potential field data using spectral moments

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Edge enhancement of potential field data using spectral moments

Yanyun Sun1, Wencai Yang2, Xiangzhi Zeng2, and Zhiyong Zhang3

ABSTRACT

Edge enhancement in potential-field data helps geologicinterpretation, where the lineaments on the potential-field fre-

quently indicate subsurface faults, contacts, and other tectonic

features. Therefore, a variety of edge-enhancement methods

have been proposed for locating edges, most of which are

based on the horizontal or vertical derivatives of the field.

However, these methods have several limitations, including

thick detected boundaries, blurred response to low-amplitude

anomalies, and sensitivity to noise. We have developed the

spectral-moment method for detecting edges in potential-field

anomalies based on the second spectral moment and its sta-

tistically invariable quantities. We evaluated the spectral-

moment method using synthetic gravity data, EGM-2008

gravity data, and the total magnetic field reduced to the pole.

Compared with other edge-enhancing filters, such as the totalhorizontal derivative (TDX), profile curvature, curvature of the

total horizontal gradient amplitude, enhancement of the TDX

using the tilt angle, theta map, and normalized standard

deviation, this spectral-moment method was more effective

in balancing the edges of different-amplitude anomalies,

and the detected lineaments were sharper and more continu-

ous. In addition, the method was also less sensitive to noise

than were the other filters. Compared with geologic maps,

the edges extracted by the spectral-moment method from grav-

ity and the magnetic data corresponded well with the geologic

structures.

INTRODUCTION

Use of potential-field data to locate edges facilitates geologic in-

terpretation because the edges on the potential-field often indicate

subsurface faults, contacts, and other tectonic features. However,

the horizontal boundaries of potential-field-anomaly sources cannot

be determined directly based on the potential-field data because of

the high frequency and low amplitude with respect to the source

boundaries. It is often necessary to enhance the horizontal edges

of the sources to assist structural interpretation, as well as environ-

mental and engineering investigations. To date, several methods ex-

ist to emphasize geologic contacts and highlight source edges,

including methods based on horizontal and vertical derivatives

(e.g., Evjen, 1936; Nabighian, 1972; Cordell, 1979; Blakely and

Simpson, 1986; Mitá šova and Jarosalav, 1993; Hsu et al., 1996;

Fedi and Florio, 2001). However, these high-pass filters mainly de-

tect the edges of high-amplitude sources but are not effective for

lower amplitudes. As a result, the tilt angle was introduced by Miller

and Singh (1994) as the first balanced filter to enhance large- and

small-amplitude anomalies, and Rajagopalan and Milligan (1995)

apply automatic gain control filters to produce a balanced image.

In recent years, a variety of new methods for edge enhancement

have emerged. To enhance the lineaments and subtle details, Ver-

duzco et al. (2004) suggest using the total horizontal derivative of

the tilt angle (THDT). Francisco et al. (2009) introduce an edge-de-

tection method based on the enhancement of the total horizontal

derivative using the tilt angle (TAHG). Cooper and Cowan

(2006) also introduce some new forms of the tilt angle for detecting

edges. Wijins et al. (2005) use the theta map, which is a normali-

zation of the horizontal gradient with the analytic signal amplitude

to highlight low-amplitude features. Hansen and de Ridder (2006)

present an approach for detecting lineaments based on the analysis

of the curvature of the total horizontal gradient amplitude (LFA) by

fitting local quadratic surfaces to a moving window of data. Another

Manuscript received by the Editor 11 September 2014; revised manuscript received 10 June 2015; published online 13 October 2015.1Formerly China University of Geosciences, Institute of Geophysics and Information Technology, Beijing, China; presently China Aero Geophysical Survey

and Remote Sensing Center for Land and Resources, Beijing, China. E-mail: [email protected] Academy of Geological Sciences (CAGS), Institute of Geology, State Key Laboratory of Continental Tectonics and Dynamics, Beijing, China.

E-mail: [email protected]; [email protected] University of Geosciences, Institute of Geophysics and Information Technology, Beijing, China. E-mail: [email protected].

© 2015 Society of Exploration Geophysicists. All rights reserved.

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GEOPHYSICS, VOL. 81, NO. 1 (JANUARY-FEBRUARY 2016); P. G1–G11, 8 FIGS.

10.1190/GEO2014-0430.1


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method that fits a special quadratic function to a window of data

points is introduced by Phillips et al. (2007) using the eigenvalues

and eigenvectors to locate the sources and to estimate their depths

and strikes.

For detecting more details, Cooper and Cowan (2006) develop

numerous excellent edge-detection methods. The normalized stan-

dard deviation (NSTD; Cooper and Cowan, 2008), based on ratios

of the windowed standard deviation of derivatives of the field, wasproposed and successfully applied to enhance low-amplitude

anomalies. Cooper (2009) suggests using the orthogonal Hilbert

transforms of analytic signal amplitudes to balance lineaments of

different-amplitude anomalies. To improve edge detection by apply-

ing the Laplacian derivative operator, Cooper and Cowan (2009)

propose to adopt the profile curvature instead. Later, they introduce

the generalized derivative operator, which is a linear combination of

the horizontal and vertical field derivatives, normalized by the total-

gradient amplitude (Cooper and Cowan, 2011). Ma et al. (2012)

present enhanced balancing filters that combine different order

derivatives to detect the source boundaries and introduce a stable

algorithm of the high-order vertical derivatives. Based on the idea

of NSTD, Zhang et al. (2014) propose the normalized anisotropy

variance method (NAV-Edge) for detecting edges, which is less sen-sitive to noise.

These edge-detection methods are useful in enhancing linea-

ments. However, there are also some disadvantages, which fall into

approximately three categories. First, the detected edges are broad

or diffuse (e.g., total horizontal derivative (TDX), theta map, and

profile curvature), which limits locating the boundaries. Second,

the response in the low-amplitude parts is blurred (e.g., TDX

and profile curvature). Finally, most of the detectors are high-pass

filters and are therefore sensitive to noise (e.g., profile curvature,

theta map, and THDT).

In this paper, we introduce a new edge-enhancement method

based on spectral moments (the spectral-moment method), which

can balance the edges of different-amplitude anomalies well andnarrow the detected edges. In addition, the spectral-moment method

can be less sensitive to noise than are the other methods by enlarg-

ing the size of the moving window. We tested the method on syn-

thetic and real data, and we also compared it with other standard

edge-enhanced filters (e.g., TDX, profile curvature, LFA, TAHG,

theta map, and NSTD).

EDGE ENHANCEMENT USING THE

SPECTRAL-MOMENT METHOD

Based on the theory of random process (Nayak, 1973; Thomas,

1982; Yang et al., 1992), the (p þ q)th order discrete spectral mo-

ment of a surface with a size of m × n

points is defined by (Longuet-Higgins, 1957; Yang et al., 1992; Li et al., 2000)

mpq ¼Xnv¼1

Xmu¼1

Gð f u; f vÞ f pu f

qvΔ f uΔ f v; (1)

where Gð f u; f vÞ is the 2D power spectral density of the surface. Thevalues f u and f v are the discrete spatial frequencies in the x- and y-

directions, respectively.

On the potential surface, a moving window (referred to as w1)

with a size of M α by N α points is used to compute the spectral mo-

ments of the surface within it. Setting p þ q ¼ 2, the spatial expres-

sions of the three elements of the second-order spectral moment of

the potential surface in the small window is derived from equation 1,

which are calculated by the following convolution:

m20 ¼XN α i¼1

XM α j¼1

g 2 xð x j; yiÞ; (2)

m02 ¼XN α i¼1

XM α j¼1

g 2yð x j; yiÞ; (3)

m11 ¼XN α i¼1

XM α j¼1

g xð x j; yiÞg yð x j; yiÞ; (4)

where

g xð x; yÞ ¼ ∂

∂ xg ð x; yÞ; g yð x; yÞ ¼

∂

∂yg ð x; yÞ; (5)

where i ¼ 1;2; : : : ; N α , j ¼ 1;2; : : : ; M α , and g ð x; yÞ is the poten-tial field data within moving window w1. Here, m20 and m02 show

the variance of slopes of the small potential field surface within w1in the x- and y-directions, respectively, whereas m11 denotes the

covariance of the slopes in x- and y-directions within w1.

Note that the spectral moments change with the rotation of the

coordinates. Therefore, the statistically invariable quantities that are

independent of the system rotation are defined as (Longuet-Higgins,

1957; Huang, 1984, 1985; Yang et al., 1992; Li et al., 2000)

M 2 ¼ m20 þ m02; (6)

Δ2 ¼ m20m02 − m211. (7)

Here, the statistically invariable quantity M 2 is the variance of the2D slope of the potential field surface within w1, which shows the

magnitude of the edges. The statistically invariable parameter Δ2represents the anisotropy of the potential field surface within w1.

We calculate the statistically invariable quantity M 2 for each mov-

ing window over the grid, we assign that value to the grid point at

the center of the window, and then the image of M 2 can be obtained.

To bring out the detail in smaller amplitude anomalies, further

enhanced processing can be conducted on the surface of M 2. Taking

consideration of information on anisotropy and amplitudes syntheti-

cally, we introduce an enhanced parameter called the edge coeffi-

cient (Sun and Yang, 2014; Yang et al., 2015):

M Λ ¼ M Λa þ M Λb. (8)

This definition decomposes the edge coefficient M Λ into two new

parameters M Λa and M Λb. Parameter M Λa is calculated by

M Λa ¼ −sgnðΔM 2Þ ×2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

n20n02 − n211

p n20 þ n02

; (9)

where n20, n02, and n11 are the three elements of the spectral mo-

ments on the surface of M 2 within the moving window (referred to

as w2) with size of M β by N β points, and Δ represents the Laplacian

operator. The opposite sign of ΔM 2 is set to separate the ridge and

valley lines because it is the ridge lines that we are interested in.

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In equation 9, the edge coefficient component M Λa is propor-

tional to the square root of Δ2, showing the anisotropy of the surface

topography, which contributes to narrow the edges. Additionally, it

is also inversely proportional to M 2, enhancing the recognition abil-

ity to weak edges on the surface.

However, when it refers to the situation that data change little

along the boundary’s strike, parameter M Λa is ineffective. Then,

an extra term must be added using the relative distance between

the origin and the distribution center of partial derivatives of data

with respect to the x- and y-directions in w2. This extra term is M Λb,

Figure 1. Comparison of several edge-detection methods. (a) Synthetic gravity data set. A, B, and C are the source bodies whose outlines areshown in solid lines. The depths of prisms A, B, and C are 5, 5, and 2 km, respectively; the density of prisms A, B, and C are 0.03, 0.5, and0.02 g∕cm 3, respectively; (b) TDX; (c) profile curvature with zero contours overlaid; (d) LFA; (e) TAHG; (f) theta map; (g) NSTD; and(h) edge coefficient computed using equation 8.

Edge enhancement using spectral moments G3


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which is another component of the edge coefficient in equation 8

given by

M Λb ¼ −sgnðΔM 2Þ ×2

π ×

π

2 − arctan

E½pro

S½pro

; (10)

where

proð x j; yiÞ ¼ W x ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiW x

2 þ W y2

q W xð x j; yiÞ

þ W y ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiW x

2 þ W y2

q W yð x j; yiÞ; (11)

Figure 2. Edge detection by existing methods. (a) Synthetic gravity anomalies, adding random noise with an amplitude of 0.1% of the anoma-lous maximum to the data in Figure 1a ; A, B, and C are the source bodies whose outlines are shown in solid lines; (b) TDX; (c) profilecurvature; (d) LFA; (e) TAHG; (f) theta map; (g) NSTD; and (h) edge coefficient computed using equation 8.

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E½pro ¼ 1

N β M β

XN β i¼1

XM β j¼1

proð x j; yiÞ;

S½pro ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

N β M β

XN β i¼1

XM β j¼1

ðproð x j; yiÞ − E½proÞ2

v uut . (12)

More parameters included in equation 12 are expressed as

W x ¼ 1

N β M β

XN β i¼1

XM β j¼1

W xð x j; yiÞ;

W y ¼ 1

N β M β

XN β i¼1

XM β j¼1

W yð x j; yiÞ (13)

and

W ð x; yÞ ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

M 2ð x; yÞp

;

W xð x; yÞ ¼ ∂

∂ xW ð x; yÞ;

W yð x; yÞ ¼ ∂

∂yW ð x; yÞ. (14)

In equations 12–14, j ¼ 1;2; : : : ; M β and i ¼ 1;2; : : : ; N β .

The key parameter of the spectral-moment method is the edge

coefficient M Λ. When the data of M 2 change little (common in syn-

thetic data) along the boundary’s strike, edge detection may be ap-

plied by the parameters M Λa and M Λb. But if the gradient of data of

M 2 is not equal to zero (common in field data) in the direction of the

boundary’s strike, parameter M Λa is enough to depict the faults

or edges.

TESTS ON SYNTHETIC DATA

The spectral-moment method is tested using a synthetic

model consisting of three prisms. Figure 1a shows the synthetic

gravity anomalies from the three bodies, and their outlines super-

imposed on the anomaly data. Prism A has dimensions of

320 × 20 × 5 km and is buried at a depth of 5 km, prism B has

dimensions of 320 × 60 × 5 km and is buried at a depth of

5 km, and prism C has dimensions of 50 × 15 × 2 km and is buried

at a depth of 2 km. The density contrasts of the three bodies (A, B,

and C) are 0.03, 0.5, and 0.02 g∕cm 3, respectively. The data set is

computed on a grid of 421 × 801 points with 0.5-km spacing. For

comparison, we present edge-detection results using TDX, profilecurvature, LFA, TAHG, theta maps, and the NSTD, respectively

(Figure 1b–1g). As shown in Figure 1b, the outlines of sources

A, B, and C have been detected by the TDX method, whereas

the edges of sources A and C are fairly faint. Figure 1c shows

the profile curvature with zero contours overlain. The zero contours

can delineate the boundaries of bodies A and B well, but boundary

c1 (indicated in Figure 1c) has not been detected because of the

effect of body B, whose center is 2.5 km north (positive direction

Figure 3. Edge detection using the spectral-moment method with different window sizes. (a) Edge coefficient of the noise-corrupted syntheticgravity anomalies in Figure 2a using a radius of three and three points for w1 and w2, respectively. (b and c) Edge coefficient of the noise-corrupted synthetic gravity anomalies using a w2 radius of three points and a w1 of eight and 14 points, respectively. (d) Edge detection using a w1 and w2 radius of eight and eight points, respectively.



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of the y-axis) of source body C when projected onto the plane sur-

face. Similar to the results in Figure 1b, detection by LFA (in Fig-

ure 1d) is also dominated by the response from larger amplitude

anomalies, although the outlines of smaller amplitude anomalies

(source C) can be delineated slightly better. TAHG (in Figure 1e)

is an effective method to balance the amplitudes of large- and small-

amplitude anomalies. The edges of bodies A and B are successfully

delineated by the theta map method (Figure 1f ), but it is less effec-tive for body C, which has the lowest amplitude. In addition, the

edges recognized by this method appear very broad, which is

not conducive to locating source boundaries. Figure 1g shows

the NSTD using a window of 3 × 3 points. The amplitudes of

the different anomalies are balanced well, and it clearly delineates

the edges of the three source bodies, whereas the delineated outlines

are a little discontinuous. Figure lh shows the results of the spectral-

moment method using the edge coefficient component M Λ. As

mentioned above, two moving window sizes should be selected

to calculate the image of M Λ; one (w1) of which is for computing

the image of M 2, whereas the other one (w2) is for calculating the

image of M Λ. In this case, the radius of both Gaussian moving win-

dows (w1 and w2) is three points. It is clear that the edge in thisfigure appears the narrowest among all the above methods. In ad-

dition, the amplitudes of detected edges from different sources are

not only significantly balanced but are also continuous.

To test the relative sensitivity of the edge-detection methods dis-

cussed above to noise, a small amount of uniformly distributed ran-

dom noise with amplitude of 0.1% of the maximum data magnitude

was added to the data in Figure 1a . Figure 2a shows the noise-cor-

rupted anomalies, and the outlines of the sources are shown in solid

lines. The TDX method appears to be affected least by the noise.

Although the profile curvature (Figure 2c), LFA (Figure 2d), TAHG

(Figure 2e), and theta map (Figure 2f ) methods can still locate thesource edges, the detected edges, especially the edges of smaller

amplitude anomalies, are blurred because of the added noise. Fig-

ure 2g is the NSTD of the data in Figure 2a using a larger window

size with 7 × 7 points. The edges of the smaller amplitude anomaly

(e.g., body C) are faint. Figure 2h is the image of the edge coeffi-

cient M Λ of the data, which is calculated using w1 ¼ 8 and w2 ¼ 3.Although several spurious edges, present in all the images, are

inevitably detected, it provides a better result than the other meth-

ods. The reason why the spectral-moment method is less sensitive to

noise than are the others is that the M 2 of each grid point is com-

puted using its surrounding data contained within w1.

We also show how the Gaussian window size affects the resulting

images (Figure 3). We chose a w2 radius of three for w1 radius sizesof three, eight, and 14 to calculate the edge coefficient from data in

Figure 2a , and the results are shown in Figure 3a –3c, respectively.

When the radius of w1 equaled three (Figure 3a ), the noise severely

Figure 4. Geologic sketch map of China. The areas covered by Figures 5a and 7a are shown. The pink color indicates platforms or massifs andthe blue color indicates orogenic or tectonic belts.

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Figure 5. Test cases of edge-detection methods based on the satellite gravity anomaly from a small section of northern China. The location isshown in Figure 4. (a) Satellite gravity anomaly over a section of northern China; (b) TDX; (c) profile curvature; (d) LFA; (e) TAHG; (f) theta map; (g) NSTD; and (h) edge coefficient computed using equation 8; the black ellipses indicate examples that edges detected by the spectral-moment method are clearer than by the other methods.

Figure 6. Map of the edge coefficient with thesimplified geologic map of the study area super-imposed. Solid lines indicate the fault and dotted

lines indicate the buried faults. Dashed ellipsesindicate examples that edges are detected bythe geophysical method but not identified inthe geophysical map.



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affected the detected boundaries, in particular, of body A. Compar-

ing the map of Figure 3b and 3c, one can see that the larger sizes of

w1 can be less sensitive to the noise than are the smaller ones, but

the edges of the small-scale anomaly are also smeared out (Fig-

ure 3c). The width of the detected edges is mainly controlled by

the size of w 2. A smaller w2 (Figure 3c) produces narrower linea-

ments than the large ones (Figure 3d).

APPLICATION TO FIELD DATA

To test the performance of the spectral-moment method, we apply

it together with the other six commonly used filters to a gravityanomaly over a small part of South Chinaoutlined in red in Figure 4.

The study area is located in the composite area of tectonic structures

of the Paleo-Asian Ocean and subduction of the Paleo-Pacific plate.

In addition to the intensive activity of magma, this region has ex-

perienced tectonic movements, such as pushing rotation and shear

(Zhu et al., 2005). The gravity data were computed using free-air

anomalies from EGM2008 gravity model (Pavlis et al., 2012),

which is derived from ground, airborne, and satellite data. The grav-

ity data from EGM2008 gravity model have a grid cell size of

1 0 × 1 0 and an accuracy of 2–4 mgal. Figure 5a shows the complete

Bouguer anomaly after applying stone slab and terrain corrections

to the EGM2008 free-air anomalies, covering approximately

900 × 450 km . As is seen from this figure, several northeast-trend-

ing anomaly belts occur, which is mainly caused by the subductionof the paleo-Pacific plate from the southeast to the northwest direc-

tion. For comparison, we carry out the six-edge-enhancement

method on this data. The results of TDX, profile curvature, and

LFA, shown in Figure 5b–5d, respectively, can delineate the linea-

ments, but the images mainly depict the lineaments from the high-

amplitude anomalies. Although the image of TAHG in

Figure 5e is effective in balancing the amplitudes of causative

sources with different amplitudes, the detected edges appear broad.

The theta map of the data is shown in Figure 5f . Most of the am-

plitudes of different anomalies are well balanced; however, some

edges of the low-amplitude anomalies are still diffuse. In contrast,

the result using NSTD (Figure 5g) with a window of 3 × 3 points

shows more details and structures. However, the amplitudes on theNSTD method image are visibly less continuous than in the other

images. The spectral-moment method has enhanced these small-

amplitude anomalies well to show more subtle details. For example,

the detected edges highlighted by black circles in Figure 5h are

clearer than in the other images, some of which are shown to be

minor faults (Figure 6). Another superior aspect of the spectral-mo-

ment method over the other filters is that the detecting boundaries

are the sharpest of all the figures. We have also compared the linea-

ments detected by the spectral-moment method with the geologic

structures. Figure 6 shows the map of edge coefficient, which is

superimposed over a simplified geologic map (Li et al., 2014) of

the study area. The map shows good correlation with the geologic

structures. However, several structures can only be inferred through

geophysical mapping. For example, the edges enclosed by dashedellipses that have been detected by most of the methods are not

identified in the geologic map. This result illustrates the usefulness

of the enhancement method for the interpretation of potential

field data.

We also applied these filters to magnetic data from a small village

in the Jiangsu Province in South China, which is outlined in blue in

Figure 4. The study area is located at the eastern part of the Qin-

gling-Dabie-Sulu orogenic belt, where there are many outcrops of

ultrahigh-pressure metamorphic rocks (Yang et al., 2005). Figure 7a

depicts the magnetic anomaly data reduced to the pole. The data

were gridded from ground observations with an interval of

Figure 7. Test cases of the edge-detection methods on magneticdata. (a) Magnetic data from Donghai Village of the Jiangsu Prov-ince in south China. The location is shown in Figure 4; (b) TDX;(c) profile curvature with zero contours overlaid; (d) LFA; (e) en-hanced horizontal derivative; (f) theta map; (g) NSTD; and (h) edgecoefficient computed using equation 8; solid ellipse indicates theexample that edges detected by the edge coefficient are stronger than by the other methods; the dashed ellipse indicates the positionof the mica-eclogite in the geologic map.

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10 m. It is difficult to distinguish the edges directly from this map.

The TDX (Figure 7b) and LFA (Figure 7d) methods do enhance the

edges, but most edges of the smaller amplitude anomalies are faint

or even invisible. Figure 7c shows the profile curvature with zero

contours overlaid. The contour resolves structures better than

TDX and LFA. More details can be detected in the TAHG

(Figure 7e) and the theta map (Figure 7f ) images, but their responses

to small-amplitude bodies are still weaker and diffuse (e.g., the por-tion enclosed by the black circle). NSTD (Figure 7g) is an excellent

filter balancing the different-amplitude anomalies, but the edges are

discontinuous. Figure 7h shows the results from the spectral-

moment method. Here, we adopt the parameter M Λ to delineate

the edges. Its response to low-amplitude anomalies is stronger com-

pared with Figure 7b–7f and similar to the NSTD filter (e.g., edges

enclosed in the black circle in Figure 7f ). As is shown in the mag-

netic susceptibility histogram of the main rocks in this study area

(Figure 8a ), the magnetic anomalies in this region are mainly caused

by serpentinites and eclogites. In this case, we have also compared

the detected results by the spectral-moment method with the sim-

plified geologic structures. Figure 8b shows the map of edge coef-

ficient with the simplified geologic map (Yang et al., 2005; Xu

et al., 2009) of this study area superimposed. The edges in the

dashed ellipse in Figure 7h correspond to the largest Mica-Eclogite

of the simplified geologic map. In addition, these small features en-hanced by the spectral-moment method should be the edges of the

small magnetic objects, such as serpentinites or ultrabasic intrusion.

DISCUSSION

The most impressive advantages of this spectral-moment method

are its ability to balance the edges of large- and small-amplitude

anomalies and narrow the detected edges. In fact, the parameter

Figure 8. The magnetic susceptibility histogram of the main rocks and the map of edge coefficient with simplified geologic map of Donghai Village

superimposed. (a) Magnetic susceptibility histo-gram of the main rocks in Donghai village.(b) Edge coefficient with simplified geologicmap of the study area superimposed.



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Λ (in equation 10) can measure the ridge strength of the surface in

the moving window (Li et al., 2000). The edge coefficient has better

balancing ability because it is computed based on the ridge strength

that is independent of the magnitude of the edges. Furthermore, cal-

culating parameter Λ on the surface M 2 is equivalent to extracting

the ridges of the edges detected by the parameter M 2, which con-

tributes to narrowing the extracted edges.

Another advantage of the spectral-moment method is that whencomparing with the other edge-enhancement methods mentioned in

this paper, it shows that it is less sensitive to the noise than are the

others when balancing the edges of different-amplitude anomalies.

Although the proposed method is not aimed at suppressing noise,

the moving window computation can make it is less sensitive to the

noise when enlarging the moving window. However, although the

results depend on the sizes of the moving windows, there is a lack of

standards for the selection of window sizes. One has to carry out

some tests before selecting appropriate window sizes.

Because the spectral-moment method picks out all edges, it is

usually difficult to interpret on its own. Interpretation efforts should

combine as many processed images as are deemed appropriate.

CONCLUSION

We have presented a new edge-detection method for the enhance-

ment of potential anomalies in which the edges are identified by the

edge coefficient. The spectral-moment method was demonstrated

using synthetic and real data. For synthetic data, the method shows

better capabilities of balancing the edges of different amplitude

anomalies and narrowing the detected edges. In addition, larger

windows (w1) are less sensitive to noise than are small ones; how-

ever, the edges, smaller than the window size of the small-scale

anomaly, are also smeared out. Furthermore, the size of the moving

window w2 mainly controls the width of the detected edges. Using

field gravity and magnetic data reduced to the pole as examples, the

edge coefficient map provides more details, and the lineaments gen-erated by the proposed method are consistent with geologic

structures.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the financial support from

the National Science Foundation of China under grant number

41574111 and the Chinese Geological Survey with the project num-

ber 12120113099000. The authors thank assistant editor V. Socco,

the associate editor, and three reviewers for their constructive com-

ments that greatly improved the original manuscript. We also thank

Y. Wang for providing the simplified geologic map.

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