Euler 3 D Deconvolution

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Journal of Emerging Trends in Engineering and Applied Sciences (JETEAS) 3(4) 711-717 (ISSN: 2141-7016)

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Euler 3-D Deconvolution of Analytical Signal of MagneticAnomal ies over Iron Ore deposit in Okene, Niger ia

1J .O. Amigun,2O. Afolabi and 2B.D. Ako

1Department of Applied Geophysics,Federal University of Technology, Akure, Nigeria

2Department of Geology, Obafemi Awolowo University, I le-Ife, NigeriaCorresponding Author: J .O. Amigun___________________________________________________________________________AbstractThe Euler deconvolution of analytical signal of the magnetic field data over the iron ore deposit in Okene, Northcentral Nigeria has been carried out to determine the locations and depths of the iron ore bodies and othergeologic sources in the area. The methodology adopted was obtaining solutions by inverting Euler homogeneityequation which relates the magnetic field and its gradient components to the location of the source of ananomaly and with the degree of homogeneity expressed as structural index. The Euler deconvolution processwas carried out on the analytical grid of aeromagnetic data of the study area using a structural index of 1.0, 2.0

and 3.0respectively. The Euler solutions for structural index of 1.0 have their depths ranges from 11 to 120m.For the Euler solutions S.I =2.0, cluster solutions of relatively deep depth of between 234 to 242m are obtained.Their anomalous source location and pattern (Northeast Southwest) coincides with the outcropped iron orebodies at the central ore zone of the study area. The estimated depths and geometries provided by the Eulerdeconvolution result will aid the mine design and the economic exploitation of the iron ore deposit in the studyarea.__________________________________________________________________________________________Keywords: Euler deconvolution, iron ore deposit, analytic signal, magnetic field, homogeneity._________________________________________________________________________________________INTRODUCTIONThe Euler deconvolution is an interpretation tool inpotential field for locating anomalous sources and thedetermination of their depths by deconvolution usingEulers homogeneity relation (Reidetal., 1990). Themethods preference over the profile techniques suchas Peters (1949) method (half slope) is that itrequires no prior knowledge of the sourcemagnetization direction, does not assume anyparticular interpretation models and the process canbe applied directly to large gridded data sets.

The Eulers homogeneity equation (Eulerdeconvolution) relates the magnetic field and itsgradient components to the location of the source ofan anomaly, with the degree of homogeneityexpressed as a structural index (Y aghoobian etal.,1992). In interpreting magnetic survey in grid form,the preference of using the analytical signal of themagnetic anomalies over the conventional standardEuler is that with the analytical signal far fewersolutions are generated from the Eulers homogeneityequation, hence few extraneous depth estimates areretained.

In this study, we will present the results from theapplication of Euler 3-D deconvolution in theinterpretation of magnetic anomalies over an iron oredeposit for its source locations and depths using thegridded magnetic map in Figure1. The total magnetic

field data (Figure1) was acquired at a mean terrainclearance of 152.4 m with flight line separation ofabout 400m along a NW SE direction.

LOCATION AND GEOLOGIC SETTING OFSTUDY AREAThe iron ore deposit lies between latitude 70 37' 22"N and 7039' 17"N and longitudes 6015' 55"E and 6017' 15"E (Fig.2). This area falls within the 1:50,000standard topographic map of Kabba sheet 246 S.E ofGeological Survey of Nigeria (GSN). The study areais underlain by rocks belonging to theMetasedimentary and Metavolcanic rocks of theNigerian Basement Complex which falls within theIgarra Kabba Jakura metasedimentary region inthe south western part of Nigeria (Olade andElueze, 1979).The deposit forms a prominent ridge,like the Itakpe iron ore deposit currently mined tofeed the National Steel Complex at Ajaokuta andAladja and its dominant lithologic units are gneisses(which are regionally emplaced), ferruginousquartzites, granites and pegmatite. The ferruginousquartzite is the source of the iron ore mineralizationin the area (Fadare, 1983; Annor and Freeth, 1985).The patterns of the iron ore mineralization in the areaas shown in Figure 2 have been discussed byAdeyemo et al (1984) and NSRMEA (1994).Structurally, the metamorphic rocks of the study areaconsists of three sets of closely related hil ls ofbasement rocks marked as the northern, central and

Journal of Emerging Trends in Engineering and Applied Sciences (JETEAS) 3 (4): 711-717 Scholarlink Research Institute Journals, 2012 (ISSN: 2141-7016)jeteas.scholarlinkresearch.org


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southern ore zones (Figure 2) and made up mainly ofmigmatite and biotite gneisses that trend in anortheast southwest direction while the iron orebodies in these gneisses are thick and strike northeast southwest.

METHOD OF STUDY

The methodology as described by Reid, (1980) andThompson, (1982) in obtaining solutions by invertingEuler homogeneity equation was adopted in thisstudy. According to Yaghoobian etal., (1992), theEulers homogeneity equation relates the magneticfield and its gradient components to the location ofthe source of an anomaly, with the degree ofhomogeneity expressed as a structural index. Eulershomogeneity relationship can be written (Reid et al.,1990) for magnetic data in the form:

where (x, y, z) are the coordinates of the observationpoint, N=-n, wheren is degree of homogeneity, andNis a coefficient, called structural index (Thompson1982). The structural index depends on the geometryof the source. For a homogeneous point sourceN =3,a linear source (line of dipoles or poles, and for ahomogeneous cylinder, rod, etc.) N =2, for extrusivebodies (thin layer, dike, etc.) N =1, for a contact,vertex of a block and a pyramid with a big heightN =0. The unknown coordinates (x

0, y

0, z

0) are estimated

by solving a determined system of linearequations (1.0) using a prescribed value for N withthe least squares method. And a solution with aminimum standard deviation is found through usingdifferent tentative values for N. In equation (1.0) Bdenote the base level of the observed field i.e.

background field.

The structural index is a measure of the fall-off rateof the field with distance from the source. The choiceof a proper S.I is a function of the geometry ofcausative bodies. Estimation of the correct structuralindex is crucial for the successful application of theEuler deconvolution method (Reid et al, 1990). Andthis is achieved by using the index that produces thebest clustering of solutions (Reid, 1995). Incorrectchoice of structural index leads to errors in estimatedsource depths (Ravart, 1996). Euler deconvolutionused the magnetic field and its three orthogonalgradients (two horizontal and one vertical) tocompute anomaly source locations (Keating andPilkington, 2004). The three dimensional (3D)analytical signal is calculated from the threeorthogonal gradients of the magnetic field (Roest etal, 1992). For a function homogeneous of degree N,Huang et al (1995) denotes the Eulers equation interms of analytic signal as:

where A denote the analytic signal of the magneticfield.

In this study, the Euler deconvolution algorithm inOasis montajTM (geophysical package) for locationand depth determination of causative anomalousbodies from gridded potential field data was used.The method starts by calculating the analytic signalgrid, finds peaks in the grid, then use these peaklocations for Euler deconvolution. The Euler

deconvolution as applied at each solution involvessetting an appropriate structural index , SI value andusing least squares inversion to solve the equationfor an optimum X0, Y0, Z0, and total magnetic fieldintensity (B). The window size and the respectivenumber of the observation points, for which thesystem of linear equations is formed are alsoparameters in solving the inverse magnetic problem.Window of 10 x 10m data points prove most suitablein this study and were used. Solutions with depths tosource above the error tolerance levels were rejected.

RESULTS AND DISCUSSIONFigures 3a - 3c show the maps of the x, y and zderivative grids of the aeromagnetic data of the studyarea in Figure 1 These maps are required for thecalculation and subsequent display of the analyticalsignal grids (map) shown in Figure 4 which is neededto perform the located Euler deconvolution adoptedfor this study. The analytical signal map (Fig. 5) isalso useful in the location of edges of magneticsource bodies particularly were remanence and / orlow magnetic latitude complicates interpretation(Thompson, 1982 and Reidetal, 1990).

In Tables 1 are some of the solutions obtained foroperating Euler deconvolution on the analytical gridof the studied area aeromagnetic data (upwardcontinued to 400 m above ground) using a structuralindex of 2.0. The solutions that have passed thespecified acceptable tolerance levels are presented inplan form in Figures 5 - 7. These figures show theestimated source positions and depths for structuralindex of 1.0, 2.0 and 3.0 in the study area. Apparentin the figures are the few solutions shown because theEuler method adopted in this study typically producesfar fewer solutions than the conventional standardEuler method i.e. many extraneous depth estimateshave been removed. The centre of the plotted circlesrepresents the plan location (x0 and y0) of theinterpreted source and the diameter is the depthestimator that is depth is proportional to diameter.Also, the depths are displayed using colour variation

to represent different ranges.

Based on the maximum amplitudes of the analyticsignal in Figure 4, the spatial distributions ofcausative magnetic sources in the area were clearlyrecognized. And the solutions from the Eulerdeconvolution in Figures 5, 6 and 7 are generallylocated around the maximum amplitudes of theanalytic signal.

x x0 T/ x + 0 T/ + z z0

(x x0) A/ x + (y y0) A/ y + (z z0)


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The Euler solutions for structural index of 1.0 of themagnetic anomalies over the iron ore deposit asshown in Figure 5, have their depths ranges from 11to 120m. The clusters of solutions (circles) producedover anomalies for S.I =1.0 as observed are not toosparely diffuse. The solutions for relatively deepdepths i.e. from green (45m) to red (77m) are located

in the northeastern part and coincide with thenorthern ore zone in the study area in Figure 2. Atthis region, the analytic signal map displaysmaximum amplitudes. Another cluster of solution atthe southern part, trending in a northeast - southwestdirection relates well in orientation with the southernore zone where magnetic anomalies of lowintensiveness are observed in Figure 4. Here, thedepths z

0are considerably shallower i.e. from 11 to

45m. It can therefore be deduced that the clusteringpattern of S.I =1.0 Euler solutions correlate with theanomaly patterns interpreted as iron oremineralization. The value of the structural index, 1.0is typical for a sill or dyke (Y aghoobian et al, 1992)

The Figure 6 represents the structural interpretationfor Euler solutions for S.I =2.0. Three linear featuresmarked (A A1, B - B1 and C - C1) were delineatedas faults. The delineated faults A A1 and B - B1

have trend and spatial location similar to the faultsdelineated on the aeromagnetic and derivative mapsof the study area (Amigun et al, 2012). Also, clustersolutions of relatively deep depth of between 234 to242m are obtained at the centre of the map. Thesesolutions both in location and pattern (Northeast Southwest direction) coincides with the iron orebodies at the central ore zone in Figure 2. Again onthe S.I =2.0 map is another cluster of solutions in theNortheastern area with depth range of 223 to 231m.

These solutions are related to the iron ore bodies ofNorthern ore zone.

The Euler solution map for the calculated structuralindex of 3.0 is shown in Figure 7. This map howeverdoes not give a satisfactory result because itssolutions are complex and unrelated in pattern to theanomalies of the aeromagnetic map and the knowngeology of the area. For further establishment, theresult of the Euler deconvolution depths wascompared with those determined by power spectrumof the Fourier transformation of the aeromagneticdata over the deposit. Figure 8 shows the calculatedspectral analysis of the aeromagnetic data. The radialaverage power spectrum plot in Figure 8b representsthe computed amplitude spectrum of the Fouriertransformation of the study area aeromagnetic dataplotted on a logarithm scale against wave-number(frequency). On the depth curve in Figure 8b, thepeak of the curve represents the first estimate of thedepth to the magnetic sources in the study area andthese depths ranged from 50 m to 300 m. Thesolutions patterns and depths obtained for operatingEuler deconvolution on the deposits magnetic fielddata using structural index of 1.0 and 2.0 agrees with

the ore bodies patterns and the estimated depthsdetermined from the spectral analysis of theaeromagnetic data over the deposit. Therefore, thestructural index of 1.0 and 2.0 are assumed theacceptable structural indices for the study area.

CONCLUSIONS

The Euler deconvolution of the analytical signal ofthe magnetic field data over the iron ore deposit hasserved as a recent improvement over techniques suchas Peters method (half slope) because the result fromits interpretation has enabled a rapid determination ofthe locations and depths of the iron ore mineralizationand other geologic sources in the area without priorknowledge of the source geometry and magnetizationdirection. The method has provided insights into thedeposits ore geometry and structural setting. And theestimated source depths and geometries provided bythe Euler deconvolution method can effectively serveas approximation for the construction of magneticmodels of iron ore bodies in the studied area.

ACKNOWLEDGEMENTThe authors are grateful to the Management ofNational Iron Ore Mining Company Limited(NIOMCO), Itakpe for granting access to theAjabanoko deposit for the data collection. Weacknowledge with immense gratitude the contributionof Late Prof. S.L. Folami. Our gratitude also goes tothe Department of Geology, Obafemi AwolowoUniversity, for permitting the use of Oasis Montajwork station.

REFERENCESAdeyemo B., Williams F.O and Adegbuyi O., 1984.Geological Exploration of Ajabanoko Hill Deposit,Okene, Nigeria. Technical Report of National SteelCouncil Explo. Div., Kaduna, Nigeria. 14pp.

Amigun J.O, Afolabi O. and Ako B.D., 2012Application of Airborne Magnetic Data to MineralExploration in the Okene Iron Ore Province ofNigeria. International Research Journal of Geologyand Mining. Accepted for Publication, July, 2012.

Annor A.E and Freeth S.J., 1985. ThermotectonicEvolution of the Basement Complex around Okene,Nigeria with special reference to DeformationMechanism. Precamb. Res. 28, p. 269-281.

Fadare V.O., 1983. Iron Ore Formations TheOkene Ajaokuta Lokoja Areas of Kwara State. APotential Supply Base for the Steel Plant atAjaokuta. J ournal of Mining and Geology, Vol. 20,209 214

Huang D., Gubbins D., Clark R.A. and Whaler K.A.,1995. Combined study of Eulers homogeneityequation for gravity and magnetic field. 57th EAGEconference, Glasgow, UK, Extended Abstracts, p144


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Keating P. and Pilkington M., 2004. Eulerdeconvolution of the analytic signal and itsapplication to magnetic interpretation. GeophysicalProspecting 52, 165-182

National Iron Ore Mining Project, NIOMP Itakpe,1994. Geological Map of Ajabanoko Iron Ore

Deposit. (Unpublished)

National Steel Raw Materials Exploration Agency,NSRMEA, 1994. Preliminary Report on AjabanokoIron Ore Deposit. (Unpublished)

Olade M.A. and Elueze A.A., 1979. Petrochemistryof Ilesha amphibolites and Precambrian Crustalevolution in the Pan-Africa of S.W. Nigeria.Precambrian, 8, p. 303 310

Peters L. J ., 1949. The direct approach to magneticinterpretation and its practical application.Geophysics, 14, 290320.

Ravart D., 1996. Analysis of the Euler method andits applicability environmental magneticinvestigations. J ournal of Environmental andEngineering Geophysics 1, 229-238

Reid A.B., 1980. Aeromagnetic Survey design,Geophysics, 45, 973 976

Reid A.B., 1995. Euler deconvolution: Past, presentand future a review. 65th SEG meeting, Houston,USA, Expanded Abstract, 272-273

Reid A.B., Allsop I.M., Grsner H, Millet A.J. andSomerton I.W., 1990. Magnetic interpretation inthree dimensions using Euler deconvolution,Geophysics, 55, 80 91

Roest W., Verhoef J ., Pilkington M., 1992.Magnetic interpretation using the 3-D analyticsignal. Geophysics 57, 116-125.

Thompson D.T. 1982. EULDPH A new techniquefor making computer assisted depth estimates frommagnetic data, Geophysics, 47, 31 37

Yaghoobian A., Boustead G.A, Dobush T.M 1992.Object delineation using Eulers HomogeneityEquation, Proceedings of SAGEEP 92, San Diego,California.

Table 2: Some Results of Euler Deconvolution Analysis of S.I =2 for the Study Area

X_Window, Y_Window: Difference between window center and

Euler solution.

X_Euler, Y_Euler : Actual location of Euler solution

Depth: Solution depth (z coordinate)

Backgrnd: Background Field

WndSize: An estimate of the peaks sizes.

dZ: Estimated error in depth.

dXY: Estimated location error in solution

X_Window Y_Window X_Euler Y_Euler Depth Backgrnd WndSize dZ dXY

198400 843520 198933.3 843764.7 364.11 -179.08 2000.00 10.29 56.10

198720 843520 198783.6 843775.4 374.85 -110.18 2000.00 15.60 55.21

199040 843520 198921 843788.6 356.93 -92.25 2000.00 12.68 40.19

199360 843520 199019.1 843679.9 403.67 -150.97 2000.00 16.37 41.28

199680 843520 199134.3 843618.2 239.65 -94.34 2000.00 30.29 68.01

200000 843520 199690.2 843468.7 147.48 6.89 2000.00 24.27 68.51

200320 843520 200228.5 843758.4 159.51 3.41 2000.00 33.31 95.29

200640 843520 200370.1 843603.3 171.64 17.84 2000.00 40.32 110.93

198400 843840 198540.9 843918.7 178.49 50.16 2000.00 33.63 111.33

198720 843840 198665.1 844011.8 203.09 146.85 2000.00 20.88 90.01

199040 843840 198625 843888 171.16 66.61 2000.00 16.24 73.96

199360 843840 198678.2 843643.1 288.89 -120.79 2000.00 18.43 44.97

199680 843840 198816.3 844070.6 530.42 -96.06 2000.00 32.15 39.40

200000 843840 199538.2 843993.5 277.13 -50.14 2000.00 19.51 47.10

200320 843840 199947.2 843833.8 278.29 -12.26 2000.00 7.84 30.34

200640 843840 199826.1 843719.4 261.16 0.45 2000.00 9.54 47.75

198400 844160 198539.6 844105.5 135.37 57.58 2000.00 19.79 74.56

198720 844160 198745 844121.8 146.87 131.27 2000.00 12.11 57.76

199040 844160 198696.9 844073.8 146.84 147.04 2000.00 6.64 31.34


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Fig 1: Digitized Aeromagnetic Map of Ajabanoko Iron OreDeposit Area.

Fig.2: Location and the Geological Map of the Study Area(Adapted from National Iron Ore Mining Project, Itakpe, 1994)


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Fig.3: The dx, dy and dz gradient grid of Aeromagnetic data of study area used for Euler Deconvolution

Fig.4: Analytical Signal Map of the Aeromagnetic Data

Fig.5: The Euler Deconvolution Depth Plot of the Study Area for SI of 1.0


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Fig. 6: The Euler Deconvolution Depth Plot of the Study Area for SI of 2.0

Fig.7: The Euler Deconvolution Depth Plot of the Study Area for SI of 3.0

Fig.8 (a) Spectrum of the Aeromagnetic data of the study Area (b) Its Radial Spectrum and Depth Estimate Plot

Euler 3 D Deconvolution

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