Journal of Applied Geophysics

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1 Journal of Applied Geophysics 88 (2013) Contents lists available at SciVerse ScienceDirect Journal of Applied Geophysics journal homepage: Structural interpretation of the Erzurum Basin, eastern Turkey, using curvature gravity gradient tensor and gravity inversion of basement relief B. Oruç a,, İ. Sertçelik a, Ö. Kafadar b, H.H. Selim c a Kocaeli University, Engineering Faculty, Department of Geophysical Engineering, Umuttepe Campus, İzmit/Kocaeli, Turkey b Kocaeli University, Kosekoy Vocational School, Department of Computer Programming, Kartepe/Kocaeli, Turkey c Istanbul Commerce University, Faculty of Engineering and Design, Department of Jewellery Engineering, Küçükyalı, Turkey article info abstract Article history: Received 28 May 2012 Accepted 7 October 2012 Available online 5 November 2012 Keywords: Gravity anomalies Curvature gravity gradient tensor Gravity inversion Structural boundaries The Erzurum Basin has received more attention in petroleum potential research because of its particularity in geographic and tectonic position. There remains debate on the basement structure of the basin since igneous rocks and faults make the structure and stratigraphy more complicated. We utilize gravity data to understand the structure of the Erzurum Basin. This study describes an edge enhancement technique based on the eigenvalues and determinant obtained from the curvature gravity gradient tensor (CGGT). The main goal of this technique is to delineate structural boundaries in complex geology and tectonic environment using CGGT. The results obtained from theoretical data, with and without Gaussian random noise, have been analyzed in determining the locations of the edges of the vertical-sided prism models. The zero contours of the smallest eigenvalue delineate the spatial location of the edges of the anomalous sources. In addition, 3-D gravity inversion of Bouguer anomalies has been used with purpose to estimate the structure of the substrata to allow modeling of the basement undulation in the Erzurum basin. For this reason, the Parker Oldenburg algorithm helped to investigate this undulation and to evidence the main linear features. This algorithm reveals presence of basement depths between 3.45 and 9.06 km in the region bounded by NE SW and E W trending lineaments. We have also compared the smallest eigenvalue zero contours with the HGM images and Tilt derivative (TDR) of Bouguer anomaly map of the study area. All techniques have agreed closely in detecting the horizontal locations of geological features in the subsurface with good precision Elsevier B.V. All rights reserved. 1. Introduction An important objective in the interpretation of gravity data is to enhance the data in order to bring out important features. Gravity prospecting delineates lateral change in density contrasting and provides information not only on lithological changes but also on structural trends. However, gradients themselves may be used directly to infer properties of subsurface structures. Horizontal-gradient analysis of gravity data delineate the vertical and lateral locations of the edges of the geological features. Cordell (1979) and Cordell and Grauch (1985) have used the maximum amplitudes of the horizontal gradients to locate near-vertical geologic boundaries from gravity or pseudogravity anomalies. They have shown the HGM maxima indicate abrupt lateral density contrasts. In recent years, gradiometers allow the measurement of all the tensor components. Many techniques for mapping have been developed to delineate structural features from potential field gradient tensor data. Foss (2001) has computed gravity tensor invariants Corresponding author. Fax: address: bulent.oruc@kocaeli.edu.tr (B. Oruç). over a complex model representing a horizontally and vertically faulted basement surface. Roberts (2001) showed the more negative eigenvalue is equivalent to the most negative curvature obtained from conventional potential field anomalies and is useful in estimating source depth. Roberts (2001) has introduced curvature attributes to seismic systematically, and defined many different curvature attributes. Murphy (2004) has used the horizontal gravity gradient tensor to locate geologic contacts. Hansen and deridder (2006) has described a linear feature analysis using eigenvalues of Hessian matrix defined by horizontal gravity gradients observed or computed from magnetic data. They have shown that the two eigenvalues of this matrix which are just the most positive and most negative curvatures and the more positive eigenvalue can be used for linear feature analysis and the more negative eigenvalue is useful in estimating source depth. Murphy (2007) has used invariants obtained from horizontal gravity gradient components to image subsurface geology. Murphy and Brewster (2007) have described a procedure for working with gravity gradient tensor. Phillips et al. (2007) have defined the quadratic surface, a curvature matrix constructed from the coefficients of the second order terms of conventional potential field anomalies. Beiki and Pedersen (2010) showed that the strike direction of quasi 2D bodies can be estimated from the eigenvector corresponding to /$ see front matter 2012 Elsevier B.V. All rights reserved.

2 106 B. Oruç et al. / Journal of Applied Geophysics 88 (2013) the smallest eigenvalue of full tensor gravity gradient matrix. Mataragio and Kieley (2009) have shown the rotational and horizontal invariants of the gravity gradient tensor are imaged sub-vertical plugs, dikes, or diatremes associated with alkaline intrusions. Murphy and Dickinson (2010) have combined the individual tensor components into invariants and defined geologic contact and body shape information. We examine the eigenvalues of CGGT in determining the edges of anomalous sources. The method has been applied to CGGT computed from the Bouguer gravity data compiled from Erzurum area in the eastern region of Turkey. In addition, we have estimated a basement undulation model from 3D gravity inversion of Bouguer anomalies and compared with the zero contours of smallest eigenvalue map. The solutions of this characteristic equation are the eigenvalues of Γ: 0 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi λ 1 ¼ 1 g x 2 x þ g y y þ g x x g! 1 u 2 y þ 4 g t x A y y 0 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi λ 2 ¼ 1 g x 2 x þ g y y g x x g! 1 u 2 y þ 4 g t x A y y It is well known that the product of the eigenvalues of a square matrix is equal to the determinant of that matrix. It is ð7þ ð8þ 2. Outline of the CGGT theory detðγþ ¼ λ 1 λ 2 : ð9þ Hansen and deridder (2006) made a different derivation, through a 2 2 Hessian matrix of the horizontal vector gradients for magnetic applications. The Hessian matrix is also called curvature which describes how bent a curve or surface is at a particular point on a geometric curve or surface. The curvature gradient matrix of the gravity field is defined as 0 g x x Γ ¼ CGGT ¼ g y x 1 g x y C g y A ; y ð1þ 3. Theoretical examples In this section, the robustness of the CGGT used for the edge enhancement is tested with gravity field anomaly map caused by four vertical-sided prisms at a depth to the top of 0.5 km (labeled 1), 1.5 km (labeled 2), 2 km (labeled 3), and 1 km (labeled 4) (Fig. 1a). where g x and g y are the horizontal gravity vectors. g x / x and g x / x are first order derivatives of gravity vector components with respect to x and y.eq.(1) is equivalent to the magnetic data defined as a Hessian matrix of the anomalous magnetic field developed by Hansen and deridder (2006).FromEq.(2), because the CGGT tensor is symmetric, off-diagonal elements relate, as follows: g x = y ¼ g y = x: ð2þ Off-diagonal elements tend to emphasize symmetries in the x and y direction. Boring (1998) has discussed detailed properties of a real symmetric tensor. When the coordinate system was rotated, the elements of the tensor reduce to the diagonal form eigenvectors of a tensor have the property that when the inner product of the original tensor and an eigenvector are taken the result is a vector that is a scalar multiple of the original eigenvector: Γx ¼ Λx ð3þ The solutions Λ to Eq.(3) are the eigenvalues of Γ. The columns of x are the eigenvectors of Γ and the eigenvalues are arranged: Λ ¼ λ 1 0 : ð4þ 0 λ 2 It is clear that the diagonal form of the tensor Γ is a simpler representation. The vectors x associated with each eigenvalue are the eigenvectors of Γ. Eq. (3) is written as ðγ ΛIÞx ¼ 0: ð5þ Omitting the null vector (x =0), Eq. (5) implies the matrix Γ ΛI is singular and its determinant zero. From the determinant of Γ ΛI, it can be constructed the homogeneous characteristic equation for a 2D tensor Γ, expandsto g x x λ detðγ ΛIÞ ¼ g y x g x y g y ¼ 0: y λ ð6þ Fig. 1. (a) Shematic representation of 3D vertical-sided prism models used for theoretical examples. (b) Gravity anomaly of vertical-sided prism models at the depths of 0.5 km (prism 1), 1.5 km (prism 2), 2.0 km (prism 3) and 1 km (prism 4). Density contrast is 1g/cm 3.

3 B. Oruç et al. / Journal of Applied Geophysics 88 (2013) Fig. 2. The curvature gradient tensor maps over vertical prism models in the upper panel and eigenvalues and determinant maps in the lower panel. Dashed lines are zero contours. Solid lines represent boundaries in plain view of the prisms. Fig. 1b shows the theoretical gravity anomaly map due to these prisms. All prisms are defined with a density contrast of 1 g/cm 3. The theoretical gravity anomalies are calculated using the formula given by Banerjee and Das Gupta (1977) on a regular grid with a spacing of 0.5 km. In Fig. 2, thecggtcomponents(g xx, g xy and g yy ) of Bouguer anomaly map have been calculated using the method based on the FFT by Mickus and Hinojosa (2001). Mickus and Hinojosa (2001) computed the FFT of the vertical gravity component and from this determined the spectra of all elements of the gravity gradient tensor. Subsequently, the gradients are computed through an inverse FFT. Then the eigenvalues (λ 1, λ 2 ) and determinant have been calculated using Eqs. (7), (8) and (9). It is clear that the zero contours of the smallest eigenvalue λ 2 delineate the spatial location of the edges of the models, responding well to the edge locations, whereas the zero contours of eigenvalue λ 1 are placed outside the source region (Fig. 2). In addition, the zero contours of determinant map have been traced at near edge, as well as observed outside the source region. Note that inside zero contours of determinant map have the same results than those of λ 2 in determining the horizontal locations of the edges of the prism models. vertical-sided prisms. It is understood that these maps will not show the significant increase in the ambiguity even if the noise level is high. 4. Field example 4.1. General geology and tectonics of the Erzurum area The surface geology of the study area is largely covered by the Oligocene-Quaternary volcano-sedimentary sequence (Fig. 5). The 3.1. Noise analysis Fig. 3 illustrates the gravity anomalies of vertical prisms in Fig. 1a in case of the presence of noise. The data were contaminated with additive pseudorandom Gaussian noise with zero mean and a standard deviation of 0.3 mgal. The CGGT components were then calculated from the gravity anomalies with noise, and were therefore obtained noisy. We have illustrated CGGT components, and eigenvalues and determinant maps from these components in Fig. 4. Fig. 4 contains a series of images that illustrates the CGGT maps computed from Fig. 3 in case of the presence of noise. The eigenvalues and determinant maps were obtained from CGGT maps with noise. It is clear that λ 1, λ 2 and determinant maps are least susceptible to noise, and work well in imaging the edges of Fig. 3. Gravity anomalies with Gaussian noise, generated from distributed random numbers with a standard deviation of 0.3 mgal.

4 108 B. Oruç et al. / Journal of Applied Geophysics 88 (2013) Fig. 4. The curvature gradient tensor maps (g xx, g xy, g yy ), eigenvalues (λ 1, λ 2 ) and determinant maps computed from gravity anomalies with noise in Fig. 3. Dashed lines are zero contours. crystalline basement in the central part of the study area is a complex high-grade metamorphic rocks. The Quaternary-aged alluvial deposits cover all units unconformably. The sediment thickness, which is the sum of all six stratigraphic units, is about 6.5 km in the region (Şaroğlu and Güner, 1981). The main structural grain of the Erzurum area is NE SW trending structures which are mainly widespread in the area as a result of phases of strike-slip faulting. As shown in Fig. 5, NE SW trending faults or zones have mapped in Erzurum area and they are associated with neotectonic deformation after Plio-Quaternary (Koçyiğit et al., 2001). The main fault zones are Çobandede Fault Zone (ÇFZ) and Dumlu Fault Zone (DFZ) which are lateral strike-slip faults (Koçyiğit et al., 2001). The ÇFZ includes both right and left lateral strike-slip conjugate faults sets. The left lateral strike-slip faults included in the fault zone are dominant (Koçyiğit et al., 1985). The smallest left lateral strike-slip fault basin, which is the contemporaneous with the initiation of faulting, has been developed on the southern block of the ÇFZ in the study area. The basement of this basin has been underlain by the Lower Cretaceous aged ophiolitic mélange (Koçyiğit et al., 1985). The old basement in this basin is overlain by a thick continental sequence alternated with the volcanic. The DFZ cuts and deforms Plio-Quaternary basin fill and volcanic rocks of both the NW part of the east Anatolian plateau, and the E SE parts of the east Pontides and has sinistral strike-slip faults formed after Late Miocene, or during the Plio-Quaternary neotectonic period (Koçyiğit et al., 2001) Gravity data The acquisition of gravity data in the study area was carried out by the Turkish Petroleum Company (TPAO) in order to assist with mapping and delineation of anomalous sources with the occurrence of oil and gas formation in the Erzurum-Pasinler-Horasan basin. Detailed reconnaissance gravity surveys in the study area were conducted using a station spacing of 0.5 km with an accuracy of 0.01 mgal. Fig. 6 shows the Bouguer anomaly map covering a portion of the Erzurum area. The Bouguer anomaly map of the study area is characterized by a broad negative gravity low indicating basin structure and low density distribution. The gravity anomalies have generally different wavelengths and amplitudes, denoting the different density contrasts of the Erzurum basin infill. Thus, the Bouguer anomalies are well correlated with the grabens and structural uplifts filling the sediment units. The large negative Bouguer anomaly (~185 mgal) in the central portion of the map is located where the sediments are the thickest CGGT components of Bouguer anomaly data The gravity anomaly map was pre-processed to prepare for analysis and interpretation. The reason for this pre-processing is that the major features in the data which may be defined by the edges and minor features that are not easily seen in the original image are to detect. In order to calculate CGGT components from the Bouguer anomaly map, the method developed by Mickus and Hinojosa (2001) was used. Fig. 7 shows the CGGT components from the Bouguer anomaly map. The CGGT components allow assembling of an overview of all buried 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 Erzurum-Pasinler-Horasan basin. The pattern of the high-gradient anomalies in CGGT maps is sharp anomalies which may be produced by buried boundaries. The NE SW trending high-gradient zones confirm these variations and attribute to the presence of discontinuities in the anomaly pattern. As shown in Fig. 8, the zero of smallest eigenvalue proves identification of the curvilinear trends within the buried basement uplifts and contains a well-defined gravity maximum that continues these trends.

5 B. Oruç et al. / Journal of Applied Geophysics 88 (2013) Fig. 5. Simplified geological map showing major compressional and extensional structures (modified from Koçyiğit et al., 2001) and location map of the study area. KÇFZ, Kelkit-Çoruh fault zone; TAFZ, Tercan-Aşkale fault zone; KBF, Kavakbaşı fault; HKB, Hasankale basin; HB, Horasan basin; ÇFZ, Çobandede fault zone; DFZ, Dumlu fault zone; MF, Malazgirt fault; KYF, Karayazı fault; TF, Tutak fault; KGF, Kağızman fault; HF, Horasan fault; LDF, Leninakan-Digor fault; SF, Süphan fault; EF, Erciş fault; HTF, Hasantimur Lake fault; BGF, Balık Lake fault; DF, Doğubeyazıt fault;if,iğdır fault; AF, Aras fault; EFZ, Erevan fault zone; PSFZ, Pambak-Seven fault zone Comparison of smallest eigenvalue with TDR and HGM of the gravity anomalies In order to compare with the locations obtained from the smallest eigenvalue zeros of the study area, we have used the TDR and HGM images. The HGM is a commonly used edge detection filter, the rate of change of the gravity field in the x and y directions and is given by Cordell and Grauch (1985): s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi g 2 HGM ¼ þ g 2 x y ð8þ Fig. 6. Bouguer gravity anomaly map of the Erzurum-Pasinler-Horasan area. The maxima of HGM highlight high-gradient locations, such as structural boundaries. However, Cordell and Grauch (1985) discussed the limitations of the HGM for gravity anomaly data and concluded that, the maxima of HGM can be offset from a horizontal location directly overtheedgesiftheedgesarenotnear-verticalandclosetoeachother. Verduzco et al. (2004) developed the tilt angle filter or tilt derivative (TDR) for potential fields. For gravity application, this filter is defined as TDR ¼ tan 1! g z HGM ð9þ

6 110 B. Oruç et al. / Journal of Applied Geophysics 88 (2013) Fig. 7. The CGGT components computed from Bouguer gravity anomaly of study area. where g/ x, g/ y and g/ z are the first derivatives of the field f in the x, y and z directions. Thus, a map of TDR can be considered an image of the tangent of the angle. The first horizontal gradients and vertical gradient of the Bouguer anomaly have been calculated by using the FFT algorithm developed by Gunn (1975). The first vertical gradient map is illustrated in Fig. 9a. As shown in Fig. 9b, mapping local maxima of the HGM of Bouguer anomaly can be used to locate structural boundaries. In Fig. 6, we observe that the pattern of the high-gradient anomalies is broad, not like sharp ones of vertical boundaries. Thus, it is concluded that the study area represents anomalies caused by a range with boundaries, are not vertical and relatively deep. The local maxima on HGM map coincides with zero contours of TDR (Fig. 9c). Fig. 10a and b shows the comparison of smallest eigenvalue zero contours with HGM maxima and TDR zero contours, respectively. It should be noted that all techniques provide similiar results in determining the edges of anomalous sources by producing only minor changes Three-dimensional inversion of Bouguer anomaly data The knowledge of the basement in continental areas is of crucial interest in many applications of geosciences. The structural elements of the basement can be useful in investigating the petroleum exploration and regional geodynamical studies. In this study, we used Parker Oldenburg inversion method (Gomez and Agarval, 2005; Oldenburg, 1974; Parker, 1973) to image a sediment-basement interface from gridded Bouguer anomaly data. The method allows us to estimate basement depths in regional tectonics. The technique is based on FFT algorithm. Given the mean depth of the density interface and the density contrast between the two media, the three-dimensional geometry of the interface is iteratively calculated. The iterative process is terminated when a certain number of iterations has been accomplished or when the difference between two successive approximations to the topography is lower than a pre-assigned value as the convergence criteria (Gomez and Agarval, 2005). Once the topographic relief is computed from the inversion procedure, it is computed the gravity anomaly produced by topographic relief. In general, the computed anomaly must be very similar to observed anomaly. Reaching up to 6.3 km depth of crystalline basement of Horasan basin studies based on geological insight (Pelin et al., 1980; Şaroğlu and Güner, 1981) revealed that this region is hopeful in terms of hydrocarbon. In the inversion scheme, the modeling has been constrained by specifying 6 km as the depth to the middle reference surface. An average density contrast of 0.4 g/cm 3 between crystalline basement (~2.8 g/cm 3 ) and volcano-sedimentary rocks (~2.4 g/cm 3 ) has been selected. The smallest and greater cut-off frequency parameters are chosen as and km 1, respectively. The inversion process is iterated until a satisfactory agreement between observed and calculated gravity is obtained. Fig. 11 shows a reasonably good agreement between the observed (Fig. 11a) and calculated (Fig. 11b) anomalies from basement undulation (Fig. 11c). It is clear that the inferred basement configuration shows a general depression of the basement in the northern part of the study area. This configuration has also illustrated thick sediments which are volcano-sedimentary sequence which consists of andesitic-basaltic volcanic rocks and marine sedimentary clastics. In large part, the gravity anomalies arise principally from variations in basement topography. Thus, one can easily conclude that gravity anomalies are correlated with basement topography. A major uplift of Erzurum-Horasan-Pasinler basin is placed at the northeastern of the study area. The bedrock topography shallows southwards and northwards, and reaches a 3.45 km. The most significant feature of the map is the ENE WSW trending basement depression bounded by NW-SW lineament. In general, note that boundaries between uplifts and grabens in the basement undulation have been generated by evolution of fault zones from structural disorder towards geometrical simplicity. Basement topographic high is associated with the anticlines and roughly NW-striking basement trough plunges into the series of basins. In order to better interpret the edge positions related to the basement undulations, we compare the results obtained from the zero contours of smallest eigenvalue and basement modeling from 3D inversion. Fig. 12 shows some detail in the area, supporting the structural complexity. The performance of two techniques is almost the same, containing the effects in determining the undulated bedrock Fig. 8. The smallest eigenvalue map (λ 2 ) of Bouguer anomaly map in Fig. 6. Dashed lines show the zero contour which corresponds to boundary curves.

7 B. Oruç et al. / Journal of Applied Geophysics 88 (2013) Fig. 9. (a) The first vertical gradient, (b) HGM, and (c) TDR images of the Erzurum area. Dashed lines show the zero contour of the TDR. topography (Fig. 12a). It should be noted that the zero contours only correspond to the edges along uplifted bedrock topography. Thus, it is therefore understood that the zero contours of smallest eigenvalue have imaged by tracking of the uplifted edges of basement topography. In Fig. 12b, the faults are superimposed on the depths to basement undulation. It is interesting that good correlations have been obtained between the basement undulation from 3D gravity inversion and known faults in the study area. In general, it is clear that Fig. 10. Comparison of smallest eigenvalue zero contours with (a) HGM computed from Bouguer anomaly data and (b) TDR zero contours of the study area.

8 112 B. Oruç et al. / Journal of Applied Geophysics 88 (2013) structural features may be located in the pathway of oil and gas, which migrates to maximize its trapping potential. On the regional scale, a structural high must be in close proximity to a structural low (Pratsch, 1986). That's why structural highs near structural lows are the preferred targets. There is currently renewed intense geological and geophysical interest in the exploration for oil and gas in the Erzurum-Pasinler-Horasan basin. We suggest that future research explore on the basement relief for a new oil and gas reservoirs. The occurrence of deep oil and gas formation in the subsurface (>3.45 km) can be expected to find preserved accumulations. 5. Conclusions Fig. 11. Observed Bouguer anomaly (a), Bouguer anomaly (b) computed from depths to the basement (bottom) derived from inversion of Bouguer anomalies using Parker Oldenburg's algorithm (c). Note that considerable similarity exists between the observed and calculated gravity. structural deformation of basement has well correlated with known faults. However, ÇFZ, DFZ and HF fault have partly shifted under the indentation pressure of the basement. As is well known, the basins became complicated geologic units with a series of basement highs, and lows or associated faults. Such Our main contribution in this study has been to present the effectiveness of the CGGT and 3D inversion results for the interpretation of gravity data. The results coming out of this study facilitate the identification of new features as well as the mapping of known main trends that represents Erzurum-Pasinler-Horasan basin. The CGGT components provide information about subsurface features that cannot be inferred from the only vertical component of the gravity field since curvature of the vertical component has higher frequency content than the field itself and can potentially provide better contact locations. Thus, the CGGT data contribute to a detailed model of edges of basement undulation. The smallest eigenvalue obtained from CGGT matrix has clear indications of utility to infer the location of the boundaries of lithologies since the analysis of this eigenvalue is only based on the zero contour. So we can say from this example that zero contour of λ 2 is an elegant solution to extract image features from gravity anomalies such as edge enhancement which require knowledge of only the zero contours of smallest eigenvalue of a CGGT matrix. The fault pattern in the basement beneath a sedimentary basin can be unraveled by analyzing the basement undulation obtained by inverting gravity data. In Erzurum area, significant hydrocarbon finding in stratigraphic sequence has not been established largely because substantial thickness of sediments exists. Application of the CGGT data and 3D gravity inversion to the gravity data of the Erzurum area has showed that the basement highs, lows, and the major faults in the direction NE SW and E W fracture systems of the basement. It is possible to conclude that the potential new oil and gas reservoirs in the study area of the Erzurum basin will be likely associated with these features. Prior to the comparatively very expensive exercise of acquisition and analysis of seismic data in the exploration for oil Fig. 12. Comparison of depths to the basement with zero contours (dashed lines) of smallest eigenvalue λ 2 (a) and tectonic lineaments (b). Dashed lines represent lineaments interpreted from the zero contours.

9 B. Oruç et al. / Journal of Applied Geophysics 88 (2013) and gas in sedimentary basins it is common recommendation to conduct preliminary investigations using CGGT data and 3D inversion. Acknowledgements The authors are thankful to the Turkish Petroleum Company (TPAO) for supplying gravity data. Thanks are also due to two anonymous reviewers for their valuable comments and suggestions. References Banerjee, B., Das Gupta, S.P., Gravitational attraction of rectangular parallelepiped. Geophysics 42, Beiki, M., Pedersen, L.B., Eigenvector analysis of gravity gradient tensor to locate geologic bodies. Geophysics 75, I37 I49. Boring, E., Visualization of Tensor Fields. Master's thesis, University of California, Santa Cruz, USA. Cordell, L., Gravimetric expression of graben faulting in Santa Fe country and the Espanola Basin, New Mexico. New Mexico Geol. Soc. Guidebook, 30th Field Conf, pp Cordell, L., Grauch, V.J.S., Mapping basement magnetization zones from aeromagnetic data in the San Juan Basin, New Mexico. In: Hinze, W.J. (Ed.), The utility of regional gravity and magnetic anomaly maps: Soc. Explor. Geophys., pp Foss, C.A., Mapping basement relief with airborne gravity gradiometri. ASEG 15th Geophysical Conference and Exhibition, Brisbane. Gomez, D., Agarval, B.N.P., DINVER.M: a MATLAB program to invert the gravity anomaly over a 3D horizontal density interface by Parker Oldenburg's algorithm. Computers and Geosciences 31, Gunn, P.J., Linear transformations of gravity and magnetic fields. Geophysical Prospecting 23, Hansen, R.O., deridder, E., Linear feature analysis for aeromagnetic data. Geophysics 71, L61 L67. Koçyiğit, A., Öztürk, A., İnan, S., Gürsoy, H., Karasu havzasının (Erzurum) tektonomorfolojisini ve mekanik yorumu. Cumhuriyet Univ., J. Engineer. Fac., Seri A-Earth Sci. 2, Koçyiğit, A., Yılmaz, A., Adamia, A., Kuloshvili, S., Neotectonics of East Anatolian Plateau (Turkey) and Lesser Caucasus: implication for transition from thrusting to strike-slip faulting. Geodinamica Acta 14, Mataragio, J., Kieley, J., Application of full tensor gradient invariants in detection of intrusion-hosted sulphide mineralization: implications for deposition mechanisms. First Break 27, Mickus, K.L., Hinojosa, J.H., The complete gravity gradient tensor derived from vertical component of gravity: a Fourier transform technique. Journal of Applied Geophysics 46, Murphy, C.A., The Air-FTG airborne gravity gradiometer system. In: Lane, R.J.L. (Ed.), Airborne Gravity 2004-Abstracts from the ASEG-PESA Airborne Gravity 2004 Workshop: Geoscience Australian Record, 18, pp Murphy, C.A., Interpreting FTG Gravity data using horizontal Tensor components: EGM 2007 International Workshop-Innovation. EM, Grav. and Mag. methods: new Perspective for Exploration. Murphy, C.A., Brewster, J., Target delineation using full tensor gravity gradiometry data. ASEG, Extented abstracts. Murphy, C.A., Dickinson, J.L., Geological mapping and targeting using invariant tensor analysis on full tensor. EGM 2010 International Workshop, Adding new value to electromagnetic, gravity and magnetic methods for exploration. Oldenburg, D.W., The inversion and interpretation of gravity anomalies. Geophysics 39, Parker, R.L., The rapid calculation of potential anomalies. Geophysical Journal of the Royal Astronomical Society 31, Pelin, S., Özsayar, T., Gedik, İ., Tokel, S., Geological ınvestigation of pasinler (Erzurum) basin for oil. MTA 729, Pratsch, J., The distribution of oil and gas reserves in major basin structures: an example from the Powder River basin, Wyoming, USA. Journal of Petroleum Geology 9, Phillips, J.D., Hansen, R.O., Blakely, R.J., The use of curvature in potential-field interpretation. Exploration Geophysics 38, Roberts, A., Curvature attributes and their application to 3D interpreted horizons. First Break 19, Şaroğlu, F., Güner, Y., Doğu Anadolu'nun jeomorfolojik gelişimine etki eden öğeler: Jeomorfoloji, volkanizma ilişkileri. TJK Bülteni 24, (in Turkish). Verduzco, B., Fairhead, J.D., Green, C.M., Mackenzie, C., New insights into magnetic derivatives for structural mapping. The Leading Edge 23,