B15 Enhancement of Linear Features from Gravity Anomalies by Using Curvature Gradient Tensor Matrix

Transcription

1 B5 Enhancement of Linear Features from Gravity Anomalies by Usin Curvature Gradient Tensor Matrix B. Oruç* (Kocaeli University) SUMMARY In this study, a new ede enhancement technique based on the eienvalues and determinant from the curvature radient tensor matrix (CGTM) has been described. The performance of the technique has been tested by usin theoretical examples. It has been shown that the zero values of smallest eienvalue of CGTM are suitable for mappin in source boundaries with a hih resolution. The method has been applied to CGTM computed from the ravity anomaly data from Aydın-Germencik eothermal area in the western reion of Turkey. The small eienvalue provides a detailed imae of the edes of basin and uplift and therefore ive the results which tend to structural trends. I have also compared the Euler deconvolution (ED) position estimates with the small eienvalue map obtained from the CGTM of residual ravity anomaly. Both techniques have areed in detectin the basin and uplift edes in the subsurface. 6 th Conress of Balkan Geophysical Society - Budapest, Hunary 3-6 October 0

2 Introduction Linear eoloic features, such as faults and contacts, are important since they reflect as lineaments in potential filed data. The automated interpretation of potential-field data is aided by evaluatin the curvature radient tensor matrix (CGTM). Hansen and de Ridder (006) described a linear feature analysis usin manetic data. Murphy (007) has demonstrated such lineament analysis by extractin anomalous sinature patterns arisin from eoloical contact information definin an ede of salt some. Philips et al.(007) have developed special functions of potential-field anomalies that produce peaks or ride crests over a variety of isolated sources. This study describes a new ede enhancement technique based on the eienvalues and determinant from the CGTM. The performance of the technique has been tested by usin theoretical examples. It has been shown that the zero values of smallest eienvalue of CGTM are suitable for mappin in source boundaries with a hih resolution. The method has been applied to CGTM computed from the ravity anomaly data from Aydın-Germencik area in the western reion of Turkey. Durin processin, residual ravity anomaly map has been computed by removin a four-order polynomial surface from the Bouuer anomaly map. The small eienvalue provides a detailed imae of the edes of basin and uplift and therefore ive the results which tend to structural trends. These results were compared with two-dimensional Euler deconvolution (ED) position estimates. Method The CGTM is expressed as x x x y xy Γ = CGTM = =, () y y yx x y where x and y is the horizontal ravity vector (Hansen and deridder, 006). CGTM, bein a symmetric matrix, can be diaonalized as V T ΓV =, () where V = v v ] and [ λ 0 = (3) 0 λ represent eienvectors and eienvalues, respectively. The eienvalues λ of the CGTM satisfy λ xy det( Γ λi ) = = 0 (4) yx λ and are iven by = + + ( ) + λ 4 xy (5) ( ) λ = xy. (6) It is well known that the product of the eienvalues of a square matrix is equal to the determinant of that matrix. It is det( Γ ) = λ λ. (7) 6 th Conress of Balkan Geophysical Society - Budapest, Hunary 3-6 October 0

3 Theoretical Examples Fiure shows the robustness of the proposed technique is tested with eien values and determinant of ravity anomaly map caused by three vertical-sided prisms at a depth to the top of km (labeled ), 0.5 km (labeled ), and 0.5 km (labelled 3). The theoretical ravity anomalies of the vertical sided prisms are calculated usin the formula iven by Banerjee and Das Gupta, 977 on a reular rid with a spacin of 0. km. All models are defined with a density contrast of /cc. The CGTM components, necessary for the calculation of Eq. (5) and (6), have been calculated usin the method based on the FFT by Mickus and Hinojosa (00). While the small eienvalue λ is positive inside the source reion, the zero contours delineate the spatial location of the edes of the models, althouh the models are located at the different depths. The zero and neative contours of the lare eienvalue λ were traced outside the source reion. It is interestin to note that the determinant map with zero contours inside of other zero contours locate source edes. This map is positive inside the source reion. Fiure Theoretical ravity anomaly map () and the plan view of the top edes of the vertical prism models. The eienvalue λ map from Eq. (5) and λ map from Eq.(6). Dashed lines indicate the zero contour. Note that the zero contour of the small eienvalue λ and inside zero contour of determinant map locate the positions of the source edes. 6 th Conress of Balkan Geophysical Society - Budapest, Hunary 3-6 October 0

4 Field Example Fiure a shows that the Bouuer anomaly data of the Aydın-Germencik area were obtained from the General Directorate of Mineral Research and Exploration, Turkey. Residual ravity anomalies were computed by removin a four-order polynomial surface from the Bouuer anomaly map and shown in Fiure b. It should be noted that Fiure b shows ravity contours with NW-SE trends. Germencik area is a eothermal reion. The central of the survey area is characterized by positive and neative ravity anomalies. These anomalies are presumably produced by lon linear NW-SE trendin structural features in the basement complex beneath the sediments. Fiure 3 shows that the CGTM components from Fiure b and the small eienvalue λ map. The λ map delineates the spatial location of the edes of the basin and uplift. Fiure (a) The complete Bouuer anomaly map of Germencik-West Anatolia reion, and (b) residual ravity map computin by removin four-order polynomial surface from Bouuer data. Fiure 3 The CGTM components computed from Fiure b, and the λ map from the CGTM components. The dashed lines represent the zero contour of the λ and refer to the edes of the basin and uplift. The solid line and vertical arrows are the position of the profile and crossin points, respectively. Note the hot sprins are located near the edes. 6 th Conress of Balkan Geophysical Society - Budapest, Hunary 3-6 October 0

5 Applyin Euler s Equation (Thompson, 98) to the first vertical ravity radient provides a solution: ( x x0 ) + ( z z0 ) = N. (8) x z z z N is the structural index, which characterizes the source eometry. If the N value is known, the source location and depth ( x 0, z 0 ) can be determined. z is the observation plane. A 5-point window is used to form simultaneous equations for the two unknowns, and solved these equations by a least squares method and is illustrated in Fiure 4. Fiure 4 Gravity anomaly () from Fiure b in accordance with the position of the profile in Fiure 3, and its vertical radient ( z ). The solutions of D Euler deconvolution applied to the vertical ravity radient usin a structural index N=0.5. Note the best clusterin for source positions indicates eneral trends associated with the lineaments. The clusters at crossin points (vertical arrows) refer to approximately the lineaments from the eienvalue λ in Fiure 3. Conclusions Main contribution in this study has been to present the effectiveness of the eienvalues and determinant from CGTM for the interpretation of ravity data. The small eienvalue λ has been able to map the edes of eoloical features. The zero contours of λ provide ood visual map in imain the subtle lineaments and are therefore interpreted easily. References Hansen, R.O., and E. de Ridder, 006. Linear feature analysis for aeromanetic data, Geophysics 7, L6 L67. Mickus, K.L., and J.H. Hinojosa, 00. The complete ravity radient tensor derived from vertical component of ravity: A Fourier transform technique, J. Appl. Geophys. 46, Thompson, D.T., 98. EULDPH: a technique for makin computer assisted depth estimates from manetic data, Geophysics 47, Murphy, C.A., 007. Interpretin FTG Gravity data usin horizontal Tensor components: EGM 007 International Workshop Innovation in EM, Grav and Ma methods: new Perspective for Exploration. 6 th Conress of Balkan Geophysical Society - Budapest, Hunary 3-6 October 0