly pattern. Consequently, imaging the boundaries of the gravity sources is important for the investigation of the structural setting. In recent years a number of methods have been developed to determine the signatures in images of gravity data so that weak, small amplitude anomalies can be amplified relative to stronger, larger amplitude anomalies. Since GGT demonstrates that the spatial rates of change of the vector field components are in nine directions, their interpretation allows a high resolution and detailed investigation of the Earth s subsurface. This presents a challenge for the gravity anomaly interpretation process. Practical gradiometer systems capable of rapidly measuring all of the components of the gravity gradient tensor have been developed (BELL et al., 1997; JEKELI, 1993). The GGT may be either measured or numerically calculated from gravity anomaly data. Procedures for numerical derivations with a good approximation of the GGT from measured gravity data are known (MICKUS and HINOJOSA, 2001; HINOJOSA and MICKUS, 2002). The technology differs from conventional gravity (G z ) in that five independent components (G xx, G xy, G yy, G xz and G yz ) of the gravity gradient field are recorded during actuated surveys (MURPHY et al., 2002; MURPHY et al., 2004). MILLER and SINGH (1994) have presented potential field tilt and showed that a map of the tilt derivative can be used in recognizing the horizontal location and the extent of sources. FITZGERALD et. al. (1997) provided the local phase-filtering approach to bring out fine detail of the images of the anomalous sources. The presence of the noise can make this approach very difficult for interpretation of geological structures. COOPER (2003) introduced a radial sunshading filter which was useful in delineating the edges of near-circular bodies, providing an estimate of the center of the feature could be given. VERDUZCO et al. (2004) discussed examples of the tilt derivative of the reduced-to-pole TMI aeromagnetic data. FAIRHEAD and WILLIAMS (2006) reviewed this method and critically evaluated using geologically realistic models. PILKINGTON and KEATING (2004) compared five edge detectors including tilt angles. The procedure presented in this paper combines the GGT and tilt derivatives and then uses these, imaging the edges of ribbon models. Further, the practical utility of the method is demonstrated to map geological trends from residual gravity anomalies in the northeast of the Biga Peninsula in northwestern, Turkey The Fundamentals of GGT 2. Methodology GGT is a second rank tensor containing the second spatial derivatives of the gravity potential and in a Cartesian reference frame with x along-line, y across-line, and z down, can be written in the form:

3 Vol. 165, 2008 Structural Setting of Biga Peninsula o 2 U ox 2 o 2 U G ¼ oyox 6 4 o 2 U ozox o 2 U oxoy o 2 U oy 2 o 2 U ozoy 3 o 2 U oxoz 2 3 G xx G xy G xz o 2 U 6 7 oyoz ¼ 4 G yx G yy G yz 5; ð1þ o 2 7 G zx G zy G zz U 5 oz 2 where U is the gravity potential, and for all pair (a, b) in{x, y, z} G ab ¼ o 2 U oaob (MICKUS and HINOJOSA, 2001). Since gravity is a conservative field and because of the commutability of the differential operators, the tensor is symmetric (G ab = G ba ) and its trace is equal to zero outside of the causative bodies. Further details regarding the gradient tensor are given in PEDERSEN and RASMUSSEN (1990). Therefore, up to five of the nine components of the GGT are independent and in free space Laplace s equation satisfies: G xx þ G yy þ G zz ¼ 0: Equations (1) and (2) results in the GGT having only five independent elements: G xx, G xy = G yx, G yy,g zx = G xz, and G zy = G yz. Additionally, the calculated vertical element G zz equals the negative sum of the tensor elements G xx and G yy from Laplace s equation Tilt derivative of GGT and MHC. A phase filter also can be defined such as the tilt derivative, tilt angle (MILLER and SINGH, 1994). The tilt derivative is the ratio of the first vertical derivative of the potential field f and the magnitudes of the horizontal gradient, so that the tilt derivative map may also be thought of as a normalization of the vertical derivative which is defined as 0 1 Tilt ¼ tan 1 B of =oz qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia: ð3þ ðof =oxþ 2 þðof =oyþ 2 The tilt derivative has interesting properties. As a dimensionless ratio it responds equally well to shallow and deep sources and to a large dynamic range of amplitudes for sources at the same level. The tilt derivative ranges -p/2 to?p/2 and easily interprets potential field data. We can start from (3) to define the signal components in which the GGT, is replacing the tilt derivatives, so that 0 1 h x ¼ tan 1 B G xz qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia; ð4þ G 2 xx þ G2 xy ð2þ

4 1916 B. Oruç and A. Keskinsezer Pure appl. geophys., 0 1 G yz h y ¼ tan 1 B qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia; ð5þ G 2 yx þ G2 yy and 0 1 G zz h z ¼ tan 1 B qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia: ð6þ G 2 zx þ G2 zy We can also define the tilt derivative of the MHC. Itis 0 1 h MHC ¼ tan 1 B MHC z qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi MHCx 2 þ A MHC2 y ð7þ where MHC is expressed as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi MHC ¼ G 2 x þ G2 y: ð8þ In theory the calculation of tilt angle filters from GGT and MHC is physically valid. The tilt derivatives can be considered an image of the tangent of the angle between the vertical components of the GGT and the horizontal. A similar definition can be used for the MHC. Figure 1 shows that the tilt derivatives are the concept of mapping angles derived from GGT and MHC Application to Theoretical Data In this section, the performance of the tilt derivatives from GGT and MHC will be analyzed using a theoretical gravity anomaly produced by two ribbons. Figure 2 shows the plan and perspective view of ribbons and gravity anomalies. Gravity anomalies have symmetrical properties since the models are symmetrically oriented. Note that the edges of the ribbons are not imaged clearly. Figure 3 shows that the GGT components are useful for understanding the approximate shape of the dominant mass anomaly. The zero contours of the G xx and G yy locate N-S and E-W edges of the ribbons, respectively. G xz and G yz image the ribbon models, highs and lows defining the edges and identify the E-W and N-S edges of the targets, respectively. The G zz defines the center of the models and combines G xx and G yy gradients. Although the G zz shows correct position related to ribbons, it is unclear in determining the edges of the models. The G xy solutions make provisions that the center of closed maxima and minima is marked on the corners of the models. The MHC from horizontal gravity vector components (G x and G y ) is illustrated in Figure 4. The MHC is generally useful in imaging of the edges, although the edge of the deeper ribbon near the shallow ribbon is insufficiently imaged.

5 Vol. 165, 2008 Structural Setting of Biga Peninsula 1917 Figure 1 Schematic diagram showing the gravity vector components (G x, G y and G z ), gradient tensors (G xx,g xy,g xz,g yx,g yy,g yz,g zx,g zy,g zz ), and tilt angles (h x, h y, h z and h MHC ). The symbol A, MHC and THDR represents analytical signal, the magnitude of the horizontal components and total horizontal derivative, respectively. Figure 5 shows tilt data sets computed using Eqs. (4), (5), (6) and (7). h x and h y produce maxima and minima of tilt angles with the edges of the ribbons enhanced in the x and y directions, respectively. A much improved result came from using the tilt angle h z of the G z and the tilt angle h MHC of the MHC. A comparison of h z and h MHC shows the characteristic solutions response to the body outline. The zero contour of h z has defined the approximate shape of the ribbons. The maxima of h MHC enhance all edges of the ribbons. In order to test the noise effect on tilt angles h x,h y, h z and h MHC, Gaussian noise with a zero mean, generated from random numbers normally distributed with variance 0.1, was added to all grids of the theoretical gravity anomaly. Figure 6 contains a series of images that illustrates the tilt derivative maps in case of the presence of noise. Note that h x and h y are very susceptible to noise since misleading results occur on both images. Although the h z is diffuse near the shallower body, it works well in imaging the edges of the models. The h MHC gives a much clearer response over sources since it

6 1918 B. Oruç and A. Keskinsezer Pure appl. geophys., Figure 2 The plan and perspective view of the ribbon models with density of 1 g/cc used for the model test and gravity anomaly. locates the edges of the models. It should therefore be noted that the h z and h MHC are less sensitive to noise in the data Application to Real Data In this section we show the tilt derivative results obtained from GGT and MHC in the study area depicted in Figure 7a. The geology of the study area is dominated by the widespread occurrence of plutonic rocks, sedimentary deposits carried out in the neotectonic period. The high natural seismicity in the northwestern part of Turkey, points out important active tectonic processes. The active fault segments of the North Anatolian Fault zone and its transition into a complex system of restraining and releasing bends of strike-slip faults within and near the Marmara Sea are the dominant tectonic structures in the northwestern part of Turkey (BARKA and KADINSKY-CADE, 1988; BARKA, 1992). The main structural grain of the Biga Peninsula is NE-SW structures which are widespread in the area as a result of phases of strike-slip faulting. The main fault zones are Biga Edremit

7 Vol. 165, 2008 Structural Setting of Biga Peninsula 1919 Figure 3 The GGT components of the gravity anomaly from ribbon models.

8 1920 B. Oruç and A. Keskinsezer Pure appl. geophys., Figure 4 The MHC calculated from horizontal gravity components (G x and G y ) of the ribbon models. Fault zone (BEFZ), Balıkesir Behramkale Fault Zone (BBFZ), Yenice Gönen Fault Zone (YGFZ) and Manyas Edremit Fault Zone (MEFZ) which are right lateral strike-slip faults (SIYAKO et al., 1989; YALTIRAK, 2002). In addition, a number of local lineaments characterizing complex local faulting in the E-SE of the study area are placed. Most of them cross each other in correspondence of the volcanic complex. Figure 7b shows that the Bouguer anomaly data were obtained from the General Directorate of Mineral Research and Exploration, Turkey. The basin is reflected with a gravity minimum in the center and a maximum on either side over the shoulders and it has undergone several tectonic processes during the geological past. The general direction of the Bouguer anomaly map corresponds to the strike of the formation in the NE-SW direction, and the peninsula is divided into two parts by the gravity gradient belt. A major part of the numerous faults in the peninsula is in this gradient belt and the areas adjacent to it. During processing, as a first step, residual gravity anomalies were computed by removing a first-order polynomial surface from the complete Bouguer gravity anomaly map and shown in Figure 8. The NE-SW trending faults in the study area are also supported by the residual gravity contours lending credence to the lineament interpretations. Local gravity anomalies result from the juxtaposition of relatively highand low-density rock types. Subsequently the GGT components from the residual gravity map have been calculated using the method given by MICKUS and HINOJOSA (2001) and

9 Vol. 165, 2008 Structural Setting of Biga Peninsula 1921 Figure 5 The h x, h y, h z and h MHC images from GGT components of the ribbon models. shown in Figure 9. The GGT component maps allow assembling of an overview of all structures and provide a general knowledge of the structural frame-work of the study area. Generally, high gradient values were observed around the low gravity of the Biga Peninsula. It is observed that the pattern of the high gradient anomalies is sharp anomalies which may be produced by several boundaries of contrasting density. However, the spatial images of the GGT components reflect different attributes of geology. They are not highly suitable for tracking linear geological structures. In general, G xx and G xz gradient data measure E-W changes in E-W gravity, whereas G xy,g yy,g zy and G zz identify the NE-SW changes in NE-SW gravity relevant to the geologic setting, i.e., structural and/or stratigraphical setting. The conventional gravity G zz high (in red) generally identifies volcanics bounded with other rock units. Therefore, the results from

10 1922 B. Oruç and A. Keskinsezer Pure appl. geophys., Figure 6 The h x, h y, h z and h MHC images from GGT components with Gaussian noise with variance 0.1. GGT provide a tentative qualitative interpretation in determining the locations of the anomalous sources. To obtain more information regarding the edges of the features, we calculate the h z and h MHC maps from residual gravity data. Interpretation of enhanced images provides objective information on gravity sources within the study area. Geologically, h z and h MHC defines the edges of the stratigraphic or structural units generating density contrasts. Figures 10a and 10b show that the application of h z and h MHC filtering effectively images the edges of the features. Note that the zero contour of h z and maxima of h MHC enhance the edges of the basement rocks and are well correlated between units of early Miocene early Pliocene age and the Holocene age. The complex local faults of BEFZ, MEFZ and BBFZ are considerably better imaged than those of YGFZ. One explanation of this pattern is that the local faults of YGFZ in the study

11 Vol. 165, 2008 Structural Setting of Biga Peninsula 1923 Figure 7 a) Geologic map of Northeast of Biga Peninsula (modified after YALTIRAK, 2002) and the location of the survey area. (b) Bouguer anomaly map. area are relatively deep. It is clear that the advantage of the method is, however, its ability to enhance important parts of anomaly structures which are not obtained from conventional gravity.

12 1924 B. Oruç and A. Keskinsezer Pure appl. geophys., Figure 8 Residual gravity anomaly map of the study area. 3. Conclusions The tilt derivatives of the GGT and MHC have shown that they have the ability to enhance linear geological structures or edges of target geology. The methods improve characterization of the geometrical contrast of the gravity sources and represent a useful form of highpass filter for enhancing subtle detail in gravity data. Therefore, the tilt derivatives of the GGT and MHC sharpen the filter response considerably. The zero contours of h z and maxima of h MHC delineate the spatial location of the gravity source edges. They are good visual maps in imaging the subtle lineaments and are interpreted easily since they have the advantage of responding well to the gravity sources. The greatest advantage of these maps is that they are least susceptible to noise in the data, and advantageously robust in delineating gravity sources. In addition, multi-directional mass information relating to target geology size, shape and geological setting can be resolved and are therefore obtained efficiently from all different boundary information. Because they contain critical directional information, the methods can provide a more detailed picture of the subsurface by reflecting the source edges as faults, contacts, and basin and uplift edges than that of GGT or conventional gravity. These methods contribute the geophysical information pertaining to the structure pattern of the Northeast of Biga Peninsula (Turkey).

13 Vol. 165, 2008 Structural Setting of Biga Peninsula 1925 Figure 9 Gravity gradient tensor components from residual gravity data of the study area.

14 1926 B. Oruç and A. Keskinsezer Pure appl. geophys., Figure 10 Comparison of features with a) h z and b) h MHC from residual gravity data. Acknowledgements The authors are grateful to the General Directorate of Mineral Research and Exploration for their kind permission to use the gravity data from Turkey. REFERENCES BARKA, A. (1992), The North Anatolian Fault Zone, Annales Tectonicae, Suppl. to V. VI, BARKA, A. and KADINSKY-CADE, K. (1988), Strike-slip fault geometry in Turkey and its influence on earthquake activity, Tectonics 7, 3, BELL, R. E., ANDERSON, R., and PRATSON, L. (1997), Gravity gradiometry resurfaces, The Leading Edge 16, BLAKELY, R.J. and SıMPSON, R.W. (1986), Approximating edges of source bodies from magnetic or gravity anomalies, Geophysics 51, COOPER, G.R. J. (2003), Feature detection using sunshading, Computer and Geosciences 29, FAIRHEAD, J.D. and WILLIAMS, S.E. (2006), Evaluating Normalized Magnetic Derivatives for Structural Mapping, SEG 2006 New Orleans Extended Abstract, pp FITZGERALD, D., YASSI, N., and DART, P. (1997), A case study on geophysical gridding techniques: INTREPID perspective, Explor. Geophys. 28, HINOJOSA, J.H. and MICKUS, K.L. (2002), Short note: Hilbert transform of gravity gradient profiles: Special cases of the general gravity-gradient tensor in the Fourier transform domain, Geophys. 67, JEKELI, C. (1993), A review of gravity gradiometer survey system data analyses, Geophys 58, MıCKUS, K.L. and HıNOJOSA, J.H. (2001), The complete gravity gradient tensor derived from vertical component of gravity: A Fourier transform technique, J. Appl. Geophys. 46, MıLLER, H.G. and SıNGH, V. (1994), Potential field tilt A new concept for location of potential field sources, J. Appl. Geophys. 32, MURPHY, C.A. (2004), The Air-FTGÒ airborne gravity gradiometer system, in (R.J.L. Lane, ed.) Airborne Gravity 2004 Abstracts from the ASEG-PESA Airborne Gravity 2004 Workshop, Geoscience Australian Record 2004/18, 7 14.

15 Vol. 165, 2008 Structural Setting of Biga Peninsula 1927 MURPHY, C.A., MUMAW, G.R., FOTLAND, B., and SOLLıD, K. (2002), Utilising FTG data to resolve salt development in the Nordkapp Basin offshore Norway, 64th Meeting, EAGE, Expanded Abstracts, D006. PEDERSEN, L.B. and RASMUSSEN, T.M. (1990), The gradient tensor of potential field anomalies: Some implications on data collection and data processing of maps, Geophys. 55, PILKINGTON, M and KEATING, P. (2004), Contact mapping from gridded magnetic data A comparison, Extended abstracts, ASEG 17th Geophysical Conference and Exhibition, August 2004, Sydney. REID, A.B., ALLSOP, J.M., GRANSER, H., MILLETT, A.J., and SOMERTON, I.W. (1990), Magnetic interpretation in three dimensions using Euler deconvolution, Geophys. 55, SIYAKO, M., BÜRKAN, K.A., and OKAY, A.I. (1989), Biga ve Gelibolu yarımadalarının Tersiyer jeolojisi ve hidrokarbon olanakları, Bull. Turk. Assoc. Pet. Geol. 1, VERDUZCO, B., FAıRHEAD, J.D., GREEN, C.M., and MACKENZıE, C. (2004), New ınsights into magnetic derivatives for structural mapping, The Leading Edge 23, YALTIRAK, C. (2002), Tectonic evolution of the Marmara Sea and its surroundings, Marine Geology 190, (Received October 18, 2007, revised July 9, 2008) To access this journal online: