TY - JOUR
AU - Yiğitbaş,, Erdinç
AB - Abstract Approximating the locations and lateral boundaries of anomalous bodies (i.e. geological structures or contacts) is an important task in the interpretation of gravity field data. Edge-approximating algorithms based on the computation of directional derivatives are widely used for enhancing the gravity anomalies of the source bodies. These algorithms effectively aid geological mapping and interpretation by locating abrupt lateral changes in density, and may also bring out subtle details in the data without specifying any prior information about the nature and type of the sources. Therefore, some model parameters of source bodies may be estimated in this way, which may guide the inverse modelling procedure. In this paper we aim to review the effectiveness of the commonly used edge-approximating algorithms such as vertical derivative, total horizontal derivative, analytic signal, profile curvature, tilt angle and theta map in terms of their accuracy on the determination of locations and lateral boundaries of source bodies. These detections were performed on both noise-free and noisy synthetic gravity data. Additionally, a real gravity data set from a well-known geological setting, the Aegean graben system (western Turkey), was considered and the derived anomaly maps were compared with known mapped geology. 93.85.Hj gravity anomalies, edge approximation, directional derivatives, geological contacts, Aegean graben system 1. Introduction Subsurface geology can be investigated by means of gravity surveys based on measuring the variations in the Earth's gravitational field arising from density differences between subsurface rocks. Gravity surveys can be performed in the investigations of both large- and medium-scale geological structures (Paterson and Reeves 1985). This method has been used extensively for oil and gas exploration, particularly in the early 20th century (Reynolds 1997). Additionally, many other applications of the use of the gravity method have been reported so far, such as regional geological studies, subsurface modelling studies, isostatic compensation determination, geodesic and seismological studies, exploration for mineral deposits, basin researches, detection of subsurface cavities and archaeo-geophysical studies (particularly microgravity), determination of glacier thickness, hydrogeological and environmental studies, and engineering applications (e.g. see references in Reynolds (1997) and in Kearey et al (2002)). The most important task in the interpretation of gravity field data is to determine the model parameters of source bodies such as location, size, extension, thickness, depth and density. If the data quality permits, many analysing procedures can be carried out that help to build a general understanding of these details. For this purpose, numerous inverse modelling algorithms are widely used for the determination of the model parameters mentioned above. Unfortunately, the non-uniqueness nature of the problem is more pronounced in the inverse modelling of potential field data (Ekinci 2008a, 2008b). Namely, according to Gauss theorem, if the potential field is known only on a bounding surface, there are infinitely many equivalent source distributions inside the boundary that can produce the same field (Li and Oldenburg 1996). However, a common way of overcoming this problem is to add prior information to constrain the solution. Gravity and magnetic field data sets can be transformed into some special functions that improve peaks and ridges over isolated source bodies (Phillips et al2007). To this end, many techniques based on the use of the directional (horizontal and vertical) derivatives of the potential field have been developed and proposed in order to estimate model parameters such as edges of the source bodies (i.e. lateral boundaries). Edge-approximating techniques not only describe lateral variations in lithology, but also yield information on structural systems and deformation styles (Zhang et al2011). Thus, these algorithms are used routinely in the visual interpretation of potential field anomaly maps to delineate the main geological bodies, geological contacts, subtle geological features, geological structures and alignments, as well as textural information about geological domains (Boschetti 2005). Edge-approximating techniques are generally based on the position of extreme or zero points using vertical or horizontal derivatives, analytical signal amplitude, or their various combinations (Wanyin et al2009). The information and findings obtained by the use of these techniques may be used as prior information which may guide inverse modelling procedure (Boschetti et al2001, Poulet et al2001, Sailhac and Gilbert 2003). As faster computers, effective commercial software packages and open source codes have become widely available due to technological developments in computational procedures during the last decade, thus edge-approximating techniques are being used more extensively (Kaya et al2007, Salem et al2008, Ateş et al2012, Balkaya et al2012). Moreover, the most important advantage is that the computation procedures do not require an assumption about the type of source body and the nature of the source. In this study, the effectiveness of commonly used edge-approximating techniques such as vertical derivative (VD), total horizontal derivative (THD), analytic signal (AS), profile curvature (PCR), tilt angle (TA) and theta map (TM), which are based on the use of horizontal and vertical derivatives or their various combinations, were compared in terms of their accuracy on the determination of locations and lateral boundaries of source bodies. Since the derivative-based filters tend to be dominated by the effects of noise, numerical simulations were performed on both noise-free and noisy synthetic gravity data generated by three-dimensional prismatic model bodies. In order to obtain optimum results, a case study was also performed with a real gravity data set obtained from a well-known geological setting, the Aegean graben system (western Turkey). 2. Edge-approximating algorithms This section describes the mathematical background of the edge-approximating algorithms. A MATLAB-based toolkit (Ekinci 2010, Ekinci and Yiğitbaş 2012) was used for the application of these algorithms and for the computation of synthetic gravity data caused by three-dimensional, vertical-sided prismatic bodies. The computations of the first VDs of gridded data, used in VD, AS, TA and TM operators, were performed in a wavenumber domain using a fast Fourier transform based on the method given by Blakely (1995). As is well known, the transformation inherently assumes that a grid is periodic, in effect repeating itself infinitely many times in all horizontal directions, which tends to cause undesirable edge effects if the edges of the data grid do not meet smoothly with their repetitive neighbours (Blakely 1995). Thus, in this study, to eliminate the discontinuities at the edges, the size of data grid was augmented to the next higher power of 2 by adding artificial data bands to the east and north edges of the data grid prior to the fast Fourier transform. The extra data bands were removed at the end of the operation. Horizontal derivatives and second-order horizontal derivatives used in the computation of edge-approximating operators were estimated using some equations based on simple finite-difference methods (Blakely 1995, Carnahan et al1969). The source codes of the edge-approximating algorithms and three-dimensional forward calculations are available from the first author on request. 2.1. VD operator VD image maps help to resolve and emphasize the shallow source bodies. In VD anomaly maps the contour values close to zero may indicate the lateral edges of the source bodies (Xu et al2011). The computation procedure is performed in a wavenumber domain using a fast Fourier transform. The procedure is framed as a three step filtering procedure. First, a fast Fourier transform of the potential field data is performed. At the second stage, transformed data are multiplied by the VD filter. The final step involves performing the inverse fast Fourier transform of the product. The definition of the VD operator is given by Blakely (1995) as follows: 1 where g is the gravity field, e is the exponential function and F(g) is the Fourier transformed grid data. Thus the first-order VD is equal to the Fourier transform of the potential times |k|, as given below (Blakely 1995): 2 where F-1 is the inverse Fourier transform and |k| is the radial wavenumber at grid intersections throughout the kx and ky plane. |k| is defined by following equation (Blakely 1995): 3 2.2. THD operator The THD amplitudes (the most commonly used source edge detection algorithm) of the gravity anomalies tend to produce maxima located almost over the lateral edges of the source bodies (Cordell and Grauch 1985, Blakely and Simpson 1986, Blakely 1995). The extreme values of the THD amplitudes on the grid plane are used to locate the lateral boundaries of the source bodies. For a gridded data set, the definition of THD amplitude is given as follows: 4 where g is the gravity field. Horizontal derivatives in equation (4) can be easily estimated using a simple finite-difference method and discrete measurements of g(x, y), as follows (Blakely 1995): 5 6 where i and j represent the discrete measurements of g(x, y)on the observation plane at uniform sample intervals Δx and Δy. 2.3. AS operator The AS amplitude, a complex quantity, is formed through a combination of the horizontal and VDs of the potential field data. The maxima locations in the AS anomaly map are used to locate the lateral edges of source bodies on the grid plane. Generally, VDs are computed in the wavenumber domain using fast Fourier transforms as given previously in equation (2), and the horizontal derivatives can be computed in both the space domain using differences (equations (5)–(6)) and the wavenumber domain using fast Fourier transform techniques (Blakely 1995). The equation for the AS amplitude is given by Roest et al (1992) as follows: 7 where g is the gravity field. 2.4. PCR operator Curvature analysis techniques have been applied to some geophysical data sets in the last decade (e.g. Blumentritt et al2006, Phillips et al2007, Cooper 2009, Lee et al2012). Curvature analysis techniques have generally been applied to the seismic reflection profile and three-dimensional seismic data volume in seismic data interpretation, and to topographic surfaces for drainage basin analysis (see the references in Lee et al (2012)). However, the technique has rarely been applied to potential field data. Thus we reviewed the response of the technique on the gridded potential field data. The curvature analysis can be defined in different forms for gridded data sets, and in this study the definition of Mitasova and Hofierka (1993) was used for the procedure. The PCR operator is defined by the following equation: 8 where g is the gravity field. The horizontal derivatives can be computed by using equations (5) and (6). The second-order horizontal derivatives in equation (8) can be defined as follows (Carnahan et al1969): 9 10 At each point in the field data, the PCR operator measures the rate of change of the slope in the direction of the steepest gradient (Cooper 2009). The operator produces a zero contour value at the source edge and either a local maxima or minima over the source (Lee et al2012). Thus PCR amplitudes can be used to locate the lateral edges of gravity source bodies. 2.5. TA operator The TA operator can be briefly explained as an amplitude normalized VD. Due to the nature of the arctan trigonometric function, the output values of the procedure are limited to values between –π/2 and π/2. The TA operator uses the zero-point location to approximate the lateral edge location of causative geological bodies on the grid plane (Wanyin et al2009). Because the TA operator is based on the ratio of derivatives, it enhances both large and small amplitude anomalies well (Cooper and Cowan 2008). The computation procedure of the TA operator can be expressed as the following equation (Miller and Singh 1994), where g is the gravity field: 11 The VD and horizontal derivatives in equation (11) can be computed by using equations (2), (5) and (6), respectively. 2.6. TM operator The TM operator is pronounced as an effective processing tool for delineating subsurface geological contacts, and the operator uses the AS amplitude to normalize the THD. The operator enhances the edges of the source bodies of all azimuths on the grid plane using a trigonometric function like the TA operator. Although the technique restricts the range of angles between 0 and π/2, it may produce well-defined images (Wijns et al2005). The normalization process introduces effective gain control and the definition of the procedure is given as follows (Wijns et al2005): 12 where g is the gravity field. Equations (2), (5) and (6) can be used for the computation of the amplitudes of vertical and horizontal derivatives. 3. Test studies 3.1. Synthetic data A synthetic data set was generated by considering two vertical-sided prisms to test the effectiveness of the proposed edge-approximating algorithms mentioned above. As is well known, in order to approximate a volume of mass, considering a rectangular prism is one of the most simple ways. The gravitational attraction of a single rectangular prism can be computed by integration over the limits of the prism (Blakely, 1995) and the following derived equation can be used for the procedure (Plouff 1976): 13 where ρ is the density contrast and γ is the gravitational constant. The other terms are given by: 14 15 3.2. Noise-free synthetic data example By using equation (13), the gravity response of two vertical-sided prisms was generated for the test studies. We used a 0.1 km × 0.1 km grid for three-dimensional forward modelling. Model parameters of the source bodies are given in table 1. Figures 1(a) and (b) show the synthetically generated noise-free gravity anomaly map and the plan view of three-dimensional prismatic model bodies, respectively. Note that model 2 produced a low-amplitude anomaly in comparison to model 1, due to its depth and thickness. Figure 1. Open in new tabDownload slide Synthetically generated gravity data set, consisting of the anomalies caused by three-dimensional prismatic source bodies (a); general plan view of the three-dimensional source bodies (b). Figure 1. Open in new tabDownload slide Synthetically generated gravity data set, consisting of the anomalies caused by three-dimensional prismatic source bodies (a); general plan view of the three-dimensional source bodies (b). Table 1. Model parameters of two prismatic bodies used for a synthetic data example. . Model parameters . Model number . x1 (km) . x2 (km) . y1 (km) . y2 (km) . h1 (km) . h2 (km) . ρ (g cm–3) . 1 14 19 13 18 0.1 0.6 0.05 2  7 12  3  8 0.2 0.6 0.05 . Model parameters . Model number . x1 (km) . x2 (km) . y1 (km) . y2 (km) . h1 (km) . h2 (km) . ρ (g cm–3) . 1 14 19 13 18 0.1 0.6 0.05 2  7 12  3  8 0.2 0.6 0.05 Open in new tab Table 1. Model parameters of two prismatic bodies used for a synthetic data example. . Model parameters . Model number . x1 (km) . x2 (km) . y1 (km) . y2 (km) . h1 (km) . h2 (km) . ρ (g cm–3) . 1 14 19 13 18 0.1 0.6 0.05 2  7 12  3  8 0.2 0.6 0.05 . Model parameters . Model number . x1 (km) . x2 (km) . y1 (km) . y2 (km) . h1 (km) . h2 (km) . ρ (g cm–3) . 1 14 19 13 18 0.1 0.6 0.05 2  7 12  3  8 0.2 0.6 0.05 Open in new tab Figure 2 demonstrates the obtained image maps from the application of edge-approximation operators. Figure 2(a) shows that VD amplitudes passed through zero directly over the edges of the source bodies. However, amplitude variations did not show a sharp transition from the edges towards the centres of the model bodies. Additionally the response of a deeper source body showed a less dramatic result than the shallower one (figure 2(a)). Figure 2(b) shows the anomaly map produced by the THD operator. Although the amplitude response of model 2 is slightly blurred due to the model's depth and thickness, extreme amplitude values clearly displayed the lateral edge locations of two model bodies where sharp transitions were observed from the edges towards the centres of the model bodies. Thus it can be stated that the THD operator produced better resolution at the edges than did the VD operator. Figure 2(c) demonstrates the responses of the model bodies using the AS operator. Amplitude responses of the model bodies are quite similar to the result of THD, but the image of the deeper body is less impressive than the image produced by the THD operator. Additionally, the decrease in AS amplitudes is less sharp than in THD amplitudes between the inner edges and the centres of the source bodies. The result of applying the PCR operator to the synthetic data set is illustrated in figure 2(d). Lateral edges of the prismatic bodies were successfully delineated by zero value between maxima and minima, but it needs to be noted that the response of the deeper body displayed a lower amplitude pattern in comparison to the shallower one. The image map (figure 2(e)) shows that although the zero values indicated the position of lateral edges, sharpened responses at the inner edges of the prismatic model bodies could not be observed by using the TA operator. Thus it may be stated that TA is not primarily an edge-approximation technique based on the obtained results from a noise-free synthetic example. Figure 2(f) indicates that the edges of the model bodies were uniformly enhanced by the use of the TM operator; even the model bodies do not have the same amplitude values in the original image map shown in figure 1(a) due to their depths and thicknesses. Moreover, a sharp amplitude transition was clearly observed from the edges towards the centres of the model bodies. Based on the results of the noise-free synthetic data example, it can be concluded that THD, AS, PCR and TM operators dramatically improved the lateral edges of the shallower model body while the TM operator clearly produced better resolution on the lateral edges of the deeper model body than the other ones did. Figure 2. Open in new tabDownload slide The results of edge-approximating algorithms applied to the synthetic data set shown in figure 1(a). VD image map of the synthetic data (a); THD image map of the synthetic data (b); AS image map of the synthetic data (c); PCR image map of the synthetic data (d); TA image map of the synthetic data (e); and TM image of the synthetic data (f). Figure 2. Open in new tabDownload slide The results of edge-approximating algorithms applied to the synthetic data set shown in figure 1(a). VD image map of the synthetic data (a); THD image map of the synthetic data (b); AS image map of the synthetic data (c); PCR image map of the synthetic data (d); TA image map of the synthetic data (e); and TM image of the synthetic data (f). 3.3. Noisy synthetic data examples In order to review the responses of the edge detectors on noisy data, we performed two simulations: one in which the synthetic data (generated by the model parameters given in table 1) were contaminated by high-level noise, and another in which the noise level was reduced somewhat by an upward continuation process. We used normally distributed pseudo-random numbers, with a mean value of 0.2 mGal and with a standard deviation of 0.04 mGal, to generate the artificial noise. A 0.2 km upward continuation process was performed on the contaminated grid data to attenuate the effect of the shortest wavelengths and to emphasize real-source anomalies by using the following equation (Blakely 1995): 16 where Δz is the upward continuation level and e is the exponential function. The other terms were given previously. The effect of the high-level noise is clearly recognized from figure 3(a). Figure 3(b) shows that the effects of the shortest wavelengths caused by the noise were attenuated somewhat, whereas the high-amplitude anomalies of the source bodies still remain. The responses of the edge detection algorithms to high-level noisy data are demonstrated in figures 4(a)–(f). The existence of a high-level noise THD operator produced greatly improved details on the edges of anomalous bodies, which can be clearly seen from figure 4(b). On the other hand, the PCR image map (figure 4(d)) shows that the response of the edges of the shallower body is dominated by very low resolution, and the edges of the deeper body were not resolved. The TM operator produced poorly resolved edges (figure 4(f)), but they seemed relatively sharper than the ones produced by the PCR operator. It can be clearly seen that sharpened responses at the inner and outer edges of the prismatic bodies could not be produced by VD and TA operators (figures 4(a) and (e)). Lastly the image map (figure 4(c)) shows that the AS operator could not produce any trace from either of the source bodies. Figure 3. Open in new tabDownload slide Image map of the high-level noisy gravity data set (a); and image map of the upward continued high-level noisy gravity data set (b). Figure 3. Open in new tabDownload slide Image map of the high-level noisy gravity data set (a); and image map of the upward continued high-level noisy gravity data set (b). Figure 4. Open in new tabDownload slide The results of edge-approximating algorithms applied to the noisy data set shown in figure 3(a). VD image map of the noisy synthetic data (a); THD image map of the noisy synthetic data (b); AS image map of the noisy synthetic data (c); PCR image map of the noisy synthetic data (d); TA image map of the noisy synthetic data (e); and TM image of the noisy synthetic data (f). Figure 4. Open in new tabDownload slide The results of edge-approximating algorithms applied to the noisy data set shown in figure 3(a). VD image map of the noisy synthetic data (a); THD image map of the noisy synthetic data (b); AS image map of the noisy synthetic data (c); PCR image map of the noisy synthetic data (d); TA image map of the noisy synthetic data (e); and TM image of the noisy synthetic data (f). As a final synthetic example, figures 5(a)–(f) show the result of applying edge-approximating algorithms to upward continued noisy data. Again, VD (figure 5(a)) and TA operators (figure 5(e)) could not produce sharper edges, and they enhanced the amplitude of the pseudo-random noise. On the other hand, the TM operator improved the edges of both source bodies well (figure 5(f)) but it notably amplified the pseudo-random noise in the area like the TA operator. Thus it can be mentioned that the use of a cosine function enhanced the edges of features of all azimuths, but it also enhanced the low-amplitude noise levels, which might make accurate edge mapping more difficult in the areas where source bodies do not produce high-amplitude anomalies. The image map obtained from the use of the AS operator (figure 5(c)) shows that the edges of the source bodies were not enhanced adequately. It is seen from figures 5(b) and (d) that the THD and PCR operators were much more successful in improving the edges than the others. More interestingly, although the PCR operator uses the second-order horizontal derivatives of the potential field data, the image map (figure 5(d)) shows that the noise level was not amplified. Consequently, this synthetic example showed that the PCR operator was found to be less susceptible to noise than the others when the noise level is not very high. Figure 5. Open in new tabDownload slide The results of edge-approximating algorithms applied to the upward continued noisy data set shown in figure 3(b). VD image map of the upward continued noisy synthetic data (a); THD image map of the upward continued noisy synthetic data (b); AS image map of the upward continued noisy synthetic data (c); PCR image map of the upward continued noisy synthetic data (d); TA image map of the upward continued noisy synthetic data (e); and TM image of the upward continued noisy synthetic data (f). Figure 5. Open in new tabDownload slide The results of edge-approximating algorithms applied to the upward continued noisy data set shown in figure 3(b). VD image map of the upward continued noisy synthetic data (a); THD image map of the upward continued noisy synthetic data (b); AS image map of the upward continued noisy synthetic data (c); PCR image map of the upward continued noisy synthetic data (d); TA image map of the upward continued noisy synthetic data (e); and TM image of the upward continued noisy synthetic data (f). 3.4. Real data example The test area considered for the real data example is located at the western part of the West Anatolia Extensional Province (WAEP; longitude 26°–29° and latitude 37°–39°) and covers an area of about 39 873 km2. Sharp topography in the area is reflected from young horst-graben geomorphology (figure 6). As is well known, WAEP is one of the most rapidly deforming continental regions in the world and is a part of the Aegean Extensional Province that extends from Bulgaria in the north to the Aegean arc in the south (Bozkurt 2003). Its relief is shaped by the late formation of core complexes and a horst-graben system. In western Anatolia, the most evident neotectonic features are E–W trending horsts known as Bozdağ horst (BH) and Aydın horst (AH), sediment filled grabens (Gediz graben (GDG), Küçük Menderes graben (KMG), Büyük Menderes graben (BMG)) and their basin-bounding active faults (figure 7). The less evident ones are NE–SW trending basins (Gördes basin (GB) and Selendi basin (SB) in figure 7) and their interposing horsts (Bozkurt 2001). Figure 6. Open in new tabDownload slide Simplified tectonic map and relief of the region and the study area (compiled with Yiğitbas et al (2004) and CGIAR-CSI GeoPortal (2012)). Abbreviations: SBT, Southern Black Sea Thrust; NAFZ, North Anatolian Fault Zone; NEAFZ, Northeast Anatolian Fault Zone; WAEP, West Anatolia Extensional Province; EAFZ, East Anatolain Fault Zone; DSFZ, Dead Sea Fault Zone; BH, Bozdağ Horst; AH, Aydın Horst; GDG, Gediz Graben; KMG, Küçük Menderes Graben; BMG, Büyük Menderes Graben; GB, Gördes Basin; SB, Selendi Basin. Figure 6. Open in new tabDownload slide Simplified tectonic map and relief of the region and the study area (compiled with Yiğitbas et al (2004) and CGIAR-CSI GeoPortal (2012)). Abbreviations: SBT, Southern Black Sea Thrust; NAFZ, North Anatolian Fault Zone; NEAFZ, Northeast Anatolian Fault Zone; WAEP, West Anatolia Extensional Province; EAFZ, East Anatolain Fault Zone; DSFZ, Dead Sea Fault Zone; BH, Bozdağ Horst; AH, Aydın Horst; GDG, Gediz Graben; KMG, Küçük Menderes Graben; BMG, Büyük Menderes Graben; GB, Gördes Basin; SB, Selendi Basin. Figure 7. Open in new tabDownload slide Simplified geological map of the study area (adopted from the MTA (General Directorate of Mineral Research and Exploration of Turkey) (2002) and Sözbilir et al (2011)). Abbreviations: BH, Bozdağ Horst; AH, Aydın Horst; GDG, Gediz Graben; KMG, Küçük Menderes Graben; BMG, Büyük Menderes Graben; GB, Gördes Basin; SB, Selendi Basin; SÇSZ, South Çine Shear Zone. Figure 7. Open in new tabDownload slide Simplified geological map of the study area (adopted from the MTA (General Directorate of Mineral Research and Exploration of Turkey) (2002) and Sözbilir et al (2011)). Abbreviations: BH, Bozdağ Horst; AH, Aydın Horst; GDG, Gediz Graben; KMG, Küçük Menderes Graben; BMG, Büyük Menderes Graben; GB, Gördes Basin; SB, Selendi Basin; SÇSZ, South Çine Shear Zone. The cause of the extension has been curiously debated for a long time and four views have been proposed so far: (i) a tectonic escape model: westward extrusion of the Anatolian Block since 12 Ma (late Serravalian) (Dewey and Şengör 1979, Şengör et al1985, Görür et al1995), (ii) a back-arc spreading model: back-arc extension by approximately southward movement of the Aegean Arc with the disputable onset age of 60.5 Ma (McKenzie 1978, Kissel and Laj 1988, Meulenkamp et al1988, 1994, Thomson et al1998), (iii) an orogenic collapse model: local extension by spreading and thinning of over thickened crust following the latest Paleocene collision across Neotethys during the latest Oligocene–Early Miocene (Dewey 1988, Seyitoğlu and Scott 1991, McClusky et al2000), (iv) a two-stage graben model: Miocene–Early Pliocene (orogenic collapse) and Plio-Quaternary (westward migration of the Anatolian Block) of the N–S extension (Koçyiğit et al1999, Bozkurt 2003, 2004). E–W and NE–SW trending basins are seismically active regions and are bounded by active faults as mentioned below, but GDG and BMG form a major set among them. Since they reveal the most pronounced and uninterrupted topographic escarpments that seem to be a footwall of steeply dipping active normal faults (figure 7), these grabens reflect the stress field of the N–S extension and its activity via numerous earthquakes (Şengör et al1985, Yılmaz et al2000). This crustal scale fault system trends over low-angle normal faults (detachment faults in figure 7) that dip northwardly along the southern edge of GDG and southwardly along the northern margin of BMG. At the southernmost edge of the area, a curve-shaped shear zone transects the Menderes Massif with south dipping as well (figure 7). Through the GDG, the footwall of the detachment faults consists of different lithologies belonging to metamorphic rocks of the Menderes Massif, described as Pre-Neogene basement in the text (figure 7). The hanging wall of the detachment fault is represented by a Miocene to Pliocene sedimentary sequence of clastics labelled as Neogene rocks and by Quaternary alluvium (figures 7 and 8, table 2). The total thickness of sedimentary fill of the GDG reaches up to roughly 2500 m (Çiftçi and Bozkurt 2009). The BMG is confined by well-developed normal faults throughout its length (figure 7). Outcropped rocks in the surrounding area of the graben are two groups (figure 8, table 2): (i) the Pre-Neogene basement that includes an extensional metamorphic core complex or rocks of the Menderes Massif in WAEP, (ii) Early Miocene to Late Pliocene–Pleistocene rocks labelled as Neogene rocks and Quaternary alluvium comprising clastic and lacustrine sedimentary package up to about 2500 m thick (Gürer et al2009, Çifçi et al2011). The KMG is bounded by BH in the north and AH in the south (figure 7). It was developed over the Pre-Neogene basement of metamorphic rocks of the Menderes Massif (figure 8, table 2). The stratigraphy starts with Middle Miocene Andesite. The Neogene-aged sedimentary sequence, Middle Miocene to Pliocene–Pleistocene, lays over andesitic rocks and consists of clastic and lacustrine sediments about 320 m thick (Sözbilir and Emre 1990, Bozkurt 2000, Emre and Sözbilir 2007, Seyitoğlu and Işık 2009). Inside the massif, the shear zone (SÇSZ) transects at the southernmost of the area (figure 7) and segregates gneisses in the footwall from metamorphosed schists and marbles in the hanging wall (Lips et al2001). GB and SB, as NE–SW trending secondary grabens in the north of GDG, are the components of WAEP (figure 7). Both GB and SB comprise Neogene rocks, which were developed through Miocene, and Quaternary (figure 8). The GB is marked with Quaternary Alluvium and Neogene (Early Miocene) aged basin fills (about 1000 m thick) consisting of clastic, lacustrine and tuffaceous rocks which unconformably overlie Pre-Neogene basement including metamorphic rocks of the Menderes Massif and ophiolitic mélange (figure 8, table 2). Each of them is cut by intrusive bodies (Purvis and Robertson 2005). The SB, developed over the metamorphic basement of the Menderes Massif and ophiolitic mélange (Seyitoğlu 1997, Purvis and Robertson 2005), starts with Early Miocene alluvial fan and fluvio-lacustrine sediments and follows with unconformably Early-Middle Miocene continental clastics to lacustrine sediments fill (figure 8, table 2). Volcanic rocks cut the Early Miocene strata. Sedimentary package overlain Early Miocene strata are coeval and intercalated with volcanic rocks (Seyitoğlu 1997). The youngest one in the succession is unconformable Pliocene-Quaternary sediment and Quaternary Volcanics (Purvis and Robertson 2005). The total thickness of the basin fill is estimated at about 1800 m (Seyitoğlu 1997). Slip faults with normal component are basin-bounding faults of NE–SW trending basins and exhibit an almost straight outcrop pattern. They occur as single or fault segments and juxtapose basement with basin fill (Bozkurt 2003). Figure 8. Open in new tabDownload slide Stratigraphic columns for Gediz graben (GDG; after Çiftçi and Bozkurt 2009); Büyük Menderes graben (BMG; after Çifçi et al2011); Küçük Menderes graben (KMG; after Emre and Sözbilir 2007); Selendi basin (SB; after Seyitoğlu 1997, Purvis and Robertson 2005); and Gördes basin (GB; after Seyitoğlu and Scott 1994, Seyitoğlu et al1994). Left and right sides of each column show formation, group and volcanic rock names. Abbreviations: Pre-Ng, Pre Neogene; Mio, Miocene; Pli, Pliocene; Ple; Pleistocene; Q, Quaternary; Vol., Volcanics. In SB and GB quaternary sediments and volcanics are not represented in figure 7 due to not extending over a wide area. Note that columns are not to scale. Figure 8. Open in new tabDownload slide Stratigraphic columns for Gediz graben (GDG; after Çiftçi and Bozkurt 2009); Büyük Menderes graben (BMG; after Çifçi et al2011); Küçük Menderes graben (KMG; after Emre and Sözbilir 2007); Selendi basin (SB; after Seyitoğlu 1997, Purvis and Robertson 2005); and Gördes basin (GB; after Seyitoğlu and Scott 1994, Seyitoğlu et al1994). Left and right sides of each column show formation, group and volcanic rock names. Abbreviations: Pre-Ng, Pre Neogene; Mio, Miocene; Pli, Pliocene; Ple; Pleistocene; Q, Quaternary; Vol., Volcanics. In SB and GB quaternary sediments and volcanics are not represented in figure 7 due to not extending over a wide area. Note that columns are not to scale. Table 2. Rock types of stratigraphic columns for each graben and basin in the study area. . Rock types . BMGa,b . KMGa,b . GDGa,b . GBa,b . SBa,b . Sedimentary rocks (Ng)a Qa Alluvium + + + + + Claystone + Conglomerate + + + + + Marl Mudstone + + + + + Sandstone + + + + + Shale + + Siltstone + Limestone + + + + Volcanic rocks (Ng)a Andesite + Basalt + Dacite + Rhyolite + Tuff + + Basement Rocks (Pre-Ng)a Gneiss + + + + (Metamorphic and Ophiolitic) Marble + + + + Ophiolitic mélange + + Schist + + + + + . Rock types . BMGa,b . KMGa,b . GDGa,b . GBa,b . SBa,b . Sedimentary rocks (Ng)a Qa Alluvium + + + + + Claystone + Conglomerate + + + + + Marl Mudstone + + + + + Sandstone + + + + + Shale + + Siltstone + Limestone + + + + Volcanic rocks (Ng)a Andesite + Basalt + Dacite + Rhyolite + Tuff + + Basement Rocks (Pre-Ng)a Gneiss + + + + (Metamorphic and Ophiolitic) Marble + + + + Ophiolitic mélange + + Schist + + + + + a Abbreviations: Q, Quaternary; Ng, Neogene; Pre-Ng, Pre Neogene; BMG, Büyük Menderes Graben; KMG, Küçük Menderes Graben; GDG, Gediz Graben; GB, Gördes Basin; SB, Selendi Basin. b See figure 8 for stratigraphic orders of rock types of BMG (Çifçi et al2011), KMG (Emre and Sözbilir 2007), GDG (Çiftçi and Bozkurt 2009), GB (Seyitoğlu and Scott 1994, Seyitoğlu et al1994, Ersoy et al2011) and SB (Seyitoğlu 1997, Purvis and Robertson 2005, Ersoy et al2010). Plus marks (+) point out outcropped rocks for each graben and basin. Open in new tab Table 2. Rock types of stratigraphic columns for each graben and basin in the study area. . Rock types . BMGa,b . KMGa,b . GDGa,b . GBa,b . SBa,b . Sedimentary rocks (Ng)a Qa Alluvium + + + + + Claystone + Conglomerate + + + + + Marl Mudstone + + + + + Sandstone + + + + + Shale + + Siltstone + Limestone + + + + Volcanic rocks (Ng)a Andesite + Basalt + Dacite + Rhyolite + Tuff + + Basement Rocks (Pre-Ng)a Gneiss + + + + (Metamorphic and Ophiolitic) Marble + + + + Ophiolitic mélange + + Schist + + + + + . Rock types . BMGa,b . KMGa,b . GDGa,b . GBa,b . SBa,b . Sedimentary rocks (Ng)a Qa Alluvium + + + + + Claystone + Conglomerate + + + + + Marl Mudstone + + + + + Sandstone + + + + + Shale + + Siltstone + Limestone + + + + Volcanic rocks (Ng)a Andesite + Basalt + Dacite + Rhyolite + Tuff + + Basement Rocks (Pre-Ng)a Gneiss + + + + (Metamorphic and Ophiolitic) Marble + + + + Ophiolitic mélange + + Schist + + + + + a Abbreviations: Q, Quaternary; Ng, Neogene; Pre-Ng, Pre Neogene; BMG, Büyük Menderes Graben; KMG, Küçük Menderes Graben; GDG, Gediz Graben; GB, Gördes Basin; SB, Selendi Basin. b See figure 8 for stratigraphic orders of rock types of BMG (Çifçi et al2011), KMG (Emre and Sözbilir 2007), GDG (Çiftçi and Bozkurt 2009), GB (Seyitoğlu and Scott 1994, Seyitoğlu et al1994, Ersoy et al2011) and SB (Seyitoğlu 1997, Purvis and Robertson 2005, Ersoy et al2010). Plus marks (+) point out outcropped rocks for each graben and basin. Open in new tab The regional Bouguer gravity data of all of Turkey were collected at about 2–5 km intervals between 1973 and 1988 by MTA (General Directorate of Mineral Research and Exploration of Turkey), and a regional Bouguer gravity anomaly map was published with a grid spacing of 2 km (MTA 2006). Figure 9(a) shows the regional Bouguer gravity anomaly map of the studied area which covers an area of 276 km × 200 km, including the sea region. The amplitude of gravity anomalies shows an increasing trend towards the Aegean Sea (E to W), but negative gravity anomalies are more dominant in the middle and eastern part of the area (figure 9(a)). As is well known, in general gravity anomalies over the continents are characterized by negative gravity values due to the thick crust and positive gravity anomalies are found over oceanic regions where the crust is very thin (Lowrie 2007). Figure 9. Open in new tabDownload slide Regional Bouguer gravity anomaly map of the study area (a); residual gravity anomaly map computed by removing a first-order polynomial surface from the map shown in the left panel (b). The black lines on the anomaly maps show coastline. Figure 9. Open in new tabDownload slide Regional Bouguer gravity anomaly map of the study area (a); residual gravity anomaly map computed by removing a first-order polynomial surface from the map shown in the left panel (b). The black lines on the anomaly maps show coastline. As is clearly seen from the regional Bouguer gravity image map (figure 9(a)), BMG and GDG are characterized by negative anomaly values, and it can be mentioned that the thick sedimentary deposits of the grabens (BMG and GDG) give rise to the lowering of gravity values, as also suggested by Sarı and Şalk (2006). In contrast to BMG and GDG, KMG does not produce a lower-amplitude anomaly pattern, which is most likely caused by the existence of very thin sedimentary cover on the massif metamorphic rocks. Inverse modelling of gravity data has also indicated the thin sedimentary cover in this area (Sarı and Şalk 2002, Göktürkler et al2003). On the other hand, the horsts of BH and AH are characterized by relatively higher gravity values due to the existence of metamorphic rocks of the Menderes massif. The GB and SB bounded by NE–SW trending normal faults produce negative gravity values. SB shows a lower anomaly pattern than GB in figure 9(a), and this case can be explained by the existence of relatively thicker sedimentary fills over SB in comparison to GB. Before the application of the edge-approximating algorithms on the real gravity data, a first-order polynomial surface was computed and then subtracted from the regional gravity data to remove the planar horizontal trend and regional background. Consider that the decreasing linear trend in the amplitude of gravity anomalies from the Aegean Sea towards an inland, first-order polynomial surface was deemed to be sufficient for removing the horizontal planar trend and the regional background. Figure 9(b) shows the trend-removed residual gravity anomaly map, and it is clearly seen that in this case this procedure provided a good compromise between the trend-removed residual gravity anomaly map and the surface geology map shown in figure 7. Thus it can be stated that removing the first-order polynomial surface from the regional Bouguer gravity anomalies enhanced the anomalies of the shallower geological sources in the Aegean graben system. In order to improve the resolution of shallower geological sources, a trend-removed residual gravity anomaly map was used for the application of edge-approximating algorithms. Image maps in figures 10(a)–(f) show the performance of edge-approximating algorithms on a residual gravity anomaly map. The anomaly map produced by the VD operator (figure 10(a)) is somewhat similar to the residual gravity anomaly map of the area. As can be clearly seen, BMG and GDG were highlighted by negative anomaly values. Although GB and SB, bounded by NE–SW trending normal faults which are located at the NE part of the study area, did not produce significant gravity anomalies (figure 9(b)), these subtle details were enhanced moderately in the VD image map. Additionally, the VD operator clearly improved the gravity anomaly signature of a curve-shaped shear zone (SÇSZ in figure 7) developed inside the Menderes Massif, which is not noticeably observed from the gravity anomaly maps in figures 9(a) and (b). Figure 10(b) shows the THD image map, which is dominated by high-amplitude responses over the normal faults through GDG and BMG as expected. When comparing VD and THD maps, it is clear that THD produced a more conspicuous anomaly pattern which is relevant to these normal faults. The traces of GB and SB, bounded by normal faults, were also improved somewhat and characterized by a high-amplitude gravity signature. Moreover, THD enhanced low-amplitude anomalies to show clear traces, highlighting the shear zone developed inside the Menderes Massif. However, it is worth pointing out that some elongated spurious high-amplitude anomalies were detected, particularly near the GB and SB. The anomaly map of the AS operator, a combination of THD and VD operators, is shown in figure 10(c). High-amplitude responses are dominant in the AS map over abrupt lateral changes in density as expected. The traces of GDG and BMG were resolved well. However, the subtle details such as the NE–SW trending normal fault systems bounding the GB and SB and the ductile detachment fault through the edges of the Menderes Massif and shear zone inside it (SÇSZ in figure 7) were not enhanced sufficiently. Figure 10(d) shows the response of the PCR operator. The image map indicated much more detail than did the previous images and tends to be the most coherent. High-amplitude responses are dominant in the image map. It can be stated that the PCR map enhanced the GDG and BMG with greater clarity than did the previous operators. Additionally, the PCR operator dramatically improved the resolution of the details even in the areas where the field does not show strong anomaly patterns (negative or positive) in the residual gravity anomaly map (figure 9(b)) such as normal fault systems bounding the GB and SB, and also the shear zone (SÇSZ) located in the Menderes Massif. Thus it is noteworthy to mention that the edges of the geological structures, faults and lineaments were well resolved by using the PCR operator. The image map of the TA operator is demonstrated in figure 10(e). Even though the TA map showed considerably more detail than did the residual gravity anomaly map, high-amplitude responses were not observed from the locations of normal faults through GDG and BMG. However, the TA operator improved the resolution of the curve-shaped shear zone developed inside the Menderes Massif and the normal faults bounding the GB and SB. It can be stated that the TA operator produced an anomaly characteristic that is similar to the VD operator, but in a weaker form. The image map produced by the TM operator is shown in figure 10(f). Even though satisfactory results were achieved using the TM operator from the synthetic examples (figure 2(f)), the image map obtained from the real data set is more diffuse than the THD and PCR images. Due to the existence of many spurious high-amplitude anomalies, the real anomaly zones seemed to be masked. Thus the TM operator is found to be less effective than the THD and PCR operators, depending on the results obtained from the real data example. Finally, the presented case study showed that the PCR solutions of real gravity data tend to be the most coherent, displaying a gain of resolution of geological contacts and faults. Figure 10. Open in new tabDownload slide The results of edge-approximating algorithms applied to the data set shown in figure 9(b). VD image map of the residual gravity data (a); THD image map of the residual gravity data (b); AS image map of the residual gravity data (c); PCR image map of the residual gravity data (d); TA image map of the residual gravity data (e); and TM image of the residual gravity data (f). The black lines on the maps show coastline. Figure 10. Open in new tabDownload slide The results of edge-approximating algorithms applied to the data set shown in figure 9(b). VD image map of the residual gravity data (a); THD image map of the residual gravity data (b); AS image map of the residual gravity data (c); PCR image map of the residual gravity data (d); TA image map of the residual gravity data (e); and TM image of the residual gravity data (f). The black lines on the maps show coastline. 4. Conclusions Numerous techniques have been suggested to track the geological contacts and to bring out subtle details which are not clearly identified in potential field anomaly maps. Edge-approximating techniques, generally based on the use of a linear combination of the horizontal and vertical field derivatives, are all affected by the model parameters (depth, size, density, etc) of the source bodies. Additionally, the resolution of the data grid and the noise level in the data play a major role in the success of the edge-approximating algorithms. Each technique has its own advantages as well as shortcomings, depending on the nature of the potential field data. Therefore, we tried to review the effectiveness of the commonly used edge-approximating techniques in this study. In order to obtain optimum results, test studies were performed on noise-free and noisy synthetic gravity data and also a real gravity data set from the Aegean graben system, western Turkey. A noise-free synthetic example clearly showed the effectiveness of the THD, AS, PCR and TM operators. Even though they produced a similar anomaly pattern for the shallower body, the best result for the edges of the deeper body was achieved by using the TM operator. Noisy data examples indicated that all operators are very sensitive to the degree of noise level in the data. In the case of a high-level noise scenario, the edges of anomalous bodies were relatively enhanced by using the THD operator, while the others were not found to be effective. Because the THD operator only requires computation of horizontal derivatives, it was found to be less sensitive to high-level noise than the others. When the noise level was moderately reduced by an upward continuation process for the second scenario, the superiority of the THD and PCR operators over the other detectors was clearly determined. More importantly, although the PCR operator uses highest-order derivatives, it enhanced the edges and appeared to have been affected least by the low-level noise. On the other hand, the TM and TA operators clearly amplified the noise and were found more sensitive to noise than the others. Based on the real data example, the PCR operator, which has rarely been applied to potential field data sets so far, produced the more detailed anomaly signatures over the abrupt lateral changes in density and appeared to be the most effective one. Thus it is concluded that the use of the PCR operator proved useful in delineating and discriminating the subtle details in gravity data dealing with geological contacts, faults or lineaments. Additionally, it must be noted that in the areas where the level of noise is high, a smoothing operation such as upward continuation would be a good strategy before applying the PCR operator for reducing the effects of noise in the data sets and increasing the coherency of the solutions. Acknowledgments Thanks are due to Rezzan Ekinci for her help in preparing high quality images. Dr Alper Demirci is also thanked for his suggestions throughout this study. Three-dimensional forward modelling of gravity data and the data processing procedures of both synthetic and real data sets were carried out at the Earthquake Monitoring and Data Processing Laboratory (DEIVIL) in the Department of Geophysical Engineering at Çanakkale Onsekiz Mart University, Turkey. 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TI - On the effectiveness of directional derivative based filters on gravity anomalies for source edge approximation: synthetic simulations and a case study from the Aegean graben system (western Anatolia, Turkey)
JO - Journal of Geophysics and Engineering
DO - 10.1088/1742-2132/10/3/035005
DA - 2013-06-01
UR - https://www.deepdyve.com/lp/oxford-university-press/on-the-effectiveness-of-directional-derivative-based-filters-on-R6SOItSI12
VL - 10
IS - 3
DP - DeepDyve
ER -