A new automatic method for estimation of magnetization and density contrast by using three-dimensional (3D) magnetic and gravity anomalies

Physics of the Earth and Planetary Interiors 204–205 (2012) 22–36

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A new automatic method for estimation of magnetization and density contrast by using three-dimensional (3D) magnetic and gravity anomalies Ozcan Bektas a,⇑, Abdullah Ates b, Attila Aydemir c a

Department of Geophysical Engineering, Engineering Faculty, Cumhuriyet University, Sivas 58140, Turkey Department of Geophysical Engineering, Engineering Faculty, Ankara University, Besevler, Ankara 06100, Turkey c Turkiye Petrolleri A.O., Sogutozu Mah. 2. Cad. No: 86, 06100 Sogutozu, Ankara, Turkey b

a r t i c l e

i n f o

Article history: Received 23 December 2011 Received in revised form 10 April 2012 Accepted 13 June 2012 Available online 28 June 2012 Edited by Kei Hirose Keywords: Gravity and magnetic anomalies Pseudogravity Ratio of magnetization to density contrast Tetbury anomaly Hanobasi anomaly

a b s t r a c t In this paper, a new method estimating the ratio of magnetic intensity to density contrast of a body that creates magnetic and gravity anomalies is presented. Although magnetic intensity and density of an anomalous body can be measured in the laboratory from the surface samples, the proposed new method is developed to determine the magnetic intensity and density contrast from the magnetic and gravity anomalies when the surface samples are not available. In this method, density contrast diagrams of a synthetic model are produced and these diagrams are prepared as graphics where the magnetic intensity (J) is given in the vertical axis and Psg (pseudogravity)/Grv (gravity) values in horizontal axis. The density contrast diagrams can be prepared as three sub-diagrams to show the low, middle and high ranges allowing obtain density contrast of body. The proposed method is successfully tested on the synthetic models with and without error. In order to verify the results of the method, an alternative method known as root-mean-square (RMS) is also applied onto the same models to determine the density contrast. In this manner, maximum correlation between the observed gravity and calculated gravity anomalies is searched and confirmation of the results is supported with the RMS method. In order to check the reliability of the new method on the field data, the proposed method is applied to the Tetbury (England) and Hanobasi (Central Turkey) magnetic and gravity anomalies. Field models are correlated with available geological, seismic and borehole data. The results are found consistent and reliable for estimating the magnetic intensity and density contrast of the causative bodies. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction Magnetic or gravity anomalies, are generally produced by buried bodies having the susceptibility ðK ¼ J=HÞ and density contrasts (Dq) where J is the magnetic intensity, H is the magnetic field. It is possible to convert the magnetic field to gravity field using the Poisson relation (Baranov, 1957). By using Eq. (1) below, magnetic field is transferred to the gravity field (Blakely, 1995). This converted field is called as the pseudogravity field while the real density of the body is not known.

V ¼

Cm M

c q

^  rpU m

ð1Þ

where V is the magnetic potential, U is the gravity potential, Cm is ^ is the direction of magnetization, M is the magnetic constant, m the magnetic intensity, q is the density, and c is the international gravity constant. ⇑ Corresponding author. E-mail address: [email protected] (O. Bektas). 0031-9201/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.pepi.2012.06.003

Interpretation of pseudogravity anomalies is important because it provides comparison of both fields. For instance, gravity anomaly and pseudogravity anomaly obtained from magnetic anomalies over the same area are compared for the same geological causative body (Kearey et al., 2002). Relative amplitudes of these fields can provide a measurement for the ratio of magnetic intensity to density contrast. Comparison of the real gravity anomaly and the pseudogravity sometimes provides additional information about the causative body. There are several studies on this subject by various authors such as Kearey (1991), Kearey and Rabae (1993) and Ates and Kearey (1995). Further, Mendonça (2004) and Mendonça and Meguid (2008) studied automatic determination for the ratio of magnetic intensity to density contrast from the gravity and magnetic anomalies. Recently, the same ratio was also calculated by Doo et al. (2009). In the most recent papers given above, authors calculated only ratio of the magnetic intensity to density contrast. However, there are different rocks which can indicate same ratio. In this paper, we determined magnetic intensity (J) and density contrast (Dq) separately and then calculated the ratio of magnetic intensity to density contrast. This gives an advantage to the new

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method to study each anomaly separately for different rock types. However, our error calculations demonstrate that it is possible to calculate the magnetization and density contrast separately. Utility of this method requires the assumption that the subsurface contains highly correlative magnetic susceptibility and density. Assumptions may also be related to the characteristics of magnetization, such as declination and inclination (Bilim and Ates, 1999, 2004). 2. Method Correlation of the magnetic and gravity anomalies to obtain the magnetization and density contrast was illustrated in a flow chart given in Fig. 1. This method is based on two main parts. These are annotated with blue and red boxes numbered with I and II in Fig. 1. In Part I intensity of magnetization and in Part II density contrast of anomalous body is calculated. Main parts I and II have sub steps

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from i to viii. The method has also Auxiliary steps shown with dashed boxes of (a–c) in Fig. 1. Main and auxiliary parts of the flow chart are explained in the following: Part I: In this part intensity of magnetization is calculated by the steps from (i) to (v). These are: (i) A synthetic model was constructed as the beginning of this investigation. Then gravity and magnetic anomalies of this model (with randomly chosen and pre-defined parameters) were created by using a Fortran program named ‘‘prism’’ (Kearey, 1977). (ii) Pseudogravity transformation was applied onto the magnetic anomaly response of the synthetic model. The ratio of magnetic intensity (J) to density contrast (Dq) was taken as 1 (J/Dq = 1) in the transformation. Relationship between the magnetic potential and gravity potential were initially defined by Poisson in early times of 19th century. According to this relationship, magnetic anomalies caused by the same

Fig. 1. Flow chart showing the computational steps of Parts I, II and Aux. Part I is annotated with blue box showing the calculating computation steps of intensity of magnetization. (i) Calculation of the synthetic magnetic and gravity anomalies, (ii) calculation of the pseudogravity anomalies, (iii) calculation of three-dimensional gravity model, (iv) re-computation of the magnetic and gravity anomalies, (v) estimation of the intensity of magnetization. Part II is annotated with red box showing the computational steps of the estimation of the density (contrast); (vi) use of the density contrast diagrams, (vii) calculation of the Psg/Grv ratio, (viii) estimating the density (contrast). Aux is the Auxiliary part shown in the dashed box: (a) estimation of the magnetization angles (Bilim and Ates, 2004, 1999), (b) estimation of the top of anomalous body by means of the power spectrum (Spector and Grant, 1970) and (c) the RMS method to estimate the density contrast.

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causative body (or structure) can be converted into gravity anomalies (Eq. (1)). Pseudogravity anomaly conversion from the magnetic anomalies was developed by Baranov (1957) for the first time. As a result of this conversion, pseudogravity anomaly is obtained independently from the real density of the body. (iii) Three-dimensional (3D) depth model of the pseudogravity anomaly was constructed using the computer program of Cordell and Henderson (1968) which is based on an iterative inverse modeling. In 3D modeling method of Cordell and Henderson (1968), the gravity anomaly is digitized on a rectangular grid. The method assumes that the causative body can be approximated by means of a bundle of vertical, elemental prisms, each having a cross-sectional area of grid square and a uniform density. Three options are available in the method; the reference plane may optionally be chosen to delimit base, top or midpoint of the prism elements. An initial approximation of structure is calculated by means of the Bouguer slab relationship given in Eq. (2) below. The ratio of observed to calculated gravity is used to iterate the first and successive models until a good match is reached. (Iteration can be performed 1 to nth step until a good fit achieved between the observed and calculated gravity data where ‘‘n’’ is the iteration number.)

t1;q ¼ Kg obs;q

ð2Þ

where K ¼ 1=2pcq, t1,q is the thickness of the prism obtained from the first iteration at the qth grid point, gobs is the observed gravity, c is the International gravity constant, q is the density, tn,q is the thickness of the prism obtained from the nth iteration at the qth grid point. (iv) Gravity and magnetic anomaly response of 3D model is recreated in this step and magnetic intensity was taken J = 1 A m1 as an initial parameter. Calculation of the gravity and magnetic effects of the rectangular prisms were introduced by Goodacre (1973). In this approximation, the data is divided into identical prisms as much as the number of grids. This is the initial model to calculate the gravity response. After this calculation, measured and calculated gravity values at the each grid point are correlated. Then the process is iterated until obtaining best consistency. The automatic 3D modeling can be calculated assuming causative body is flat topped or flat bottomed. In this study, causative bodies are accepted as flat bottomed. Density contrast is the key parameter for construction of models. The magnetic and gravity anomalies of the model are calculated for uniform magnetic intensity and

Table 1 Parameters of density contrast diagrams and first synthetic model. Parameters given in the bold rows are the inclusions to the parameters of density contrast diagrams to construct the synthetic model. Model parameters Dimension Grid Top depth (km) Bottom depth (km) Inclination of the earth’s magnetic field Declination of the earth’s magnetic field Inclination angle of the body magnetization Declination angle of the body magnetization Dq (g/cm3) J (A m1) Top depth (km) Bottom depth (km)

15  15 48  48 1 5 55° 4° 55° 4° 0.08 1 2 6

Fig. 2. Density contrast range diagrams, (a) Low, (b) medium and (c) high density contrast. Vertical axis is the intensity of magnetization, horizontal axis is the ratio of the pseudogravity/gravity (Psg/Grv).

density contrast (J = Dq = 1). Gravity and magnetic responses of rectangular prism are given in Eq. (3) and (4), respectively.

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Fig. 3. (a) Magnetic anomalies of first synthetic model. (b) Gravity anomalies of synthetic model. (c) Pseudogravity anomalies of synthetic model. (d) Three-dimensional gravity model of synthetic model. (e) Calculated magnetic anomalies of the model presented in Fig. 3d adjusted by factor of 1.0 A m1. (f) Calculated gravity anomalies of the model presented in Fig. 3d with uniform density (Dq = 1.0 gr cm3). (g) Density contrast diagram for values of density contrast for synthetic model. N sign shows the estimated density contrast of body. (h) RMS correlation function for values of the synthetic model density contrast.

Gz ðx;y;zÞ ¼ cq

Z

xu2

xu1

Z

yv 2

yv 1

Z

zw2

zw1

w ðu2 þ v 2 þ w2 Þ3=2

du dv dw

ð3Þ

where Gz(x, y, z) is the vertical attraction at the point (x, y, z), (u1, v1, w1), (u2, v1, w1), (u1, v2, w1) are the corners of the prism, q is the density of the prism; c is the gravitational constant, and z is the positive upwards      J @Gz @Gz @Gz @Gx @Gx @Gx Aðx;y;zÞ ¼  m3 f1 þ f2 þ f3 þ m1 f2 þ f3 þ f1 cq @x @y @z @y @z @x   @Gy @Gy @Gy þ f1 þ f2 ð4Þ þm2 f3 @z @x @y

where J is the intensity of magnetization of the prism, m1, m2, and m3 are the directional cosines of the total magnetization vector and f1, f2, and f3 are the directional cosines of the Earth’s magnetic field. (v) Calculated magnetic anomaly is correlated with the magnetic anomaly response of the original synthetic model in the second phase of this flow. This correlation is iterated by changing value J until a good consistency is obtained. When the best correlation is achieved, the correct magnetic intensity (J) will have been determined by this adjustment. Part II: In this part, the density contrast is calculated by the steps from (vi) to (viii).

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(viii) In order to obtain density contrast of a body, magnetic intensity (J) which was determined at the first partition of the flow chart and Psg/Grv values are overlaid on the diagram. The appropriate density contrast is obtained according to its proximal position to the nearest linear curve on the graphic. Auxiliary computations (Aux): In this part, it is aimed to constrain the parameters of the anomalous body. Aux has three sub branches. These are; (a) Determination of declination (D) and inclination (I) angles: (Bilim and Ates, 2004, 1999) suggested new method to estimate body magnetization directions from the magnetic and gravity anomalies. The method is related with the search of maximum correlation between magnetic and gravity anomalies caused by the same body for determining magnetization directions. (b) Top and bottom of the causative body in the 3D model is iteratively obtained under the control of the power spectrum for pseudogravity anomaly (Spector and Grant, 1970) and it is correlated to the result of the 3D modeling. Depth of any causative body can be found by the power spectrum of the anomaly. Spector and Grant (1970) proposed the energy spectrum of the model in polar coordinates as given in Eq. (5):

hEðs; wÞi ¼ 4p2 M2 R2G he2hs ihð1  ets Þ2 ihS2 ðs; wÞihR2p ðwÞi 2

ð5Þ

2 0.5

where hi indicates the expected value, s = (u + v ) (magnitude of the frequency vector), w = tan1u/v (direction of the frequency vector), M is the magnetic moment/unit depth, h is the depth to the top of the prism, t is the thickness of the prism, S is the factor for the horizontal size of the prism, RP is the factor for magnetization direction of the prism and RG is the factor for geomagnetic field direction. (c) Results of the density contrast determination are verified by using root-mean-square (RMS) method that is based on minimizing the RMS correlation between the observed and calculated gravity anomalies to expose the maximum consistency. In other words, minimum RMS value between those two anomalies gives the density contrast of the causative body and confining environment. Correlation process is given by the square root average (Eq. (6)) as follows:

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N M uXX RMS ¼ t ð½Gobs ði; jÞ  Gcalc ði; jÞ2 =ðN  MÞÞ

Fig. 3 (continued)

ð6Þ

i¼1 j¼1

Table 2 Parameters of second synthetic model.

where Gobs is the observed gravity anomaly, Gcalc is the calculated gravity anomaly, and N and M is the number of grid points along the x and y directions, respectively.

Model parameters Dimension Grid Top depth (km) Bottom depth (km) Inclination of the earth’s magnetic field Declination of the earth’s magnetic field Inclination angle of the body magnetization Declination angle of the body magnetization Dq (g/cm3) J (A m1)

15  15 48  48 4 8 55° 4° 60° 50° 0.3 1.2

(vi) Parameters of the density contrast diagrams for the synthetic model given in Table 1, as a priori. In order to draw a graphic to obtain the density contrast, the pseudogravity to gravity (Psg/ Grv) ratio is represented on the horizontal axis of the diagram while the magnetic intensity is represented at the vertical axis. (vii) Pseudogravity (Psg) stands for the maximum value of pesudogravity anomaly and gravity (Grv) is the maximum value of the gravity anomaly. The density contrast diagrams are prepared as three different subdiagrams to show low, middle and high ranges (Fig. 2a–c).

3. Application of the method 3.1. Synthetic models (without any error) The method was tested on gravity and magnetic anomalies of synthetic models. In this study, gravity and magnetic anomaly of a single vertical prism model (with 15  15  4 km dimensions in x, y and z directions) were used. Inclination and declination of the earth magnetic field were taken as 55° and 4°, respectively. These are values in central Turkey and also they are accepted as the values of Case 2 in the following section of this paper. Model parameters of the density diagrams (Table 1) were also used to construct this synthetic model. In addition, density and intensity of magnetization shown in the Table 1 (written with bold letters) were included to produce the synthetic model. In the course of the flow chart in Fig. 1, magnetic and gravity anomalies of this synthetic model are initially created and presented in Fig. 3a and b. Pseudogravity transform was performed on the magnetic anomalies of the model (Fig. 3c. Then, pseudogravity anomalies were modeled using the 3D gravity modeling program (Fig. 3d) based

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on the Cordell and Henderson’s (1968) method. A flat bottomed model was chosen and depth of the base adjusted iteratively until the top of the model reached to the depth of 2 km. Thus, the base of the model lies at a depth of 6 km and presented in Fig. 3d which indicates a good correlation with the depth parameters of the model given in Table 1. The magnetic (Fig. 3e and gravity (Fig. 3f anomalies of this model were calculated using uniform magnetic intensity and density contrast (J = Dq = 1) ratio. In this way, adjust-

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ment factor for the total magnetic intensity of the body which was estimated as 1.0 A m1 (Fig. 3e same as the initial value. The method was also applied to determine the density contrast of the model and the contrast was found as 0.08 gr cm3 from the diagrams (Fig. 3g. In this case, the ratio of magnetic intensity to density contrast (J/Dq) is found as 12.5 mA m2/kg. Finally, RMS method was applied to the anomalies of the same region for controlling the results. In this method, observed and calculated gravity anomalies

Fig. 4. (a) Magnetic anomalies of second synthetic model. (b) Gravity anomalies of synthetic model. (c) Pseudogravity anomalies of synthetic model. (d) Three-dimensional gravity model of synthetic model. (e) Calculated magnetic anomalies of the model presented in Fig. 4d adjusted by factor of 1.2 A m1. (f) Calculated gravity anomalies of the model presented in Fig. 4d with uniform density (Dq = 1.0 g cm3). (g) Density contrast diagram for values of density contrast for synthetic model. N sign shows the estimated density contrast of body. (h) RMS correlation function for values of the synthetic model density contrast.

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was also applied to the anomalies of the second model once again and same result (0.3 gr cm3) was obtained for the density contrast (Fig. 4h). 3.2. Synthetic model (with error) In this stage of the study, the same synthetic model studied in Fig. 3 was used to produce the gravity and magnetic anomalies by introducing 20% random error into the amplitude of the magnetic data values. Magnetic anomaly with the 20% error is shown in Fig. 5a. Pseudogravity transformation and 3D gravity models were produced in the same way as given in previous section (Fig. 5b and c). Fig. 5c shows nearly a good correlation with the depth parameters of the model given in Table 1. The magnetic (Fig. 5d) and gravity (Fig. 5e) anomalies of the model were calculated for uniform magnetic intensity and density (J = Dq = 1) with the adjustment factor of body estimated as 1.0 A m1. The method was also used to determine the density contrast of model and the density contrast for the body was estimated approximately 0.08 gr cm3 using the density contrast diagrams (Fig. 5f). In this case, the ratio of magnetic intensity to density contrast (J/Dq) is found as 12.5 mA m2/kg. The RMS method was also applied to the anomalies of the same model, once again and same result (0.08 gr cm3) was obtained for the density contrast (Fig. 5g). 3.3. Error analysis

Fig. 4 (continued)

have been correlated using Eq. (6) and density contrast of the body was also estimated approximately 0.08 gr cm3 from the verification of the RMS method that coincides with the lowest RMS value (Fig. 3h). In the second synthetic model experiment, gravity and magnetic anomaly of another vertical prism model (with 15  15  4 km dimensions in x, y and z directions) were used. Inclination and declination of the earth magnetic field were taken as 55° and 4° similar to the previous one. In difference, inclination and declination of the body magnetization for the second model were taken as 60° and 50°, respectively. Table 2 indicates the parameters of the prismatic body in the considered example. Magnetic and gravity anomalies of the second model are shown in Fig. 4a and b. Pseudogravity transformation and 3D gravity model were produced in the same way as given in previous section (Fig. 4c and d). Fig. 4d shows nearly a good correlation with the depth parameters of the model given in Table 2. The magnetic (Fig. 4e) and gravity (Fig. 4f) anomalies of the model were calculated for uniform magnetic intensity and density (J = Dq = 1) with the adjustment factor of body estimated as 1.2 A m1 (Fig. 4e). According to this estimation, the density contrast for the body was found approximately 0.3 gr cm3 using the density contrast diagrams (Fig. 4g). In this case, the ratio of magnetic intensity to density contrast (J/Dq) is found as 4 mA m2/kg. The RMS method

Two different error analyses were performed to test the stability of the magnetic intensity and density contrast diagrams: one of them is the error addition to the J/Dq ratio, other is the error addition to the top depth of the causative body. In the first error analysis, 20% random error was added to the magnetic intensity and ratio of Psg/Grv of model given in Table 1. Fig. 6a indicates new density contrast values on the diagram after the random error was added. In this figure, magnetic intensity values vary between 0.8 and 1.2 A m1 while the ratio of Psg/Grv varies between 10.15 and 14.68. Original magnetic intensity and ratio of Psg/Grv values were 1 A m1 and 12.23 respectively. In the second error analysis, 20% random error was added to the top depth of the causative body. New depths to the top of the body and ratio of Psg/Grv values were given in Table 3. Fig. 6b shows new density contrast values on the density contrast diagram after the random error was added. In this application, density contrast values are not changed when the top depth of the causative body changed with the same previously used magnetic intensity and density contrast values (1.0 A m1, 0.08 gr cm3). It can thus be suggested that magnetic intensity and density contrast are independent from the changes of dimensional parameters of the causative body. This can also be inferred from the retained Psg/Grv ratios given in Table 3. 4. Field examples The method was applied on two different field cases. In case 1, gravity and magnetic anomalies have already been studied and interpreted, while gravity and magnetic anomalies were previously unprocessed and un-interpreted in Case 2. 4.1. Case 1 First example is located in the Worcester Graben which is a major N–S oriented, fault-related sedimentary basin in England (Fig. 7a). The Worcester Graben is a major basin containing a thick sequence of Permo-Triassic sediments. Gravity and magnetic anomalies of this basin was studied and modeled by Ates (1992).

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Further palaeomagnetic investigation was performed analyzing the potential field data by Ates and Kearey (1995). In the application of the new method on the Worcester Graben, aeromagnetic anomaly map was re-digitized from Ates and Kearey (1995) with 1 km grid intervals (Fig. 7b). Aeromagnetic data over the Worcester Graben shows a large positive anomaly with 100 nT amplitude near the town of Tetbury. The surface geology gives no indication or no out-

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crop of the magnetic causative body (Ates and Kearey, 1995). In accordance with the processing sequence given below, the pseudogravity anomalies were produced from the aeromagnetic anomalies using 67° inclination and 351° declination angles for the geomagnetic field in this region. Then, inclination and declination of the body magnetization were accepted as 90° and 0° respectively for the new method. Because the anomaly is a large positive

Fig. 5. (a) Magnetic anomalies of model with 20% random error shown in Fig. 3a. (b) Pseudogravity anomalies of model with 20 %random error shown in (a). (c) Threedimensional gravity model of model with 20% random error. (d) Calculated magnetic anomalies of model with 20% random error in (c) adjusted by factor of 1.0 A m1. (e) Calculated gravity anomalies of model with 20% random error in Fig. 4c with uniform density (Dq = 1.0 gr cm3). (f) Density contrast diagram for values of density contrast for model with 20% random error. N sign shows the estimated density contrast of body. (g) RMS correlation function for values of density contrast for model with 20% random error.

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Fig. 5 (continued)

anomaly (not bi-polar), the causative body is accepted as a vertical magnetized mass (inclination, 90°). In this case, declination should be considered as 0° (otherwise, it may be accepted as any angle; 0° and 360°). The pseudogravity anomalies constructed by using these parameters are shown in Fig. 7c. Previously, Ates and Kearey (1995) applied azimuthally averaged power spectrum to the aeromagnetic anomalies and estimated top of the source depth at 3.12 km. The pseudogravity anomalies were modeled using a 3D gravity modeling program based on the Cordell and Henderson (1968) method. A flat bottomed model was chosen and depth of the base was iteratively adjusted until the top of the model reached to 3.12 km estimated by power spectrum analysis. Thus, base of the model lies at a depth of 6.0 km (Fig. 7d). Aeromagnetic anomalies of this model (Fig. 7e) were calculated for uniform magnetic intensity (1.0 A m1). In this way, adjustment factor for the total magnetic intensity of the body was estimated as 1.22 A m1. Gravity anomalies of the study area indicate no correlation with the causative body. Therefore, Ates and Kearey (1995) constructed a 2D gravity model and estimated the density contrast of the body as 0.04 gr cm3 (Fig. 7f). By using new method proposed in this paper, density contrast of the Tetbury body was determined as 0.05 gr cm-3 (Fig. 7g), which is very close to previously estimated value. The ratio of magnetic intensity to density contrast (J/Dq) is found as 24.4 mA m2/kg.

Fig. 6. (a) Error analysis of density contrast diagram for the magnetic intensity and ratio of Psg/Grv values with 20% random error. Sign shows the values of the magnetic intensity with 20% random error along the Y axis. sign shows the values of ratio of Psg/Grv with 20% random error along the x-axis. N Sign shows the estimated density contrast of body. (b) Error analysis of density contrast diagram for top depth of model 20% random error. Sign shows the values of density contrast value with 20% random error of top depth. Sign shows the estimated density contrast of body.

Table 3 Parameters of synthetic model after addition of 20% random error to top depth of the body. Model

Top depth (km)

Bottom depth (km)

Psg (mgal)

Grv (mgal)

Psg/ Grv

1 (original model parameters) 2 3 4 5 6 7 8

5.0

8.0

56.0

14.69

3.81

4.7 4.5 4.3 5.2 5.55 5.75 6.0

8.0 8.0 8.0 8.0 8.0 8.0 8.0

63.2 68.2 73.5 51.3 43.6 39.3 34.2

16.56 17.86 19.20 13.49 11.47 10.37 9.036

3.82 3.82 3.82 3.80 3.80 3.79 3.79

4.2. Case 2 The second case (Fig. 8a) is about the Hanobasi Anomaly (Aydemir, 2005) in central Anatolia, Turkey. The aeromagnetic

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and gravity data of the second case were obtained from the General Directorate of Mining Exploration and Research (MTA). The general description of both Turkish gravity and aeromagnetic data was provided by Ates et al. (1999). The data were interpolated on a regular grid with an interval of 2.5 km. The Hanobasi Anomaly located to the southeast corner of the Lake Tuzgolu (Salt Lake) is an apparent magnetic anomaly observed in all aeromagnetic maps of the Central Anatolia. It is unique and independent anomaly from the Cappadocia Magnetic Anomaly region (Buyuksarac, 2007) which

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covers quite large area to the east. The Hanobasi Anomaly does not have any surface evidence such as topographical heights or outcrops, either. It was named as the ‘‘Hanobasi Anomaly’’ by Aydemir (2005) for the first time and its independency from the Cappadocia Anomalies was determined by the application of the upward continuation method (Aydemir and Ates, 2005). Bilim and Ates (2004) estimated the inclination and declination angles of the causative body magnetization for this anomaly as 30° and 35°, respectively. The aeromagnetic and gravity anomalies of the

Fig. 7. (a) Location map of the study area. (b) Aeromagnetic anomaly map of Tetbury Region. (c) Pseudogravity anomalies of the aeromagnetic anomaly presented in Fig. 7b. (d) Three-dimensional gravity model of the Tetbury anomaly. (e) Calculated magnetic anomalies of the model presented in Fig. 7d adjusted by factor of 1.22 A m1. (f) Twodimensional gravity anomaly (Ates and Kearey, 1995). (g) Density contrast diagram for values of density contrast for the Tetbury anomaly. N sign shows the estimated density contrast of Tetbury anomaly. T: Location of Tetbury.

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Fig. 7 (continued)

Case 2 are shown in Fig. 8b and c. Pseudogravity transformation was applied to the aeromagnetic data (Fig. 8d) using the estimated body magnetization angles given above. Seismic line SL-1 (Fig. 8e and f) extends in the E–W direction over the northern part of the anomaly while Line SL-2 (Fig. 8g and h) crosses the anomaly right in the middle in the N–S direction. Locations of two seismic sections to be used for correlation are also indicated in these maps. A bright and strong reflection interpreted as the basement, outcomes at the bottom from the SW end of the seismic section SL-1 through the surface at the NE end (Fig. 8e). The bright reflection is faulted at about Shot Point (SP: 800) by a normal fault, and its synthetics and antithetics (Fig. 8f). Age of this fault is probably older than the Cihanbeyli Formation which is deposited with terrestrial and lacustrine lithology in Upper Miocene–Pliocene (Akarsu, 1971). The formation was deposited quite thick on the hanging wall of the fault which created a half-graben observed between the SP: 820–1100. Causative body for the Hanobasi Anomaly probably extends in the reflection-free zone between SP: 960–1430. Deepest point of this reflection-free zone can be followed until 1300 ms at SP: 1200 where the systematic, regular reflections coming from the deeper parts of the seismic section are suddenly clipped. Causative magmatic body for the Hanobasi Anomaly might have been created by or intruded into this fault zone composed of synthetics-antithetics. In this case, this

body may be interpreted as an andesitic intrusion produced from the fault related partial crustal melting. If the body was a basaltic intrusion with the mantle origin, we would have expected continuation of destructive effects in seismic sections below the causative body. On the contrary, there are continuous and regular reflections beneath this intrusion at the deeper sections of both seismic lines. Moreover, reflections on the southwestern end of the Line SL-1 can be followed from the lower to upper part of the seismic section for different seismic times. Upper surface of the magmatic intrusion is almost flat and there are neither fluctuations nor irregularities on it. However, deepest part of the causative body is located to the south and seismic line SL-2 (Fig. 8g and h) crosses almost in the middle of the anomaly (Fig. 8b). Geometry of this intrusive mass is similar to a basin geometry that is represented by a flat surface on top and a basin shape curvature at the bottom (Fig. 8h). This geometry can clearly be observed on both seismic sections. Causative body is followed from SP: 200 (to the north) to SP: 480 to the south of the SL-2 seismic section. Deepest point is located around 1900 ms at the SP: 400. Top of this mass is observed around 500 ms at the same SP (Fig. 8h). Because there is no well drilled on or around the causative body, RMS velocities of seismic sections are the only velocity data for depth conversion to determine the top and bottom of the intrusive mass. Depth calculations for both seismic sections at the considered SP’s are presented in Table 4 including two-way times and RMS velocities. Top and bottom surface of the causative body were found at about 300 and 3000 m, respectively. Meanwhile, seismic traces are recorded in a horizontal offset distribution. As a result of this phenomenon, RMS velocities are always lower than the borehole velocity measurements that are acquired in vertical, downhole form. In addition, seismic traces may hold some residuals of static corrections that is a process to remove the effects of weathering zone and low velocity layers on the surface. In particular, surface of the Salt Lake Basin where the Hanobasi Anomaly takes place is covered by very low velocity layers (about 1400–1700 m s1). Moreover, velocity of such an intrusion in a low velocity sedimentological environment may be low-estimated in seismic sections, because the seismic data are recorded in an areal acquisition that allows seismic waves traveling inside the low velocity layers. In cumulative view of all these involving effects, deepest part of this causative body can be expected deeper than 3000 m, probably around 3500 m and this depth value is consistent with the suggested depth from the 3D modeling results in the new method. There is about 30 exploration wells drilled in the Salt Lake Basin. Average sonic log velocity of the sedimentary basin fill is calculated as 4000 m s1 by Aydemir (2005). Reciprocal density value for this velocity is found as 2.40 g cm3 in the velocity–density diagram of Ludwig et al. (1970). Since the causative body is interpreted as an andesitic intrusion, average density of andesite can be taken as 2.61 gr cm3 (Telford et al., 1990). The Cihanbeyli Formation overlies almost all sedimentary horizons and the reflection free zone representing causative intrusion. Because the contact at the bottom of this formation is recognized as discordance (Akarsu, 1971) and this discordance can be observed clearly in both seismic sections with a bright continuous reflection, there should be a time gap and an alteration phase after settlement of the magmatic body. In this case, density contrast between the causative body and surrounding sedimentary units can be approximated as 0.15 gr cm3 as a result of alteration before the deposition of Cihanbeyli Formation. The pseudogravity anomalies of the Hanobasi Anomaly were modeled using the 3D gravity modeling program based on the Cordell and Henderson (1968) method. Bottom depth of the body adjusted until the top of the model reached to the depth of 0.4 km estimated by seismic line SL-2 (Table 4). Thus, the base of the model lies at a depth of 3.5 km (Fig. 8i). Magnetic and gravity anomalies

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of the model were calculated uniformly for the same magnetic intensity and density contrast (J = Dq = 1) (Fig. 8j and k). In this way, adjustment factor for the total magnetic intensity is estimated as 1.33 A m1. The density contrast of this anomaly was determined for the body 0.15 gr cm3 using the density contrast diagrams (Fig. 8l) and same density contrast was accepted from the evaluation of seismic sections. The ratio of magnetic intensity to density contrast (J/Dq) is 8.867 mA m2/kg. Finally, observed and calculated gravity anomalies were calculated and density contrast of the body was found as a 0.18 gr cm3 from the RMS method (Fig. 8m). This correlation procedure was applied only to the apex of the anomalies to mitigate edge effects. 5. Discussions and conclusions In this study, we proposed a new method to estimate the ratio of magnetic intensity to density contrast of a body causing magnetic and gravity anomalies by means of simple correlation. Normally, the magnetic intensity and density of an anomalous body

33

are determined in the laboratory environment after sampling from the surface. However, the magnetic intensity and density contrasts can be calculated from the magnetic and gravity data by using this new developed method in case of having no hand samples. In this method, three diagrams of density contrasts with low, middle and high levels are produced. In these diagrams the vertical axis represents the magnetic intensity (J) while the horizontal axis stands for the ratio of the pseudogravity and gravity anomalies (Psg/Grv). Density contrast can also be estimated by the (RMS) method to verify the results of proposed method. The method was tested on the gravity and magnetic anomalies of synthetic models with and without random error. For 20% random error applied into the amplitude of the magnetic data, no change was observed for the magnetic intensity and density contrast of the synthetic model (Table 1). Error analyses were also performed for the density diagrams by adding 20% error into the magnetic intensity and ratio of Psg/Grv values. Another error analysis was made adding 20% errors to the top depth of causative body. It can be suggested from all of the error analyses that the proposed method is reliable. Results obtained from the synthetic models present a good correlation

Fig. 8. (a) Location map of the Lake Tuzgolu (Salt Lake) region. Annotated rectangle shows the study area. (b) Aeromagnetic anomaly map of the Hanobasi anomaly. SL-1 and SL-2 are seismic lines in study area. (c) Gravity anomaly map of the Hanobasi anomaly. (d) Pseudogravity anomalies of the aeromagnetic anomaly presented in (b). (e) Uninterpreted seismic line SL-1. (f) Interpreted seismic line SL-1. (g) Un-interpreted seismic line SL-2. (h) Interpreted seismic line SL-2. (i) Three-dimensional gravity model of the Hanobasi anomaly. (j) Calculated magnetic anomalies of the model presented in (i) adjusted by factor of 1.33 A m1. (k) Calculated gravity anomalies of the model presented in (i) with uniform density (Dq = 1.0 g cm3). (l) Density contrast diagram for values of density contrast for the Hanobasi anomaly. N sign shows the estimated density contrast of Hanobasi anomaly. (m) RMS correlation function for values of density contrast for the Hanobasi anomaly.

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Fig. 8 (continued)

Fig. 8 (continued)

O. Bektas et al. / Physics of the Earth and Planetary Interiors 204–205 (2012) 22–36

35

Fig. 8 (continued)

with the model parameters. Initial magnetic intensity and density contrast used for the synthetic models were also estimated by means of the correlation and controlled by RMS procedures.

The method was applied on the field examples (real data). Case 1 is about the Tetbury magnetic anomaly in the Worcester Graben, England (Ates, 1992). The magnetic intensity of the Tetbury

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Table 4 Parameters of the hanobasi causative body obtained from the seismic lines. Line name and shot point (SP)

Time (ms)

RMS velocity (ms1)

Depth (m)

SL-1 (SP: 1200)

400

1348

270

1300

3046

1980

500

1878

470

1900

3074

2920

SL-2 (SP: 400)

Top of causative body Bottom of causative body Top of causative body Bottom of causative body

Anomaly was estimated as 1.22 A m1. By means of correlation procedure, density contrast of the body was obtained as 0.05 gr cm3. Ates and Kearey (1995) suggested that the density contrast of the Tetbury magnetic body is 0.04 gr cm3 from the 2D gravity modeling (Fig. 7f). The RMS method was not applied to the Tetbury magnetic anomaly because the gravity anomalies indicate a reasonable correlation with the surface geology (Ates and Kearey, 1995). Case 2 is the Hanobasi Anomaly of Central Turkey (Aydemir, 2005). Density contrast of the body is determined as 0.15 gr cm3 from the correlation between the new method and seismic interpretation, and 0.18 gr cm3 from the RMS method. The magnetic intensity of 1.33 A m1 was calculated by means of 3D processes. It is possible to reach a statement that the parameters and results of new proposed method are consistent with the density contrast obtained from the seismic and sonic log velocities together with the literature data in this region. Another confirmation for depth values of the model study is the depth conversion results at some certain SP’s in seismic sections. Bottom depth (3500 m) of the causative body is quite reasonable in comparison with the depth value obtained at SP: 400 of seismic line SL-2. Although the Hanobasi Anomaly is a large, apparent magnetic anomaly, it does not have any surface evidence. Its depth and other parameters such as density contrast and the magnetic intensity were obtained and confirmed by the seismic data. Although the magnetic intensity of both Tetbury and Hanobasi bodies are close to each other, density contrast of Tetbury body is lower. It may be concluded that, rocks with high ratio of the magnetic intensities to low densities are unlikely to have volcanic origin. Thus, to the north of Tetbury area, around Malvern Hills, Precambrian rocks outcrop (Ates and Kearey, 1995). It is highly considerable that buried Tetbury body may be composed of such formation with high ratio of J/Dq, but low density contrast. On the other hand, the Hanobasi body could have the volcanic origin with its medium ratio of J/Dq and density contrast. It is thus necessary to know the magnetic intensity or density contrast of an anomalous body as well as knowing its J/Dq ratio. In general, results obtained from the new method present good correlation for both cases. This correlation leads to a conclusion that proposed method could successfully be used on magnetic and gravity anomalies to obtain quite reliable results in the absence of any seismic and well data to correlate. In comparison with the other recent papers, this new method has an advantage of studying each anomaly separately for different rock types. Other methods enable to calculate only ratio of the magnetic intensity to density contrast independently from the rock types. However, it should be considered that different rocks can give the same ratio.

Only restrictive aspect of this method is that; magnetic and gravity data should be originated from the same buried, causative body. Acknowledgments Authors would like to thank the Mineral Exploration and Research Institute of Turkey for the use of gravity and aeromagnetic data that were provided for a TUBITAK Project (Project No: YDABCAG-118). Our appreciations are also extended to the General Directory of Petroleum Affairs (GDPA) for provision of seismic sections. We are the grateful to Dr. Kumar Hemant Singh and other anonymous reviewer for their constructive suggestions. Many thanks are extended to Dr. Kei Hirose for his delicate management of editorial process. References Akarsu, I., 1971. II. Bolge AR/TPO/747 Nolu sahanin terk raporu (unpublished). Petrol Isleri Genel Mudurlugu, ANKARA. Ates, A., 1992. Geophysical investigations into the deep structure of the Bristol area. PhD Thesis, University of Bristol, England. Ates, A., Kearey, P., 1995. A new method for determining magnetization direction from gravity and magnetic anomalies: application to the deep structure of the Worcester Graben. J. Geol. Soc. 152, 561–566. Ates, A., Kearey, P., Tufan, S., 1999. New gravity and magnetic maps of Turkey. Geophys. J. Int. 136, 499–502. Aydemir, A., 2005. Investigation of structural geology and hydrocarbon potential of the Tuzgolu Basin and surrounding area by using geophysical methods. Ph.D. Thesis (unpublished), Ankara University, Turkey (in Turkish with English abstract). Aydemir, A., Ates, A., 2005. Preliminary evoluation of Central Anatolian basins in Turkey, using the gravity and magnetic data. J. Balkan Geophys. Soc. 8, 7–19. Baranov, V., 1957. A new method for interpretation of aero-magnetic maps: pseudogravimetric anomalies. Geophysics 22, 359–388. Bilim, F., Ates, A., 1999. A computer program to estimate the source body magnetization direction from magnetic and gravity anomalies. Comput. Geosci. 25, 231–240. Bilim, F., Ates, A., 2004. An enhanced method for estimation of body magnetization direction from pseudo-gravity and gravity data. Comp. Geosci. 30, 161–171. Blakely, R.J., 1995. Potential Theory in Gravity and Magnetic Applications. Cambridge University Press, UK. Buyuksarac, A., 2007. Investigation into the regional wrench tectonics of inner East Anatolia (Turkey) using potential field data. Phys. Earth Planet. Inter. 160, 86– 95. Cordell, L., Henderson, R.G., 1968. Iterative three-dimensional solution of gravity anomaly data using a digital computer. Geophysics 33, 596–601. Doo, W.-B., Shu-Kun, H., Ching-Hui, T., Yin-Sheng, H., 2009. Using analytic signal to determine magnetization/density ratios of geological structures. Geophys. J. Int. 179, 112–124. Goodacre, A.K., 1973. Some comments on the calculation of the gravitational and magnetic attraction of a homogeneous rectangular prism. Geophys. Pros. 21, 66–69. Kearey, P., 1977. Computer program ‘‘prism’’ to compute gravity and magnetic anomalies of right rectangular prism (unpublished). Earth Sciences Department, Univeristy of Bristol. Kearey, P., 1991. A possible source of the South-Central England magnetic anomaly: basaltic rocks beneath the London platform. J. Geol. Soc. 148, 775–780. Kearey, P., Rabae, A.M., 1993. Source of the Bicester magnetic anomaly. Geol. J. 28, 191–203. Kearey, P., Brooks, M., Hill, I., 2002. An Introduction to Geophysical Exploration, third ed. Blackwell Publishing. Ludwig, J.W., Nafe, J.E., Drake, C.L., 1970. Seismic refractions. In: Maxwell, A.E. (Ed.), The Sea, vol. 4. John Wiley, New York, pp. 53–84. Mendonça, C.A., 2004. Automatic determination of the magnetization-density ratio and magnetization inclination from the joint interpretation of 2D gravity and magnetic anomalies. Geophysics 69, 938–948. Mendonça, C.A., Meguid, A.M.A., 2008. Programs to compute magnetization to density ratio and the magnetization inclination from 3-D gravity and magnetic anomalies. Comp. Geosci. 34, 603–610. Spector, A., Grant, F.S., 1970. Statistical models for interpretating aeromagnetic data. Geophys. 35, 293–302. Telford, W.M., Geldart, L.P., Sheriff, R.E., 1990. Applied Geophysics, second ed. Cambridge University Press, UK.