leveling hem and aeromagnetic data using differential polynomial fitting

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GEOPHYSICS, VOL. 75, NO. 1 �JANUARY-FEBRUARY 2010�; P. L13–L23, 14 FIGS., 1 TABLE.10.1190/1.3279792

eveling HEM and aeromagnetic data using differentialolynomial fitting

ajid Beiki1, Mehrdad Bastani1, and Laust B. Pedersen1

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ABSTRACT

We introduce a new technique to level aerogeophysicaldata. Our approach is applicable to flight-line data withoutany need for tie-line measurements. The technique is basedon polynomial fitting of data points in 1D and 2D sliding win-dows. A polynomial is fitted to data points in a 2D circularwindow that contains at least three flight lines. Then the sameprocedure is done inside a 1D window placed at the center ofthe 2D window. The leveling error is the difference between1D and 2D polynomial fitted data at the center of the win-dows. To demonstrate the reliability of the method, it wastested on a synthetic aeromagnetic data set contaminated bysome linear artifacts. Using the differential polynomial fit-ting method, we can remove the linear artifacts from the data.The method then was applied to two real airborne data setscollected in Iran. The leveling errors are removed effectivelyfrom the aeromagnetic data using the differential polynomialfitting. In the case of helicopter-towed electromagnetic�HEM� data, the polynomial fitting method is used to levelthe measured real �in-phase� and imaginary �quadrature�components, as well as the calculated apparent resistivity.The HEM data are sensitive to height variations, so we intro-duce an average-height scaling method to reduce the heighteffect before leveling in-phase and quadrature components.The method also is effective in recovering some of the attenu-ated anomalies. After scaling, the differential polynomial fit-ting method was applied to the data and effectively removedthe remaining line-to-line artifacts.

INTRODUCTION

Aerogeophysical data often suffer from inconsistencies betweendjacent lines called leveling errors. Sources of leveling errors areifferent in aeromagnetic and airborne electromagnetic �AEM� data.

Manuscript received by the Editor 6 March 2009; revised manuscript recei1Uppsala University, Department of Earth Sciences, Geophysics, U

[email protected] Society of Exploration Geophysicists.All rights reserved.

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ith increasing altitude, the amplitude of helicopter-towed electro-agnetic �HEM� responses decreases. The HEM systems work with

ctive sensors. Pairs of transmitter and receiver coils with differentrequencies are installed in a bird. A primary magnetic field is trans-itted, and primary and secondary magnetic fields are recorded by

he receiver coils. Inside the sensor, a bucking coil is installed touck out the primary field. These coils have two configurations, co-xial and coplanar. The change in the response to different frequen-ies provides information on conductivity corresponding to differ-nt skin depths. Each configuration is sensitive to geometrical varia-ions in ground conductivity. For example, in the case of coplanaroils directly over a vertical thin conductor, i.e., a vertical thin dike,he primary magnetic field is vertical. It passes parallel to the verticalonductor and has minimum coupling. But for coaxial coils, the gen-rated magnetic field is directed horizontally below the transmitteroil, so the induced eddy currents are maximum in the vertical con-uctor. The primary field in the coplanar configuration generatesaximum coupling to horizontal layers. Valleau �2000� provides an

xcellent overview on processing and interpretation of HEM data.he dependency of the recorded secondary field on the resistivity of

he subsurface and altitude variations is strongly nonlinear �Siemon,009�. Figure 1a-c shows a real example of recorded altitude, in-hase, quadrature, and aeromagnetic data, respectively. The 900-HzEM data shown in Figure 1b were collected using the DIGHEM

ystem in Bazman, Iran. This example illustrates clearly that HEMata are correlated with altitude variations. However this relation-hip is not so strong for aeromagnetic data. Consequently, Huang2008� categorizes HEM data as altitude sensitive and aeromagneticata as altitude insensitive.

Temperature variations are another source of HEM leveling errorsHuang and Fraser, 1999; Siemon, 2009� affecting the secondaryeld measurements. Temperature variations can change coil separa-

ion and also can influence electronic systems.For aeromagnetic measurements, some tie-lines are flown per-

endicular to flight lines. Tie-line spacing is normally 3–10 times theight-line spacing. The recorded magnetic field on tie-lines andight lines differ by the so-called mis-ties. It is safe to assume that

ugust 2009; published online 27 January 2010.Sweden. E-mail: [email protected]; [email protected];

SEG license or copyright; see Terms of Use at http://segdl.org/

https://www.researchgate.net/publication/223765406_Levelling_of_helicopter-borne_frequency-domain_electromagnetic_data?el=1_x_8&enrichId=rgreq-0c79320c-d633-418d-b75f-83a932389433&enrichSource=Y292ZXJQYWdlOzI0OTg2NjM0ODtBUzoxNDk5MTY1MzM5MjM4NDVAMTQxMjc1NDI5NTMzOQ==

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he recorded magnetic field is relatively insensitive to aircraft alti-ude variations at flight-line/tie-line intersections. Therefore, mis-ies can be used to level the data �Huang, 2008�. Several examples ofie-line leveling procedures have been published �Foster et al., 1970;arger et al., 1978; Bandy et al., 1990; Luyendyk, 1997; Huang andraser, 1999�. They use statistical methods to eliminate mis-ties.Af-

erward, microleveling techniques are recommended to remove theemaining leveling errors.

Mauring and Kihle �2006� introduce a general approach using aifferential median filter �DMF�. They present a quick-levelingechnique that works on regular and irregular patterns of flight lines.hey show the application of DMF on aeromagnetic and airborneery-low frequency �VLF� data.

This paper describes a new technique based on differential poly-omial fitting using sliding windows. This technique is statisticalnd can be used regardless of the sources of leveling errors. To showhe reliability of the method, it is applied to a synthetic data set after arief description of the theory. We also have studied the effect of alti-ude variations on the leveling of aeromagnetic and HEM data. Thenhe differential polynomial fitting �DPF� method is applied to someeal data. Field examples shown in this paper suggest that this meth-d can be used to level a variety of aerogeophysics data.

METHOD

Polynomial fitting is a simple way to remove outliers from a dataet and acts like a low-pass filter. Mauring and Kihle �2006� point outhe advantage of median filtering, which removes spikes effectivelyhile preserving edges. In the moving median filter, the window

ength is the only parameter that controls the smoothness of data.he moving polynomial fitting filter has the same properties; fur-

hermore, the smoothness of the filter can be better controlled by set-ing the proper polynomial order. Figure 2 shows the application ofolynomial fitting and median filter using a moving window on aoisy data set. A window length of 1000 m is used for both filters.olynomials of order 1 and 2 are compared with the moving medianlter. The moving polynomial fitting of order 2 contains more high-requency anomalies than the polynomial of order 1, which is close

Distance (m)

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igure 1. HEM and aeromagnetic data collected using the DIGHEMystem. �a� Altitude variations, �b� in-phase �black� and quadraturedashed� data, and �c� magnetic field.


o the moving median filter. The stability of the moving polynomialtting at the ends of the line data, in comparison with the moving me-ian, is an advantage of the polynomial fitting technique.

For the 2D case, a polynomial surface is fitted to the data points.he polynomial fitting procedure in 2D is almost the same as the 1Dase. Likewise, spikes and high-frequency anomalies are rejectedor the surface fitted to the data points encircled by the 2D window.he idea behind this approach is to find the difference between the

evels of neighboring lines by rejecting high-frequency anomalies.hen the level difference between adjacent lines is the main charac-

eristic of the leveling errors, which can be exploited by this method.Two types of windows are formed: a 1D rectangular window that

ncloses a certain number of data points along one flight line and aD sliding circular window that encloses the data points located ont least three flight lines. The circular window has an adjustableearch radius r to correct the data at the center of the circle. The 1Dindow, located in the middle of the circular window, covers theoints along the flight line �r around the center of the circular win-ow. The data enclosed in the 2D window are assumed to be continu-us. Any line data that is free of leveling errors should be almost athe same level as the adjacent lines. Thus the 2D polynomial fittedalue at the center is very close to the one acquired in the 1D rectan-ular window. In case the lines are not on the same level, the levelingifference can be large. Figure 3 illustrates the concept with 1D andD sliding windows. The data point considered is at the center ofindows.Apolynomial is fitted to the data points inside the 1D win-ow, and also a surface is fitted to the observed values in the 2D win-ow using a least-squares approach. The polynomial coefficients areherefore calculated by minimizing the expression

S��d� f�x��2, �1�

here d is the observed data inside the window and f�x� is a polyno-ial function. In general, a polynomial is defined as

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here n is order of the polynomial and number of the terms is equalo �n�1��n�2� /2. A simple model that can fit to the data for 1D

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igure 2. Measured magnetic field �thin gray�, moving polynomialtting of order 1 �solid black�, moving polynomial fitting of order 2thick gray�, and moving median filter �dashed black� with a windowength of 1000 m.


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Leveling of aerogeophysical data L15

nd 2D windows is a polynomial of order 1. Thus, for 1D and 2Dodels we have:

f�x�1D�a1x�a0, �3�

f�x,y�2D�a1,0x�a0,1y�a0,0. �4�

t the center of the circle that is the origin of the coordinate system,e get f�0�1D�a0 and f�0,0�2D�a0,0.If the central and neighboring lines are at the same level, the esti-ated values of a0,0 for 1D and 2D polynomials should be close.herefore, we refer to the difference e�a0,0�a0 as the leveling er-

or. The leveling correction can be applied by adding this value to theeasured data at the current point. The sliding windows then areoved point by point to correct the rest of the data.The principle of this approach is similar to the DMF method intro-

uced by Mauring and Kihle �2006�. The DMF is efficient to use as aeveling/microleveling method when there are no tie-line data oright lines are nonparallel. Mauring and Kihle �2006� show the ap-lication of their approach on real data. This technique, however, isery sensitive to 2D anomalies that lie along flight lines. We haveenerated a synthetic data set to study such an effect. The data arelong eight flight lines of 100-m spacing. Figure 4 shows the totalagnetic field caused by a prism with a strike parallel to the flight

ines. The prism has dimensions of 50�500�100 m3 and the deptho the top of the body is 10 m. The susceptibility of the body is 0.01I and the magnetic field intensity is equal to 60,000 nT. Results of

he differential polynomial fitting are compared with the DMF alongine 4 �Figure 4b�. The 1D and 2D polynomials of order 2 with aearch radius of 150 m are used to process this data. As no error isdded to the synthetic data, we expect results to be the same as therue magnetic field. The DMF has eliminated the anomaly complete-

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y, whereas the DPF has preserved the anomaly appropriately. Theackground, which is close to zero, dominates the median valuehen the number of data points enclosed by the 2D window is more

han twice the number of data points in the 1D window �Figure 4a�.ut the median value of the 1D window is dominated by the anomaly

hat is about 135 nT. Then the difference between the 1D and 2D me-ian values, which is considered as leveling error, is equal to thenomaly. In the case of the DMF, by subtracting the calculated level-ng error from the data points at the center of the windows, the anom-ly is eliminated entirely. The process, for both methods, can be-ome highly effected in cases where a strong regional field with largeradients exists in an area. This case is more probable for aeromag-etic data. The HEM data are much better suited for this techniqueecause the anomalies have much shorter wavelengths comparedith magnetic-field anomalies.

SYNTHETIC DATA

To study the applicability of the method, we first test it on a syn-hetic data set. Figure 5 illustrates a 3D view of the synthetic model.

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igure 4. �a�Asingle synthetic prism along flight lines direction withnclination and declination of 90° and 0°; �b� DPF �black�, DMFgray�, and calculated magnetic field �dashed�.


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he physical and geometric properties of the synthetic model areiven in Table 1.

The inducing magnetic field has an inclination and declination of5°, 45°. The magnetic-field intensity is 60,000 nT and the suscepti-ility is equal to 0.01 SI for all bodies. The magnetic-field data werealculated on a surface 50 m above the ground at a 10-m samplingnterval along flight lines with 400-m line spacing. The syntheticata shown in Figure 6 covers an area of 4.8�25 km2. The calculat-d magnetic field is gridded with a cell size of 100 m �Figure 6a�. Inhe synthetic data set, the distance between the flight lines is mucharger than the flight heights. This can introduce severe aliasing ef-ects in the direction perpendicular to the flight lines. To illustrate aealistic case, diurnal variations from a real data set were added tohe calculated magnetic field. The wavelength of diurnal variationsaries along the lines. The resulting magnetic field is shown in Fig-re 6b. The DPF and DMF methods then were used to level the ma-ipulated data. After some tests, a search radius of 2000 m and aolynomial of order 1 were chosen to level the data.

Figure 6c shows the leveled magnetic field using the DPF method.he leveling error is removed from the manipulated magnetic fieldppropriately. High-frequency anomalies can be enhanced effec-ively using the gray-scale image of a second vertical derivative ofhe magnetic field. The second vertical derivative of the magneticeld before and after applying the DPF method are shown in Figuree and f, respectively. Most of the leveling errors, enhanced in Fig-re 6e, are removed successfully in Figure 6f. The difference be-ween calculated and leveled data is almost �5% of the manipulated

agnetic field. The DMF also is applied to the manipulated data withhe same search radius. The resulting map �Figure 6d� shows that theMF method has a good performance on this synthetic data set to re-ove the leveling errors. The second vertical derivative of the lev-

led magnetic field using the DMF is very similar to Figure 6f. Tohow more details, the calculated, manipulated, and leveled magnet-c fields along line 8 �see Figure 6� are presented in Figure 7 for both

ethods. The leveling errors removed from the manipulated datand the difference between calculated and corrected magnetic fieldlso are shown in this figure.An rms error was calculated using

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REAL DATA

eromagnetic data example

We tested the DPF method on a data set from the Bazman area, inouthwest Iran, collected in 2005 by Fugro Airborne Surveys on be-alf of the Geological Survey of Iran �GSI�. The purpose of the sur-ey was to provide data for mineral exploration. Airborne �helicop-er� magnetic data were acquired with a sampling interval of approx-mately 3 m using two magnetometers separated horizontally by

m, perpendicular to the flight lines. Measurements were carriedut along north-south flight lines with 400-m line spacing. The nom-nal height of the sensors was 30 m. Figure 8a shows the gridded to-al magnetic-field anomaly with a cell size of 100 m after removinghe diurnal variations using a base station magnetometer.An interna-ional geomagnetic reference field �IGRF� correction has been ap-lied using the model from 2005.

To remove linear artifacts, we processed the Bazman data set withhe same method applied to the synthetic data. In this case, we triedo fit polynomials of order 1 and 2 to flight lines. The resulting mapith a polynomial of order 2 looks more reliable. Use of higher orderolynomials demands longer search radii to avoid singular values inhe least-squares estimation and also requires a much longer pro-essing time. Therefore, orders higher than 2 were not used. Usingquation 2 we have:

f�x�1D�a2x2�a1x�a0, �6�

f�x,y�2D�a2,0x2�a0,2y2�a1,1xy�a1,0x

�a0,1y�a0,0. �7�

After a few attempts with different search radii,the data were leveled with a search radius of1500 m in which the circular window covered amaximum of seven flight lines.Application of themethod successfully removed the linear artifacts.Figure 8b depicts the leveled magnetic-field datausing the DPF method. The DMF method alsowas applied to the same data with a 1500-msearch radius �Figure 8c�. The leveling errors re-moved from the magnetic field using the DPF andDMF methods are illustrated in Figure 8d and e,respectively. A comparison between Figure 8dand e shows that the DMF removes longer wave-lengths along flight lines from the data than theDPF. As an example, the data along flight line12,041 �shown in Figure 8� is illustrated in Figure9. One of the major linear artifacts that can beseen in the observed magnetic data �Figure 8a� iscaused by inconsistent levels between line 12,041

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nd adjacent lines. Figure 9b shows the observed and leveled mag-etic field along this line. The difference between the magnetic fieldnd leveled magnetic field using the DPF and DMF are shown inigure 9c. The leveling error for this specific line varies between40 nT to �40 nT for the DPF and �30 to �85 nT for the DMF.The DPF and DMF methods have applied large error corrections

see Figure 8d and e� in some parts of the study area �e.g., northwestnd central-east of the area� where there are no obvious level prob-ems. This can be caused by the parameter setting of both methods.se of different search radii can improve these processing artifacts.asically, the search radius �for both methods� and order of the poly-omial �for the DPF� should be a function of the dominant wave-ength in different parts of the study area, but in practice, use of vary-ng parameters in different subareas demands more computationalime.

EM data example

The same technique has been applied to an HEM data set from theiroft area, in south Iran, collected by GSI in 2006. The HEM dataere acquired with a sampling interval of about 4 m using theIGHEM system. The survey was done with five frequencies withifferent coil configurations along northwest-southeast flight lines.wo vertical coaxial coils with frequencies of 1000 Hz and500 Hz, and three horizontal coplanar coils with frequencies of00 Hz, 7200 Hz, and 56 KHz, are used in this system. TheIGHEM system was calibrated with the Fugro Autocal system to

djust the gain for any changes in the output of transmitters. Theight-line spacing was 250 m with a nominal sensor height of 30 m.The raw HEM data show a time-dependent drift largely because

f temperature variations. It is therefore necessary to remove thisrift from the recorded HEM data. This procedure is called zero lev-ling and is done by flying at high altitudes �usually 400 m or higher�efore and after each flight �Valleau, 2000�. At high altitudes, alongo-called test lines, the secondary field detected from the ground isractically zero. The estimated drift at test lines is subtracted fromhe secondary-field data to yield zero levels. The zero-level process-ng was applied to the raw HEM data presented in this study prior to

able 1. Physical and geometric properties of bodies used in t

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ny other corrections. The data we use here are zero-leveled HEMata, which are referred to as the measured data.

Because of the sharp relief over large parts of the survey area, itas not possible for pilots to maintain a constant ground clearance of0 m for the sensors. In some places, the height of sensors changedonsiderably. It should be noted that a towed bird HEM system suf-ers from pendulum-like motion with differences in in-line andross-line frequencies, which can lead to significant errors in the la-er altimeter height �Davis et al., 2006�. Therefore, some errorhould be expected in the recorded altitude. Figure 10 shows a mapf sensor height variations. The inverse relation between height vari-tions of the sensor and HEM data was described in the introduction.uang and Fraser �2001� introduce an approximation to reduce theeight sensitivity of HEM data by a simple transformation. They usen approximation introduced by Fraser �1972�. In that study, Fraserhows that for a homogeneous half space, the ratio between second-ry magnetic-field intensity Hs and primary magnetic-field intensityo at the receiver can be written as

Hs/Ho� �s/h�3�M�� ,�r�� iN�� ,�r��, �8�

here h is the height of the HEM sensor, s is the coil separation, i��1 and M and N are referred to as the in-phase and quadrature

omponents normalized by height variations of the HEM sensor.he � is a dimensionless complex induction number for the halfpace equal to ��2��h2� i��h2�1/2, where � is the angular frequen-y, � is the conductivity, � is the magnetic permeability, �r is the rel-tive magnetic permeability, and � is the dielectric permittivity.hen they used this approximation to estimate the normalized in-hase and quadrature components by

M � I�h/s�3 and N�Q�h/s�3, �9�

here I and Q represent the measured in-phase and quadrature com-onents. Equations 8 and 9 can be used if s3�h3 and for surveysown over conductive ground. Huang �2008� recommends lower or-ers of �s /h� for a more resistive earth. He shows that the sensitivityf the transformed HEM data to height variations is considerablyess than the original data. Afterward, he levels the calculated M and

thetic model.

� Depth extent �m� Dip Strike Length �m�

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, and later he transforms the leveled M and N, back to the in-phasend quadrature components using equation 9.

Following Huang’s approach, we transform the original data to Mnd N, and then we inversely transform them to the in-phase anduadrature components, but at a predefined reference height. Thenhe measured in-phase and quadrature components become scaled tohis reference height. Effectively, this can be accomplished by a sin-le scaling

Ir� I�h/s�3� �h̄/s��3� I�h/h̄�3 and Qr�Q�h/s�3

� �h̄/s��3�Q�h/h̄�3, �10�

here h̄ is the reference height, and Ir and Qr are in-phase and

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igure 6. �a� Calculated magnetic field for synthetic model shown inigure 5, �b� manipulated magnetic field, �c� leveled magnetic fieldsing the DPF, �d� leveled magnetic field using the DMF, �e� secondertical derivative of Figure 6b, and �f� second vertical derivative ofigure 6c.


uadrature components scaled to the reference height, respectively.he data recorded above the nominal height are scaled to the refer-nce height using the scaling factor. This kind of scaling can amplifyoise and signal. It can be more reasonable to scale data to the possi-le lowest height, but the risk of amplification of noise can be in-reased. A reasonable choice of difference height could be the aver-ge height. The aim of this correction is to scale amplitudes of anom-lies to a constant level within the area prior to leveling. Here weresent the application of the DPF method only on the 5500 HzEM data after height scaling. The mean value of the height varia-

ions in the area �44 m above the ground� is considered to be the ref-rence height.

A polynomial of order 2 was used in the leveling procedure for allEM data shown here. Figures 11a and 13a show the measured in-hase and quadrature data. Some linear artifacts can be identified inhe maps. The measured quadrature component �Figure 13a� con-ains leveling errors with shorter wavelength than the measured in-hase component �Figure 11a� along the flight lines. The scaled in-hase and quadrature components are illustrated in Figures 11b and3b, respectively. The DPF method with a search radius of 1500 mas used to level the data with results shown in Figures 11c and 13c,

espectively. Most of the linear artifacts are attenuated considerably.he difference between scaled and leveled-scaled in-phase anduadrature components is illustrated in Figures 11d and 13d. Line4,780 is chosen to show the corrections in more details. Figure 12ahows the height variations of the sensor along line 14,780. Theeasured, scaled, and leveled in-phase and quadrature data along

he same line and leveling errors are shown in Figure 12b-d, respec-ively.

Apparent resistivity can be calculated for each frequency used in

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igure 7. Line data before and after correction along line 8 shown inigure 6c. �a� Calculated magnetic field �solid gray�, manipulatedagnetic field �solid black�, leveled magnetic field using the DPF

dashed black�, and leveled magnetic field using the DMF �dashedray�. �b� Added errors to the magnetic field �dashed black�, re-oved error using the DPF �solid black�, and removed error using

he DMF �solid gray�. �c� Difference between leveled magnetic fieldsing the DPF and calculated magnetic field �gray� and differenceetween leveled magnetic field using the DMF and calculated mag-etic field �black�.


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he survey. The apparent resistivity shown in Figure 14a is calculatedsing the altitude-amplitude method �Cheesman, 1998� for the verti-al coaxial coil with frequency of 5500 Hz. In the calculated appar-nt resistivity data, high-frequency high-amplitude anomalies can

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N)

)

)

d)

e)

� � �

� � �

� � �

� � �

� � �

igure 8. �a� Measured magnetic field, �b� leveled magnetic field us-ng the DPF, �c� leveled magnetic field using the DMF, �d� differenceetween a and b, and �e� difference between a and c.


e seen where the height of the sensor is increased. The DPF methodas applied to level the apparent resistivity data calculated directly

rom the zero-leveled, in-phase, and quadrature components. Aearch radius of 1300 m yielded the leveled map. Figure 14b and chow the corrected and leveling errors of apparent resistivity data,espectively.

10050050−

Levelingerror(nT)

N SDistance (m)

0 5000 10,000 15,000 20,000

45403530250 5000 10,000 15,000 20,000A

ltitude(m)

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0 5000 10,000 15,000 20,000N S

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)

)

)

igure 9. Measured and corrected magnetic field along line 12,041hown in Figure 8. �a�Altitude variations �solid� and nominal heightf 30 m �dashed�. �b� Measured magnetic field �solid black�, leveledagnetic field using the DPF �solid gray�, and leveled magnetic field

sing the DMF �dashed gray�. �c� Difference between leveled mag-etic field using the DPF and measured magnetic field �black� andifference between leveled magnetic field using the DMF and mea-ured magnetic field �gray�.

31 34 36 38 39 41 43 45 48 55

Altitude(m)

Scale 1:1000001000 0 1000 2000

(meters)

3000

2000 6000 10,000 14,000 18,000 20,0000

4000

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igure 10. Altitude variations of the sensor from the ground surfaceecorded by radar altimeter.


P

ipHtatif

lvmts

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L20 Beiki et al.

DISCUSSION

arameter setting

A key point in the DPF method is to find optimal parameters. Thiss done mainly by trial-and-error adjustments. A critical step in thearameter setting is to choose an appropriate polynomial order.igh-order polynomials are not recommended because they may fit

he smaller wavelength anomalies in the windows. They also requirelarger window to include more data points and avoid instabilities in

he least-squares estimation process. The computational time alsoncreases with larger numbers of data points. From experience, weound that polynomials of orders 1 and 2 are suitable choices.

Line 14,7808 14 20 25 30 37 47 63 95157

In-phase(ppm)

681

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681

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a)

b)

2000 6000 10,000 14,000 18,000 20,000x (m)

2000 6000 10,000 14,000 18,000 20,000x (m)

igure 11. �a� Measured in-phase data, �b� in-phase data scaled to theveling errors removed from scaled in-phase data.


For a proper search radius, we suggest a 2D window that covers ateast three neighboring flight lines. With the algorithm we have de-eloped, the parameters are fixed for the entire study area, but thisight not be the optimal choice. A changing set of optimal parame-

ers might be the best solution. The optimal parameter settingshould be done by skilled users based on trial and error.

omparison between the DPF and DMF

In this study, the DPF was compared with the DMF method forynthetic and real data. Although the DMF method removes anoma-ies striking along flight lines, the DPF method preserves them suffi-

Line 14,7808 14 20 25 30 37 47 63 95157

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�27 �12 �6 �3 0 2 4 7 10 20In-phase

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Line 14,780

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ence height, �c� leveled scaled in-phase data using the DPF, and �d�

c

d

e refer


Fsgd

F�


200150100500 0 5000 10,000 15,000 20,0005000 10,000 15,000 20,000

In-phase(ppm)

SE NWDistance (m)

b)100806040200 5000 10,000 15,000 20,0005000 10,000 15,000 20,000

Altitude(m)

SE NWDistance (m)

a)

200150100500

Quadrature(ppm)

0 5000 10,000 15,000 20,0005000 10,000 15,000 20,000SE NW

Distance (m)

c)40200

−20−40

SE NWDistance (m)Le

velingerror(ppm)

0 5000 10,000 15,000 20,0005000 10,000 15,000 20,000

d)

igure 12. �a� Altitude variations of the sensor �solid� and the reference height of 44 m �dashed� along line 14,780; �b� Measured �solid black�,caled �dashed black�, and leveled scaled �solid gray� in-phase data; �c� Measured �solid black�, scaled �dashed black�, and leveled scaled �solidray� quadrature data; �d� Leveling errors removed from the scaled in-phase data �black� and leveling errors removed from the scaled quadrature
ata �gray�.
c)

d)

Line14,78017� �8�5 3� �1 1 2 4 6 9

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17 27 35 42 49 59 72 88 111 516

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igure 13. �a� Measured quadrature data, �b� quadrature data scaled to the reference height, �c� leveled scaled quadrature data using the DPF, andd� leveling errors removed from scaled quadrature data.

Downloaded 28 Jan 2010 to 130.238.140.35. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/

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L22 Beiki et al.

iently. The only variable that controls smoothness of the DMF is theindow size, whereas smoothness of the DPF can be controlled by

hanging the order of the polynomial. For the synthetic data exam-le, the results look more or less the same for both approaches. How-ver, the DPF method provided smaller rms errors. But for the real-ata example, results look more different. Comparing Figure 8d andshows that the leveling errors removed from the magnetic field for

he DPF have shorter wavelengths than the DMF. The leveling errorsor DPF along a single flight line �Figure 9c� show smoother anoma-ies removed from the magnetic field. Also, the amplitude variationsf leveling errors for the DMF are greater than those for the DPF.

The DPF requires a longer processing time to estimate polynomi-l coefficients. However, with developing computers and commer-ial software, this should not be an obstacle for using this technique.

0.27 0.57 0.74 0.921.14 1.56 2.60

Apparent resistivityLog10 (Ohm-m)

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a)

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igure 14. �a� Calculated apparent resistivity data, �b� leveled apparealculated apparent resistivity data.


CONCLUSION

A new approach has been introduced to remove leveling/mi-roleveling errors from aerogeophysical data. This technique isased on 1D and 2D polynomial fitting in sliding windows. Resultsrom the test with a synthetic magnetic-field data set show that gen-rated linear artifacts can be reduced substantially using this ap-roach. This technique can be applied regardless of the sources ofeveling errors. In the case of microleveling errors, the presentedechnique can be used as a microleveling approach with small win-ows that cover only three to five flight lines. Another advantage ofhis method is that no tie-lines are needed to correct the flight-lineata. This makes the method particularly useful for data sets collect-d without any tie-lines flown perpendicular to the flight lines. This

Line 14,780

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stivity data using the DPF, and �c� leveling errors removed from the

0.20 0.37

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ethod can be applied for regular and irregular flight-line patterns.owever, irregular patterns of flight lines are not considered in this

tudy.Aeromagnetic and HEM data from the Bazman and Jiroft areas in

ran were leveled using the differential polynomial fitting technique.he method removed linear artifacts in aerogeophysics data present-d in this paper, so that the resulting maps looked much more realis-ic.

The linear features seen in the magnetic-field data along severalight lines were removed effectively while preserving the long andhort wavelength anomalies. The HEM data is scaled to a referenceeight prior to leveling correction. Using this scaling, amplitudes ofnomalies are scaled up or down corresponding to the height varia-ions of the sensors. However, for large height variations, this proce-ure could be risky because it can amplify noise.

ACKNOWLEDGMENTS

Authors thank the Geological Survey of Iran �GSI� for permissiono use its data in this study. We also thank Haoping Huang for his use-ul comments. Appreciation is expressed to Hediyeh Nazi for heromments on the acquired results. The constructive comments madey Mark Pilkington and three anonymous reviewers are highly ap-reciated.


REFERENCES

andy, W. L., A. F. Gangi, and F. D. Morgan, 1990, Direct method for deter-mining constant corrections to geophysical survey lines for reducing mis-ties: Geophysics, 55, 885–896.

heesman, S., 1998, HEMRES2 GX documentation �online Help for the am-plitude-altitude resistivity inversion algorithm in Oasis montaj software�:Geosoft Inc.

avis, A. C., J. Macnae, and T. Robb, 2006, Pendulum swing in airborneHEM systems: Exploration Geophysics, 37, 355–362.

oster, M. R., W. R. Jines, and K. V. Weg, 1970, Statistical estimation of sys-tematic errors at intersections of aeromagnetic survey data: Journal ofGeophysical Research, 75, 1507–1511.

raser, D. C., 1972, A new multicoil aerial electromagnetic prospecting sys-tem: Geophysics, 37, 518–537.

uang, H., 2008, Airborne geophysical data leveling based on line-to-linecorrelations: Geophysics, 73, no. 3, F83–F89.

uang, H., and D. C. Fraser, 1999, Airborne resistivity data leveling: Geo-physics, 64, 378–385.—–, 2001, Mapping of the resistivity, susceptibility and permittivity of theearth using a helicopter-borne electromagnetic system: Geophysics, 66,148–157.

uyendyk, A. P. J., 1997, Processing of airborne magnetic data: AGSO Jour-nal ofAustralian Geology & Geophysics, 17, 31–38.auring, E., and O. Kihle, 2006, Leveling aerogeophysical data using amoving differential median filter: Geophysics, 71, no. 1, L5–L11.

iemon, B., 2009, Levelling of helicopter-borne frequency-domain electro-magnetic data: Journal ofApplied Geophysics, 67, 206–218.

alleau, N. C., 2000, HEM data processing — a practical overview: Explora-tion Geophysics, 31, 584–594.

arger, H. L., R. R. Robertson, and R. L. Wentland, 1978, Diurnal drift re-moval from aeromagnetic data using least squares: Geophysics, 46, 1148–1156.


leveling hem and aeromagnetic data using differential polynomial fitting

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