This paper deals with the application of continuous wavelet transform (CWT) and Euler deconvolution methods to estimate the source depth using magnetic anomalies. These methods are utilized mainly to focus on the fundamental issue of mapping the major coal seam and locating tectonic lineaments. The main aim of the study is to locate and characterize the source of the magnetic field by transferring the data into an auxiliary space by CWT. The method has been tested on several synthetic source anomalies and finally applied to magnetic field data from Jharia coalfield, India. Using magnetic field data, the mean depth of causative sources points out the different lithospheric depth over the study region. Also, it is inferred that there are two faults, namely the northern boundary fault and the southern boundary fault, which have an orientation in the northeastern and southeastern direction respectively. Moreover, the central part of the region is more faulted and folded than the other parts and has sediment thickness of about 2.4 km. The methods give mean depth of the causative sources without any a priori information, which can be used as an initial model in any inversion algorithm.

One of the fundamental issues in exploration geophysics is to detect differences in susceptibility and density between rocks that contain ore deposits, hydrocarbons or coal. These differences are reflected in the gravity and magnetic anomalies and also delineation of structural features, which are interpreted using several techniques (Blakely and Simpson, 1986). One of the most important objectives in the interpretation of potential field data is to improve the resolution of the underlying source, delineating a lateral change in magnetic susceptibilities that provides information not only on lithological changes but also on structural trends. The edge detection techniques are used to distinguish between different sizes and different depths of the geological discontinuities (Cooper and Cowan, 2006, 2008; Perez et al., 2005; Ardestani, 2010; Hsu et al., 1996; Hsu, 2002; Holschneider et al., 2003). The derivatives of magnetic data are used to enhance the edges of anomalies and improve significantly the visibility of such features.

Gravity and magnetic signature infer that there is a dominance of sediment over Jharia coalfield (Verma et al., 1973, 1976, 1979). Thus the difference between the depths estimated using the Euler deconvolution method (EDM) (Thompson, 1982; Reid et al., 1990) and tilt depth method (TDM) (Salem et al., 2007; Cooper, 2004, 2011) may help to detect the thickness of the coal bed. Wavelet transform and EDM have been theoretically demonstrated on magnetic data. These methods provide source parameters such as the location, depth, geometry of geological bodies and interfaces in an easy and effective way. However, it may be more difficult to characterize the source properties in cases of extended sources (Sailhac et al., 2009).

Jharia coalfield in Dhanbad, India, forms an east–west trending belt of Gondwana basin, Damodar valley, in the northeastern part of India. This study region is the most coal-rich area of Gondwana basin. Analysis of Jharia coalfield suggests that the magnetic anomalies provide encouraging results which are well correlated with available gravity data and some borehole information.

Geological map of Jharia coalfield and surrounding regions (Verma et al., 1979).

Geology of the Jharia coal basin is shown in Fig. 1. The basin has been
formed because of crustal subsidence during Gondwana periods (Fox, 1930).
The coalfield has an extension along the east–west in Gondwana
basin of Damodar valley in northeastern India. Gondwana
basin is surrounded by crystalline gneisses of several categories from all
directions. Sedimentary strata have inclination away from the gneiss
contact in this region. The sedimentary strata include the rocks which
belong to the Talchir series, Raniganj series, Barren Measures formation and Barakar
series (Verma et al., 1979). Raniganj, Barakar and Talchir
series, including Barren Measures formation, cover areas of about 58,
218 and 181 km

Talchir and Barakar formations rest over the northern margin and dip towards the southern margin. The Barakar series covers the northern half of this coalfield. It produces one of the best quality coal in India. An elliptical outline is formed by the Raniganj formation in southwestern region of the coalfield. Geology of the Jharia coalfield has been divided into many blocks, such as the Parbatpur, Mahuda, Jarma and Moonidih blocks. There are many faults over the Jharia coalfield. A normal tensional fault exists over the southern boundary. In the southwestern part of the basin, Damodar river (Fig. 1) flows very close to the southern boundary fault (Verma et al., 1973, 1979; Verma and Ghosh, 1974).

Total magnetic field anomaly (nT) map and location of the profiles over Jharia coalfield and surrounding regions (Verma et al., 1979).

The magnetic data were obtained from Verma et al. (1979) to study the region. We prepared the total magnetic anomaly map of magnetic data of this province as shown in Fig. 2. Magnetic anomaly variations are very smooth over the basin and irregular over Precambrian outcrops. This variation may be affected by the difference in magnetic susceptibility, weathering of the outcrop, magnetization of the outcrop by lightening, etc. At the northern portion of the basin anomalies form a semi-circular arc and are parallel to the southern boundary fault. There is no clear indication of the anomaly at the southern boundary because of uneven basement and faulting associated with Patherdih horst. So it is clear that this portion of the basin is highly folded/faulted and coal seams have been highly deformed. A noticeable part of the magnetic anomaly is the presence of major anomalous sources which are ascribed to some features within the Precambrian basement's underlying sediments.

The continuous wavelet transform is the conversion of any signal into a matrix
made of sum scaler products in Fourier space. Wavelet transform method for
potential field has been established by Moreau et al. (1997, 1999). This
method was previously used for homogeneous, isolated and extended potential
field sources (Sailhac et al., 2009). Chamoli et al. (2006), Cooper (2006), Goyal
and Tiwari (2014) and Singh and Singh (2015) used wavelet transform method on
various synthetic as well as field data. This method uses a Poisson group of
wavelets as a mother wavelet in order to interpret the potential field data.
To analyze the signal by mother wavelet, a wavelet domain signal is
decomposed into the orthogonal wavelets of finite duration. The CWT
coefficient

Synthetic magnetic anomaly of isolated extended source and depth
estimation by wavelet transform for a Poisson wavelet for

Potential field signal analyzed by CWT allows for estimation of depth and
homogeneous distribution order of the source generating the analyzed signal.
Source depth is calculated through the intersection of the converging
extrema lines (Fig. 3). In addition to this, Moreau et al. (1997, 1999)
established the Poisson semi-group kernel

Euler deconvolution was first developed for the interpretation of magnetic profile data by Thompson (1982), and later Reid et al. (1990) extended its approach to gridded magnetic data. Reid et al. (1990) developed the special case for the magnetic field of a contact of finite depth extent and coined the term “Euler deconvolution”. Klingele et al. (1991) and Zhang et al. (2000) used it over vertical gravity gradient and tenser gravity gradient respectively. Moreover, it has been generalized by Mushayandebvu et al. (2001, 2004), and Ravat (1996) further investigated the wider range of source nature by this method. Since then, it has been adapted and improved by Keating (1998) to interpret the gravity data. EDM makes rapid depth estimations from magnetic and gravity data in grid form using Euler's homogeneity relation (Thompson, 1982; Reid et al., 1990; Barbosa et al., 1999). Euler deconvolution is insensitive to magnetic inclination, declination and remanent magnetization and is very suitable for 3-D analyses (Keating, 1998; Mushayandebvu et al., 2004; Stavrev and Reid, 2007; Melo et al., 2013, Silva, et al., 2001).

The global acceptance of Euler deconvolution is mainly due to its simplicity
of implementation and use, making it the tool of choice for a quick and
reliable interpretation of potential field data (FitzGerald et al.,
2004; Gerovska and Arauzo Bravo, 2003) and for finding the source information in
terms of depth and geological structure. Euler deconvolution uses three
orthogonal gradients of any potential quantity as well as the potential
quantity itself to determine depths and locations of a source body. This
method primarily responds to the gradients in the data and effectively
traces the edge and defines the depth of the source body. Reid et al. (1990) and Thompson (1982) defined the 3-D Euler equation as

The source points that are calculated as solutions by EDM are positioned at the estimated edge of the susceptibility inhomogeneities. Thus, the EDM relies on the derivatives of the magnetic data; the resulting depth estimates relate mainly to the areas of basement heterogeneities identified as distinct sources of the field. The first vertical gradient of magnetic data is calculated by using the fast Fourier transform (FFT) method (Gunn, 1975). The vertical and horizontal derivatives of the first vertical gradient, essential for the calculation of Eq. (9), are also been calculated using the FFT method. The horizontal source locations from EDM solutions can be used to explain of lithological and structural trends. A location in the map where these solutions tend to cluster is considered to be the most probable location of the source.

Equation (9) can be explained in terms of least squares to estimate the
source coordinates and structure. Since the absolute value anomalous field
(

For the 2-D model, total magnetic field (

Using the Taylor series, an unidentified regional field (

Dewangan et al. (2007) and Gerovska and Arauzo Bravo (2003) chose the second-order terms of the Taylor series expansion and favor a procedure of
rational calculation in which the infinite Taylor series expansion is
estimated by two polynomials (one lies in the numerator and other one in the
denominator). Kopal (1961) suggested that the maximum accuracy in rational
calculation may be possible when the polynomials of the numerator and
denominator hold the same power. The rational function is used to calculate
the background; this function can be defined as

The synthetic examples demonstrate the application of the CWT technique on
the magnetic anomaly due to isolated and extended homogeneous magnetic
sources at 300 m, with depth about 20 m. The first analysis
(shown in Fig. 3) corresponds to the magnetic anomaly of a finite length
vertical dipole. The wavelet coefficients of the magnetic field due to vertical
dipole computed with the help of wavelet are shown in this figure (for
horizontal derivative

The wavelet coefficients are computed by applying CWT to the anomaly. Figure 4
shows the calculated values of CWT coefficients for different dilations
(1–64.5) of magnetic anomaly. The maxima of modulus of CWT provide cone-like
structures and are clearly shown pointing towards the position of the
upper corner of the model. Whereas an approximate
horizontal location has been estimated, an intersection of modulus maxima
lines in the subsurface has been placed below the base line (

Also, this example illustrates the application of wavelet transform to potential
fields (horizontal derivative,

CWT and EDM are applied on field magnetic anomaly collected from Jharia
coalfield and surrounding regions in Dhanbad, India. For CWT analysis, six
profiles (AA

The remanent magnetization of the body also appears to contribute to the anomaly. It is interesting to note that in the region of this magnetic anomaly a number of dykes and sills are found as intrusive into the sediments as shown in Fig. 1. This anomaly therefore could be ascribed to the presence of a basic or ultrabasic body which could be the source for the basic dykes and sills which intruded into the basin during Gondwana times. Alternatively, this anomaly could also represent a basic intrusive of Precambrian age underlying the sediments. There are practically no basic intrusives present in the region of positive anomaly. Therefore, this anomaly could be more definitely ascribed to an intrusive body of Precambrian age (Verma et al., 1979).

In order to check the reliability of the interpreted results obtained from Euler deconvolution, CWT and geological sections, construction information was collected from published results of boreholes drilled by Geological Society of India (GSI), Bharat Coking Coal Limited (BCCL), National Coal Development Corporation (NCDC) and Central Mines Planning and Design Institute (CMPDI). Therefore, the depth to the basement configuration inferred from gravity data as well as drilled borehole information is discussed below.

Jharia coalfield and surrounding areas have been considered to estimate the
source depths on the basis of technique of intersections of modulus maxima
lines of CWT. The mean depths of causative sources along the profile
AA

Magnetic field inclination, declination and azimuth angle (clockwise from
true north) of this profile are 36.44,

The central part shows a flat sedimentary region and the magnetic anomaly shows a high value on either side of the profile. Raniganj formation exists on the southern side whereas Talchir formation exists on the northern side of this profile. However, the Barren Measures and the Barakar formation lie between the Raniganj and the Talchir formations. There is an intrusion of Archean metamorphics in Talchir formation which appears as an outcrop over the surface near Amdih (Fig. 5c). Some of the boreholes provide information about the metamorphics along this profile. The maximum thickness of the sediment along this profile is observed to be about 0.8 km.

Boreholes JM-1, JM-4 and JK-26 are located close to this profile, which touches metamorphics at a depth of about 0.4, 0.55 and 0.3 km respectively. These boreholes are located west of Bansjora and Telmuchu. The depth to the basement obtained from magnetic data is nearly equal to the depth obtained from gravity data along these profiles (Singh and Singh, 2015).

The depth estimates obtained from Euler deconvolution (SI

The mean depths of causative sources along the profile BB

Mean depth of causative sources calculated from magnetic anomaly by CWT, EDM and Daubechies' wavelet along the profiles drawn over Jharia coalfield and surrounding regions.

Profile BB

The following magnetic susceptibility used to prepare the geological sections. Susceptibility values are taken from the standard chart compiled by Clark and Emerson (1991) and Hunt et al. (1995).

Magnetic field inclination, declination and azimuth angle of this profile
are 36.42,

The boreholes JK-7 and JM-8 are located near this profile. From borehole JM-7, it is obtained that maximum thickness of the Raniganj formation is about 0.22 km and Barren Measures lies below it. It touches the Barakar formation at a depth of about 1.2 km, east of Bansjora. From the obtained results from borehole JK-8, it is clear that sediment thickness is about 0.3 km and the borehole touches the Barren Measures at a depth of about 300 m.

The mean depths of causative sources along the profile CC

Magnetic field inclination, declination and azimuth angle of this profile
are 36.41,

Similar to profile BB

The mean depths of causative sources along the profile DD

Magnetic field inclination, declination and azimuth angle of this profile
are 36.40,

Geological sections along this profile were also deduced from the analysis of borehole information, gravity data and geological information. Boreholes NCJA-14, JK-5 and NCJP-32 are located east of Katras, north west of Dubrajpur and west of Parbatpur respectively. The individual maximum thickness of various formations near the deepest part of the basin is about 0.8 km for Talchir, 0.4 km for Barren Measures and about 2 km for Barakar formation.

The mean depths of causative sources along the profile EE

Magnetic field inclination, declination and azimuth angle (clockwise from
true north) of this profile are 36.39,

Geological sections along this profile are also deduced from the gravity data, borehole information and available geological information. Individual thickness of each formation is also deduced with the help of boreholes JK-4, NCJP-42, NCJP-16 and NCJP-12, which are located southwest of Kustore, west of Nunikdih, west of Dungri and south of Dungri respectively. Maximum thickness is about 0.45 km for Barren Measures, 1.5 km for Talchir and 1.4 km for Barakar formation.

The mean depth of causative sources along the profile FF

Magnetic field inclination, declination and azimuth angle of this profile
are 36.33,

It is found that in this region of magnetic anomaly remanent magnetization of the body also appears to contribute to the magnetic anomaly. A number of sills and ultrabasic dykes (mica peridotites) are found to be intrusive into the sediments. Geology over this profile could be ascribed to the presence of a basic or ultrabasic body which was the main source for the sills and basic dykes that intruded (Fig. 10c) into the basin during Gondwana times (Verma et al., 1973).

Geological strata along this profile are highly disturbed. Therefore, dips of the formations vary abruptly. The thickness of the formations is extrapolated from gravity data, boreholes NCJB-9, NCJB-25 and JFT-8 information as well as geological information. Boreholes NCJB-9, NCJB-25 and JFT-8 are located west of Chhatabad, west of Patherdih and west of Bhojudih respectively. Borehole JFT-8 has the cross contact between Barren Measures and Barakar formation and it touches the metamorphics about 0.4 km west of Bhojudih. The depth of the individual formations is approximately equal to the depth obtained from interpretation of gravity data (Singh and Singh, 2015).

The interpretation of magnetic anomaly over Jharia coalfield has been compared with some information from interpretation of gravity data (Verma and Ghosh, 1974). The mean depth of the causative sources estimated by Euler deconvolution method (Fig. 11) ranges about 0.6 to 3.2 km. The mean depth of the profiles has been shown in the Table 1.

Results from the total magnetic field of Jharia coalfield (Fig. 2) show that magnetic field anomalies are predominant due to irregular undulations of Precambrian outcrops and faults. The magnetic data are sampled at roughly 50 m along the profile direction. To enhance the signal-to-noise ratio, a high cut filter was applied in the wavenumber domain and partial derivative in the vertical direction was obtained by extending the field grid before the calculation. The SI is supposed to vary between 0 and 3, covering all plausible geological bodies. The estimates of source location and depth are obtained by minimizing the error function using the nonlinear optimization technique of Coleman and Li (1996).

Figure 11 shows two sets of fractures, predominantly oriented in the northeast and southeast at the northern and southern boundary respectively. The orientation of fractures sets are similar to that of the orientation obtained from regional magnetic interpretation (Verma et al., 1973). In the southern region, the depth of the Precambrian basement derived from the faults is less than that in the northern region. Furthermore, intense fracturing is detected at the center of the study area. In the western and southern regions, the basement depth is shallower compared to that of the eastern and northern region.

Profile analysis suggests that most of the basement lies below 700 m, which is reasonable as calculated by wavelet transform method. The faults and depths obtained from the Euler deconvolution, CWT and Daubechies' wavelet are related to each other according to the results obtained from the regional magnetic interpretation.

The present analysis demonstrates the efficiency of continuous wavelet transform to delineate the locations of causative sources of potential
field. Mean depth of the causative source along the profile AA

Thus, the wavelet transform and Euler deconvolution methods provide sufficient and relevant information necessary to find the depth and location of the causative sources. The application of the CWT methods to the synthetic and field magnetic data across Jharia coalfield demonstrates that the technique is quick, easy to use and very efficient. Continuous wavelet transform and Euler deconvolution can give the mean depth of causative sources of magnetic field data, which can be interpreted qualitatively and quantitatively to determine the cause of anomaly. Also, these methods provide a way to infer the location of causative sources without any a priori information in a very short time and can be further used as a priori models in inversion to improve accuracies.

The data used in this paper can be found in the online Supplement for this article.

The authors declare that they have no conflict of interest.

Authors are very thankful to D. C. Panigrahi, Director of IIT (ISM) Dhanbad, for providing the necessary infrastructure for this research to be successfully carried out. We are very grateful to Lev Eppelbaum, Associate Editor of this journal, who gave the initial reviews on earlier versions of the manuscript that greatly improved the final paper. We would also like to show our gratitude to Sanjay Prajapati, O. Menshov and an anonymous reviewer for their positive comments. Edited by: L. Eppelbaum Reviewed by: S. K. Prajapati, O. Menshov, and one anonymous referee