gravity

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2D Gravity Inversion Technique in The Study of Cheshire Basin

Nadiah Hanim Shafie

Postgraduate Student, School of Environmental Science and Natural Resources, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600

Bangi, Selangor, Malaysia [email protected]

Umar Hamzah

Professor, School of Environmental Science and Natural Resources, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi,

Selangor, Malaysia [email protected]

Abdul Rahim Samsudin

Professor, School of Environmental Science and Natural Resources, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi,

Selangor, Malaysia [email protected]

ABSTRACT The gravity method involves measuring the Earth’s gravitational field at specific locations influenced by differences in density of sub-surface rocks. It has found numerous applications in engineering, environmental and geothermal studies especially in locating voids, faults, buried stream valleys, water tables and geothermal heat sources. A total of 753 gravity data acquired from the northwestern part of the United Kingdom by the British Geological Society were used in this study with the aims of studying the major structural patterns within the Cheshire basin. The data were processed and analysed with the aid of Oasis Montaj software to determine the fault trends within the entire sedimentary basin. The Bouguer gravity map shows positive anomaly in the northwestern part of the study area indicating the presence of high density sedimentary rocks while negative anomaly observed in the southern part corresponds to low density sediments. The regional and residual isostatic maps derived from different cut-off wavelengths reflect changes in anomalies corresponding to different types of sedimentary rocks such as mudstone, sandstone and limestone. The major faults patterns in Cheshire basin were clearly observed from the Bouguer gravity total horizontal derivative map. Most of the major faults observed in the south of study area are trending in NW-SE and NE-SW directions. The N-S trend minor faults are found in the west and east, while the E-W trends were dominant in the north and south of the study area. The limestone basement depth of about 3736m was estimated from the 2D-modeled cross section developed along the E-W border.

KEYWORDS: Gravity anomaly, 2D modeling, Cheshire basin, Oasis Montaj software

INTRODUCTION Gravity method is a non-destructive geophysical technique that has been widely used to

measure the earth’s gravitational field at specific locations on the earth’s surface due to the difference in subsurface density values. This method works when the buried targets have densities very much different as compared to the host material. The gravity technique has successfully

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delineated the Nash dome in coastal Texas which was considered the first geophysical oil and gas discovery (LaFehr, 1980; Nabighian et al. 2005). Its application was also considered as fruitful in both mineral (Hoover et al. 1991; Dransfield 2007) and oil exploration (Badmus et al. 2011) in terms of its ability in determining the thickness of overburden material overlying the bedrock or the volume of any sedimentary deposit. This method is also popularly used in exploring the geological faults (Gao & Song 2006), buried ancient stream valleys (Lyatsky & Dietrich 1998), cavities (Hajian et al. 2012), geothermal deposits (Mariita 2010) and changing of subsidence levels in sinkholes development (Rybakov et al. 2001).

The purpose of this study is to produce improved gravity anomaly map by using the Oasis Montaj software which enable applications of isostatic regional and residual filtering as well as the total horizontal derivative filtering applied to the gravity data. The resulting anomaly maps were then used in the interpretations of faults trend and tectonic system of the subsurface geological formations in the study area. The 2D inversed model was generated to estimate the depth and thickness of the subsurface geology overlying the bedrock. The study area covered 50 km x 20 km and located in the northern part of Cheshire Basin, North West of United Kingdom. A total of 753 gravity data measured along 1.6 x 1.6 km each were obtained from the British Geological Society (BGS) for used in this study.

Figure 1: Location of the study area as shown in the black box.

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Geologically, Cheshire Basin (Figure 1), Carlisle Basin and Irish Sea Basin are located in North-Western England. McLean (1978) observed that the Cheshire Basin and East Irish Sea Basin formed part of NW-SE trending Clyde Belt of Triassic troughs extending from the Highland Boundary Fault to the Cheshire Basin. Figure 2 shows the geological map of the study area indicating the Cheshire Basin which generally lies within a NNW-SSE trending Permo-Triassic rift that extends from the Wassex Basin to the Scottish Inner Hebrides. This half-graben is bordered on the east by the Wem-Red Rock fault system, which has depth to Permo-Triassic base at 3500 m (Chadwick and Evans, 1995). Colter and Barr (1975) found that the Triassic succession thins out by depositional onlap at the western margin. In the early 1970s, several oil companies conducted seismic surveys across this area and discovered that the seismic sections had problems in defining the base of Permo-Triassic sediment. Therefore, Lamb et al. (1983) stated that the assumption of no flat-lying Coal Measures in the Permo-Trias layer was uncertain.

Figure 2: Geological map of the study area.

THEORY Solution of inverse problem in finding acceptable geological models representing measured

gravity field variations is a complex task. Figure 3 shows one or several 3D layers model which are defined in a bounded space. The inversion procedure requires no explicit matrix inversion leads to a simple factorization of the forward problem in the frequency domain. The earlier 3D methods divided the subsurface into a several vertical infinite depth prisms which can be determined by least squares inversion in the space domain (Cordell and Henderson 1968; Gerard

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and Debeglia 1975; Chai and Hinze 1988). This method lies in speed and good convergence even though it is limited to small data sets. The theoretical basis follows closely to several studies by Parker (1973) for forward problem and Pilkington and Crossley (1986) for inverse problem.

Figure 3: Geometry of the forward problem.

The constant density contrast of the gravitational potential bounded below the horizontal plane, z = 0 and above the surface, z = h(r) is as shown in Fig 3. The ro position is given by

(1)

where G is Newton's gravitational constant, σ is the density contrast and z is positive upwards. Parker's method manipulates Fourier transformation of (1) by lessen computational demanding form of

(2)

where ĝ (k) is the gravity anomaly in frequency domain, F[ ] indicates the Fourier transformation, zo is height of the observation plane and k is the wavefactor. The Fourier transform can be frequently evaluated and easy to used for large gridded data sets makes the equation (2) effective. Parker (1973) also stated that the z = 0 level must be placed at the average h(r) value in (2) for the optimum convergence series.

When the density contrast of the sediment in the sedimentary basin is constant, the non-linear inversion for depth to source in the model are varying. The linearized method of the forward problem is used to solve non-linear problems. The linearized form in (2) can be simplified by keeping the first term

(3)

Using (3), the gravity values in vector unit will then become

(4)

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where T is a diagonal matrix with elements,

(5)

E* and E are inverse Fourier and matrix equivalents of Fourier transform respectively and h is the first-order topography. Equation (4) is similar to the singular value decomposition of the forward problem, where T contains the eigenvalues ti while E and E* correspond to eigenvector matrices.

The topographic inversion problem can be solved by using an iterative scheme based on equation (4) and the non-linear problem as follows;

(6)

where gobs is the observed gravity data and gn is the calculated effects of hn model where topography ho= 0, to ensure the result of the inversion will have minimal affect by initial estimate. This equation uses a constant inverse (E*T-1E) during the iterative procedure to differentiate from the standard inverse method. Small eigenvalues coresponding to large wavenumbers lead to instability in the resulting problem. Magnitude of the eigenvalues of matrix T affect on the stability of the inverse in (6). There are many ways to eliminate instability in this problem. The latter approach is taken and considered as more approriate when no clear distinction can be made between the small and large eigenvalues.

MATERIALS AND METHOD Gravity method was carried out in investigating the subsurface geology or the information

about the earth’s subsurface. In this technique, a qualitative examination of the gravity grid values, contour maps and the gravity profiles were developed to determine the lateral location of gravity variations in order to quantify the subsurface feature causing the gravity variations. Data gridding was performed in the editing stage and further stages in the data processing techniques can be performed semi-quantitatively to detect tectonic structural and fault such as shaded relief of the anomaly map, vertical derivatives anomaly map and the amplitude of the analytic signal (Klingele et al., 1991; Marson and Klingele, 1993; Lyatsky et al., 2004). The presence of faults can be inferred from positive and negative lineaments in the gravity anomaly maps and the dominant trends are estimated by rose diagram plots.

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Figure 4: Positions of gravity stations.

The Bouguer gravity anomalies are calculated with reference to the Geodetic Reference System 1967 (GRS67), International Gravity Standardisation Net 1971 (ISGN71) and National Gravity Reference Net 1973 (NGRN73). The gravity reduction were carried out by the BGS. Fig. 4 shows the location of the gravity stations in this study. All the gravity data have been tied up to the Ordnance Survey Great Britain 1936 (OSGB36) datum and grid by British National Grid. Oasis Montaj software is used for processing including the projection, gridding, countering, filtering and plotting. The data were shown in latitude, longitude and length of gravity stations. The grid interval chosen was 1.4km x1.4km grid spacing using minimum curvature. Bouguer anomaly (BA) gravity map were calculated by using an equation (7) as shown below;

hcG

z

gggBA t )2(0

(7)

where g0 is the observed gravity value, gt is theoretical gravity value, zg is vertical gradient gravity value (0.3086 mgal/m), G is gravity constant (6.672×10-6 m2kg-1mgal), ρc is rock density and h is station elevation above the datum. The density value used in this study is 2675 kg/m3 and g is given in the equation (8) as written below;

g = 978.03185(1 + 0.005278895 sin2 Φ + 0.000023462 sin4 Φ) (8)

where g is gravity value in Gals and Φ is the latitude.

Low-pass and high-pass wavelength filters were applied to the gravity data to produce isostatic regional and residual map. The high-pass filtering is used to separate the regional and local anomalies. Low-pass filtering is applied to cut the desired wavelength where the wavelength lower than the required one will be cut off. This low-pass filter is performed by Fast Fourier Transform (FFT) technique in the frequency domain.

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Total horizontal derivative (THD) function is used to enhance the linear features in the gravity contour which reveal the presence of faults, dykes, and lineaments in the study area. This operation measures basically the rate of change of gravity field in X and Y directions and creates a resultant grid (Cordell, 1979). This has the effect of highlighting high gradient areas such as might occur at faulted boundaries which is useful for delineating structural trends and the azimuth specific horizontal derivative can also be calculated to further highlight any particular trends (Cordell and Grauch, 1985).

Gravity modelling will be carried out in the final stage of gravity interpretation with the aims of determining the density, depth and geometry of one or more subsurface bodies. The GM-SYS modelling is an interactive software for 2D-modeling of geological cross sections perpendicularly constructed to the strike of the body or structure. It also has the ability to calculate and display gravity responses of any subsurface body. The method used to calculate the gravity responses of any structure or subsurface body are based on the formulations given by Talwani et al. (1959), Chakravarthi and Sundararajan (2005), and make use of algorithms described in Won and Bevis (1978). The calculated gravity responses will be compared with the observed gravity anomaly and the model dimensions will be adjusted so that the calculated gravity response of the model and the observed anomaly are matched. The final model will be considered to represent the actual subsurface body for the observed anomaly.

RESULTS AND DISCUSSION

The Bouguer anomaly gravity map (Figure 5) shows gravity values ranging from -4.2 to 18.2 mGal. Basically, the gravity values are decreasing towards the southeastern part of the study area and increasing towards the north and west. In general, the highs and lows are associated with rock densities as well as the thickness of rock formation overlying the basement. The low density zone may be corresponding to a much thicker subsurface sedimentary overlying the limestone basement. The high gravity trend is most likely interpreted as thinning of sedimentary formation towards the east and ended with higher density material in the east and southwestern part of the study area. The minimum or lowest density zone observed in the central part of the study area can be associated with the thickest sedimentary bedding or basin depocenter.

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Figure 5: Bouguer anomaly map and the locations of profile 1 and 2.

Figure 6 shows the 30km wavelength cut-off map of regional gravity or isostatic regional map of the study area indicating the shape of basement rock underlying the sedimentary deposits. The gravity values increase to the northwest and decreased towards the southwest. This indicates the higher basement rock position in the northeast and deeper towards the southeast.

Figure 6: Isostatic regional map.

Figure 7 shows the isostatic residual map obtained by subtracting the Bouguer from regional gravity values. This kind of map is meant for estimating the presence of structures in the

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sedimentary basin above the basement in the study area. A band of high gravity values trending from northwest to southeast is observed in the isostatic residual map. This high gravity zone is sandwiched between lower gravity values in the north and south. This trend can be interpreted as representing a possible anticlinal fold (F) with the crest located in the middle part of the study area. The fold dips towards the north and south which is covered by thicker sediment.

Figure 7: Isostatic residual map. F denotes the position of a fold

The total horizontal derivative map obtained from bouguer gravity map is shown in Figure 8 The general trends of faults in the Cheshire basin are shown in this map. Most of the major faults found in the southern part of the study area are trending in NW-SE and NE-SW directions as shown in the rose diagram (Figure 9). The minor faults are found in the western and eastern parts of the study area with N-S trending faults while in the northern and southern part the faults are trending E-W.

F

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Figure 8: Total horizontal derivative map and the trend lines of potential faults.

Figure 9: Rose diagram indicating the major and minor trends of faults observed from THD map. Major trends of faults are NW-SE and NE-SW.

Two cross sections along E-W were developed from the Bouguer anomaly map purposely for 2D modeling (Figure 10 a, b). Models were estimated based on borehole and geological cross section of the study area consisting mainly of sedimentary rocks. The top Triassic mudstone density is assigned as 2.34 g/cm3 while the Permo-Triassic sandstone underlying it has a density of 2.54 g/cm3. The highest density of 2.58 g/cm3 is assigned to the Lower Palaeozoic limestone basement.

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(a)

(b)

Figure 10: The cross section of (a) Profile 1 and (b) Profile 2 based on 2D inverse modeling.

The results of 2D modeling show the estimate depth to limestone basement of about 3736 m. Gale et al. (1984) reported that the basement depth based on Prees and Knutford boreholes drilled within the Chesire basin were 3726 m and 2992 m respectively. Therefore the depth to

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basement based on 2D gravity modeling and drilling are quite similar. Interestingly, the 2D modeling reveals the presence of a basinal sedimentary structure separating the Permo-Carboniferous sandstone and mudstone and the Palaeozoic limestone basement. Based on previous study, coal beds are found in the boarder of sandstone-limestone upper carboniferous Millstone Grit.

CONCLUSIONS

Gravity anomaly maps were developed from the Oasis Montaj software. The difference in Bouguer anomalies referred to difference in rock types and densities. The isostatic maps with different cut-off wavelengths indicate changes in rock compositions in the study area. The THD Bouguer gravity anomaly maps show NW-SE and NE-SW dominant fault trends. 2D modeling across several profiles discovered the presence of a sedimentary basin structure and successfully estimated the depth of limestone basement. Further study will be carried out in future by integrating gravity, magnetic, seismic and borehole data for detail basin analysis.

ACKNOWLEDGEMENT

The authors appreciate the British Geological Society (BGS) for providing the gravity data and information needed for this study.

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