Optimal Design of a Gravity Survey Network and its Application to Delineate the Jabera-Damoh...

Optimal Design of a Gravity Survey Network and its Application

to Delineate the Jabera-Damoh Structure in the Vindhyan Basin,

Central India

RAVI PRAKASH SRIVASTAVA, NIMISHA VEDANTI, and V. P. DIMRI

Abstract—Fractal dimension analysis was carried out for optimal designing of 2-D gravity survey

network and to determine an optimum range of gridding interval to generate least aliased Bouguer

anomaly maps. As a test case, this method has been successfully applied to the Jabera-Damoh region of the

Vindhyan Basin, which is considered as a potential hydrocarbon bearing area. In particular, we aim to

delineate accurately the lateral extent of a possible hydrocarbon bearing structure. To achieve this aim,

fractal dimension of survey network was computed using 2-D distributions of observation points in the

planning phase of the survey so that the optimum station spacing for gravity survey can be obtained. A

range of optimum gridding interval for the gravity data set was suggested using the box-counting method

of fractal dimension determination. Bouguer anomaly maps of the region are prepared utilizing the

optimum gridding interval. For the first time, these anomaly maps clearly outline the gravity evidence of an

anomalous rifted structure, which is bounded by parallel faults on either side. This structure is interpreted

as a favorable basin for the occurrence of hydrocarbons. Another finding of this study has been the

delineation of an apparently small ridge-like structure running east-west, dividing this basin in two parts. A

subsurface geological model along a profile across the Jabera structure has also been presented.

Key words: Fractals, sampling, gridding, gravity anomaly, Vindhyan Basin.

Introduction

Design of a survey network plays an important role in optimizing the number of

data points. Most of the geophysical data sets, especially gravity observations, are

often irregularly distributed, thus survey design becomes a critical step, both to

obtain sufficient data at a minimum cost and to avoid problems related to survey

spacing (i.e., data sampling). Data sampling problems generally cannot be resolved

during processing and therefore must be dealt with at the survey design stage only. A

careful data acquisition can significantly streamline subsequent quality control tasks

and helps to minimize related processing costs. Processing and interpretation of

acquired 2-D gravity data requires interpolation of data at regular grid intervals.

National Geophysical Research Institute, Uppal Road, Hyderabad 500 007, India.E-mail: [email protected]

Pure appl. geophys. 164 (2007) 2009–20220033–4553/07/102009–14DOI 10.1007/s00024-007-0252-1

� Birkhauser Verlag, Basel, 2007

Pure and Applied Geophysics

Previous studies carried out by KEATING (1993), SEDARAT and NISHIMURA (2000),

FEATHERSTONE and KIRBY (2000) reveal that the fractal dimension (FD) of a data

distribution can in theory be used to select an optimum gridding interval so as to

minimize the aliasing due to interpolation. However, if aliasing due to acquisition

exists in the data, then no processing technique can give accurate results.

Further, detectability limits of geophysical surveys also depend on the FD of

survey network (LOVEJOY et al., 1986; KORVIN et al., 1990; DIMRI, 1998). As a rule of

thumb, for very near-surface sources, spatial extent of gravity anomaly has the same

order of magnitude dimension as its causative body.

Keeping these points in mind, we designed a gravity survey network with

optimum fractal dimension to delineate a domal structure (Jabera dome) reported in

earlier studies (SRIVASTAVA et al., 1983; MISHRA et al., 1998) in the southeastern part

of the Vindhyan Basin (Fig. 1). This area is known as a ‘high risk-high reward’

frontier area for hydrocarbon exploration (DAS et al., 1999). Our aim was to

delineate the shape and lateral extent of the reported domal structure, using acquired

gravity data at optimum station spacing.

Design of Gravity Survey Network

A gravity survey network was designed in the Jabera-Damoh region of the

Vindhyan Basin, central India as outlined by a red polygon in Figure 1. This region is

covered by patches of dense forests and rivers; hence optimum designing of the

survey network was mandatory to delineate the geologically reported domal

structure near Jabera, which outcrops in an approximate area of �35� 15 km

within the Vindhyan Basin. For a detailed survey, we selected an approximate area of

70� 60 sq km. Since cost of acquisition is related to the sampling density, hence the

initial focus was to determine the optimal tradeoff between the spatial resolution and

sampling density of gravity observations. It is known that a 2-D survey network of

FD = 2 can detect objects of any dimension (LOVEJOY et al., 1986; DIMRI, 1998).

This reveals that for enhanced detectability of the geophysical anomaly, one should

try to design a measuring network with fractal dimension �2. It has been observed

that if FD is considerably less than 2, then the field being sampled cannot be fully

recovered and some aliasing will occur (LOVEJOY et al., 1986; KEATING, 1993).

However, in real field scenario, it becomes practically difficult to design a survey

network with FD = 2, due to many logistic problems.

Because of inaccessible terrain in the study area, it was difficult to acquire gravity

data on a regular 2-D grid. Thus, before moving to field, we carried out a synthetic

study to plan the survey network in its initial phase. In the synthetic study, we

computed the FD of various networks (grids) designed according to the shape of the

study area to find out optimum station spacing for enhanced detectability limit. We

choose 2-, 3- and 4-km station spacings to design three different synthetic 2-D

2010 R. P. Srivastava et al. Pure appl. geophys.,

networks. Fractal dimension (Fig. 2) of these synthetic grids was computed using the

well-known box-counting method (TURCOTTE, 1992). A comparative analysis based

on the cost of the survey and the detectability limit of these synthetic grids is shown

in Table 1. It is clear from Table 1 that FD of synthetic grid decreases with an

increase in station spacing. In this case one can prefer to acquire data at 2-km

spacing because of higher FD (dense coverage). Since it was difficult to acquire data

Figure 1

Geological map and location of the studied area in the Vindhyan Basin, central India. Red polygon is the

surveyed area. A profile AA’ across the target structure, Jabera dome is selected for the modeling.

Vol. 164, 2007 Optimum Design of Survey Network 2011

Figure 2

Fractal dimension analysis of designed synthetic survey networks at station spacing: (a) 2 km, ln(r) = 0.7,

r ¼ 2:01 km, (b) 3 km, ln(r) = 1.1, r ¼ 3:0 km and (c) 4 km, ln(r) = 1.4, r ¼ 4:05 km, respectively.


at the regular grid of 2-km spacing in the study area, acquisition of data at 3-km grid

spacing is suggested in the studied region.

For comparative study, gravity data were also acquired at approximately 2- and

4-km spacing, though it was not suggested for practical purposes. The acquisition

pattern for 2-, 3- and 4-km station spacing is shown in Figure 3, where synthetic

observation points are shown in red color and actual observation points are shown

in blue color. Figure 3 shows that observed data points are quite close to the

designed grid points for 3- and 4-km station spacings. Computation of FD of a real

survey network with observation points approximately at 2-, 3- and 4-km spacing

respectively, is shown in Figure 4. The value of FD is obtained as 1.65, 1.66 and

1.67, respectively for 2-, 3- and 4-km station spacing. This slight increase in fractal

dimension with station spacing is observed because of the fact that the real data

acquired at approximately 2-, 3-and 4-km intervals is not at regular intervals, and

there are some blank patches as shown in the Figure 3. The gravity data acquired

at 4-km station spacing were more homogeneous and hence have high fractal

dimension.

Optimum Gridding of Gravity Data

Preparation of Bouguer anomaly maps requires interpolation of data using

statistical methods, which introduces aliasing. Hence, appropriate processing is

required to generate the least aliased anomaly maps. To overcome this problem,

KEATING (1993) suggested the use of well-known fractal dimension analysis to

determine an optimum gridding interval, exploiting the concept of scaling regime of

the data. The FD analysis is done using the box-counting method.

In the box-counting method, the area is subdivided into a number of equal size

squares with side length r. The logarithm of the number of such squares (ln NðrÞ),which have at least one observation point, is plotted against ln(r) and the slope of this

plot gives the value of the fractal dimension. The smallest length r at which the

scaling regime ceases to be constant gives the optimum sampling interval. It was

Table 1

Comparative study of designed survey networks using different station spacings and cost of the survey, which

corresponds to man-days to acquire the data. It is assumed that at 2-km spacing about 15 data points, at 3-km

about 12 data points, and at 4-km about 10 data points can be collected in a day, in a difficult terrain. This

assumption is based on practical experience in the field

Station

Spacing

FD of Designed 2-D

Grid

Detectability

limit (2-FD)

No. of Stations Man-Days

2 km 1.79 0.21 1436 95

3 km 1.75 0.25 636 53

4 km 1.74 0.26 357 36


0 20 40 60 80 100 1200

20

40

60

80

100

120

X (km)

)mk(

Y

Designed Grid

Acquired Stations

(a)

(b)

(c)

0 20 40 60 80 100 1200

20

40

60

80

100

120

X (Km)

)m

K(Y

Designed GridAcquired Stations

0 20 40 60 80 100 1200

20

40

60

80

100

120

X (Km)

)m

K(Y

Designed GridAcquired Stations

Figure 3

Acquisition network with actual observation points plotted over: (a) Station spacing 2 km, (b) station

spacing 3 km, and (c) station spacing 4 km. Synthetic grid nodes are shown in red and actual observations

are shown in blue.


0 1 2 3 4 50

1

2

3

4

5

6

7

ln(r)

)N(nl

(a)

0 1 2 3 4 50

1

2

3

4

5

6

7

ln(r)

)N(nl

(b)

0 1 2 3 4 50

1

2

3

4

5

6

ln(r)

)N(nl

(c)

Figure 4

Optimum gridding interval and fractal dimensional analysis of real data acquired at: (a) 2-km station

spacing, ln(r) = 1.07, r ¼ 2:92 km, FD = 1.65, (b) 3-km station spacing, ln(r) = 1.23, r ¼ 3:42 km, FD=

1.66, (c) 4-km station spacing, ln(r) = 1.41, r ¼ 4:09 km, FD = 1.67.


observed that only in the case of synthetic data, one can get a unique gridding

interval which is equal to the station spacing (Fig. 2). Whereas, in the case of real

data (Figs. 4a, b), the scaling regime does not cease suddenly at a point, hence a

range for an optimum gridding interval is suggested from the curve. This range is

encircled in FD analysis plots (Fig. 4) obtained by using observed data at 2-, 3- and

4-km station spacing. We therefore suggest that instead of looking for an optimum

gridding interval, anomalies can be computed within an optimum interpolation

range. The interpolation range for the real data acquired in the studied region is

2:92� 0:5 for 2-km spacing, 3:42� 0:5 km for 3-km station spacing and

4:09� 0:5 km for 4-km station spacing as encircled in Figures 4 a,b,c.

Gridding/Interpolation Method

Interpolation is a procedure of predicting values of attributes at unsampled sites

from measurements made at point locations within the same area. Among several

techniques available for the interpolation of the data, kriging is found most suitable

for the interpolation of irregular spatial data (ECKSTEIN, 1989; ISHIDA and

KAWASHIMA, 1993; HUTCHINSON and GESSLER, 1994). The input data for kriging

are usually an irregularly-spaced sample of points. This technique is an exact

interpolator of the data. Exact interpolators honor the data points upon which the

interpolation is based. Keeping in view the robustness of the kriging for sparse data

we have used point kriging, which estimates the values of the points at the grid nodes

using commercial software ‘Surfer’, developed by Golden Software, Inc (www.gold-

ensoftware.com). The software ‘Surfer’ uses a linear variogram model as default for

point kriging and we have used the same for the interpolation of the data presented

in this paper.

Bouguer Anomaly Map of the Jabera-Damoh Region

Bouguer anomaly maps of the studied region are prepared using an interpolation

interval obtained by fractal dimensional analysis. The anomaly maps (Figs. 5a,c)

produced by the fractal method look more smooth and free from aliasing errors,

hence produce the best representation of the subsurface features of the study area

rather than the maps produced by the conventional method (Figs. 5b,d). In our view,

the conventional way of gridding the data is to take the interpolation/gridding

interval less than the actual spacing of the data locations. If the survey is done at a

random interval then the mean spacing of the data locations is normally used to grid

the data. In the fractal method we select the interpolation interval based on fractal

dimension analysis (KEATING, 1993) of the data location. It is clearly evident from

Figure 5 that the Bouguer anomaly map obtained by the fractal method is almost


free from the spurious anomalies, which are prominent in the form of small circular

contours in the anomaly map obtained by the conventional method. We have also

attempted to quantify the superiority of the fractal method over the conventional

method, however due to less data points and inhomogeneous coverage of the area,

we could not provide any statistical index for quantitative analysis, hence the analysis

presented here is only qualitative.

Results and Discussions

The oval shaped anomalies near Jabera (Fig. 6) clearly reveal the presence of an

anomalous geological feature with a negative Bouguer anomaly in the range of )60

20 40 60 80

(a) (b)

(c) (d)

100 120 20 40 60 80 100 120

X(km)

20 40 60 80 100 120X(km)

20 40 60 80 100 120X(km)

10

20

30

40

50

60

70

80

90

100

110

Y(k

m)

Y(k

m)

-74-70-66-62-58-54-50-46-42-38-34-30

mGal

A’

R

AR’

10

20

30

40

50

60

70

80

90

100

110

-74

-70

-66

-62

-58

-54

-50

-46

-42

-38

-34

-30

mGal

20

40

60

80

100

-74-72-70-68-66-64-62-60-58-56-54-52-50-48-46-44-42-40-38-36-34-32-30

mGal

20

40

60

80

100

Y (

km)

-74

-70

-66

-62

-58

-54

-50

-46

-42

-38

-34

-30

mGal

Figure 5

Bouguer anomaly maps over the region: (a) for 2-km station spacing using the fractal method, (b) for 2-km

station spacing using the conventional method, (c) for 3-km station spacing using the fractal method, and

(d) for 3-km station spacing using the conventional method.


to )74 mGal. The boundary of this structure is clearly demarcated by our study. The

delineated structure appears to be a rifted basin bounded by faults on either side.

Further, a new finding of this study is the delineation of an apparently small ridge-

like structure marked as RR’ in Figure 5a. This ridge-like structure running east-west

divides this region (basin) in two parts, which has not yet been observed in earlier

studies. It is also seen in the anomaly map that this basin extends further south-west

than hitherto known.

The anomaly pattern of the studied region does not conform to the geologically

reported domal structure near Jabera. This may be due to the fact that the particular

domal structure has a gentle dip of around 10�. This means that the domal structure

is not a deep-seated feature, rather it could be an erosional feature. It is further

observed that the Bouguer anomaly maps prepared at 2-km and 3-km spacing

convey the same geological information. This suggests that there is no loss of useful

information in acquiring data at 3-km spacing in this area, which was suggested in

the synthetic study.

Figure 6

Bouguer anomaly map of the region superimposed over the geological map of Jabera–Damoh region

extracted from Figure 1.


For quantitative interpretation we selected a profile AA’ (Fig. 5a) across the

target structure and modeled the gravity data using the Marquardt inversion

approach with the help of SAKI program (WEBRING, 1985). The target structure is

shown in the geological map of the area (Fig. 1) and the profile AA’ across the

structure is not at the boundary, thus interpolation effects at the boundary will not

affect the modeling results and the best possible model of the target structure is

obtained. The proposed subsurface model along the profile AA’ is shown in Figure 7.

This profile is selected in order to estimate the tentative geological crosssection across

the conspicuous low gravity anomaly observed in the southern part of the study area.

Deep Seismic Sounding (DSS) studies (KAILA et al., 1989) indicate maximum

thickness of sediments in this part of the Vindhyan Basin. Since this area lies in the

vicinity of Jabera, we termed it as Jabera Basin.

Using constraints from the borehole data (DAS et al., 1999) and DSS studies

(MURTY et al., 2004) the inverse modeling of this profile (AA’) has been attempted.

The preliminary depth values of the major interfaces were obtained from the 2-D

Figure 7

Gravity model along the profile AA’.


scaling spectral analysis (MAUS and DIMRI, 1994, 1995a,b, 1996) of the data. The

modeling result (Fig. 7) shows that the anomaly corresponds to a deep faulted basin

in the crystalline basement in which the upper layer with density value of 2.46 g/cc

corresponds to the upper Vindhyan rocks. This layer is underlain by 5.5-km thick

lower Vindhyan sediments. The layer of lower Vindhyan sediments is gently sloping

from NW to SE direction, which sits over the high density rocks possibly comprising

the Bijawar/Mahakoshal group. It was difficult to fit the observed anomaly pattern

without introducing this high density (2.80 g/cc) layer. In the absence of this layer,

the thickness of sediments would have increased to such an extent that it would have

not matched with the known seismic and well log results. It is also seen in the model

that the granite layer is missing in the right margin of the faulted basin whereas it has

a thin patch in its left side of the faulted segment. This conforms to the reported DSS

modeling (MURTY et al., 2004).

There is a possibility that the Bijawar/Mahakoshal groups of rocks were

deposited directly over the high-velocity (6.5 km/s) and high-density (2.93 g/cc)

exhumed lower crustal segment.

Concluding Remarks

The fractal approach of data interpolation reduces aliasing effects due to

interpolation and suggests an optimum grid interval value for interpolation of

randomly distributed data. In this case study, aliasing is reduced by optimum

designing of survey network in the Jabera-Damoh area of the Vindhyan Basin.

Modeling of the gravity anomaly along a profile across the target structure has been

done and the results reveal that the anomaly corresponds to a faulted basin in the

crystalline basement.

It is worth mentioning that the fractal dimensional analysis of finding an

optimum sampling interval is found very useful, which avoids unnecessary dense data

acquisition efforts. It is evident from the anomaly maps, produced by conventional

and fractal methods, that the later reduces spurious anomalies. Therefore use of

fractal dimensional analysis is recommended for the acquisition of data and

preparation of anomaly maps for a more realistic interpretation. However, before

designing a survey network, the following points must be taken in account:

1. Objective of survey, whether the survey target is a shallow or deep feature.

2. Station spacing should be properly judged based on the dimension of the target

and accessibility of the terrain.

3. Stations should be evenly distributed across the target to obtain a higher fractal

dimension rather than clustering them on easily accessible areas, because such

data points will add only modest information towards delineation of the target in

the case of the 2-D survey.


We suggest that the fractal dimension study should be carried out in the planning

phase of gravity/magnetic surveys using synthetic stations. Well-designed surveys

with higher fractal dimension and optimum sampling intervals produce desired

gravity maps with the least or no aliasing, as has been demonstrated in this case

study.

Acknowledgements

The authors acknowledge the Department of Science and Technology, Govt. of

India for sponsoring this work. We are thankful to Drs. Stefan Maus and O.P.

Pandey for critically reading the manuscript. Comments of an anonymous reviewer

helped us to improve the quality of the manuscript.

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(Received October 1, 2006, accepted March 2, 2007)

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