Lithologic characterization using magnetic and gravity gradient data over an iron ore formation∗Cericia Martinez†,Yaoguo Li†, Richard Krahenbuhl†, Marco Braga‡

†Center for Gravity, Electrical, and Magnetic Studies, Department of Geophysics, Colorado School of Mines‡Vale, Brazil

ABSTRACT

Magnetic and gravity gradient data over part of the GandarelaSyncline iron formation in the Quadrilatero Ferrıfero have beenutilized to obtain a 3D susceptibility and density contrast modelusing inversion. It is possible to use these detailed 3D physi-cal property distributions of subsurface features for lithologicinterpretation purposes. We group the two physical propertydistributions into geologically representative units. A distribu-tion of these lithologic units can then be organized in a modelsimilar to the susceptibility and density distributions in orderto help characterize subsurface structure.

INTRODUCTION

The combined interpretation of gravity and magnetic data hasoften been useful in characterizing an exploration target. Withthe advent of accessible systems to measure gravity gradients,it is natural to pair gravity gradient and magnetic data for in-terpretation purposes where applicable.

Direct interpretation of maps aside, there has been much workin exploiting the potential field relationships to extract moreinformation from the data. Kanasewich and Agarwal (1970)explored the validity of using the magnetization to density ra-tio in the wavenumber domain as an interpretation tool. Di-rectly combining magnetic and gravity derived gravity gradi-ent data through the Poisson relation has been accomplishedby Dransfield et al. (1994) and Price and Dransfield (1995) inorder to generate psudolithology maps based on the ratio ofapparent susceptibility to density. Thanks to technological de-velopments, gravity gradient and magnetic measurements canbe made and pseudolithologic maps can be derived in a moredirect manner from observed data as in Braga et al. (2009).

Beyond direct utilization of data to generate apparent suscep-tibility and density maps, inversion of potential field data fora susceptibility and density distribution can be explored forlithologic differentiation. Lane and Guillen (2005) exploredinversion guided by lithologic categories with density and sus-ceptibility properties being ancillary information. Williamsand Dipple (2007) explored estimating mineral abundance withdrill data and 3D property distributions obtained by inversionof magnetic and gravity data with geologic reference models.

More recently, Kowalczyk et al. (2010) use 3D inversion ofmagnetic and gravity data to obtain regional susceptibility anddensity contrast models that were used to divide the region intoclass distributions based on a scatterplot of the physical prop-erties.

Here, we utilize a similar approach to obtain a 3D lithologicmodel by combining susceptibility and density distributions

Figure 1: Geologic map of the Quadrilatero Ferrıfero, with redlines indicating where the Minas Series is present; modifiedfrom Dorr (1965).

obtained via inversion of magnetic and gravity gradient data.Inversion of the magnetic data was carried out based on themethodology of Li and Oldenburg (1996). The algorithm wasthen adapted for use with gravity gradiometry data by Li (2001).

FIELD SITE

The Quadrilatero Ferrıfero, or Iron Quadrangle, is an area ofsignificant mineral resources in the state of Minas Gerais, Brazil.Iron and gold are just a few mineral resources that have his-torically been produced from the Quadriltero Ferrfero region(Dorr, 1969). The Quadrilatero Ferrıfero covers approximately7,000 km2. The area has rugged terrain with canyons, plateaus,and valleys composing the landscape. The climate is semitrop-ical with an average annual rainfall of nearly 250 cm.

Dorr (1969) gives a detailed description of the stratigraphy ofthe Quadriltero Ferrfero in general and the structure of inter-est, the Gandarela Syncline. The iron bearing formation occurswithin the Minas Series, which is composed of metasedimen-tary rocks thought to be Precambrian in age. The Minas Se-ries is characterized by folding structures and is present todayin regional synclinal features such as the Gandarela Syncline.The structurally controlled occurrence of the Minas Series isshown in Figure 1. The eastern flank of the Gandarela synclinehas been overturned while the western flank remains upright.

Within the Minas Series, the Caue Itabirite hosts the majorityof the iron mineralization and is sandwiched between the over-

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Lithologic characterization

lying Gandarela Formation and underlying Batatal formation.The Caue Itabirite averages 300-500 m in thickness, but canrange from a few meters to over 1400 m. The ore bodies tendto be shallow and can range anywhere from 25 to 150 m belowthe surface (Dorr, 1965). The ore deposits follow the structureof the host formation and are generally tabular and dippingsoutheast with an approximate dip of 25◦. The contact be-tween the ore and host itabirite can be gradational or featheryin nature, but is usually abrupt. The high-grade ore typicallycontains an average of 66% Fe with the intermediate grade orescontaining an average of 63% Fe. The high-grade deposits areeasily differentiated from the dolomitic and quartz-rich coun-try rock by the stark density contrast. The host rocks containaverage densities close to the typical 2.67 g/cc, while target oredensities can range from 3 g/cc to 5 g/cc.

Gravity Gradient DataGravity gradient data were collected in August-September 2005.The 93 km2 survey was acquired with 100 m line spacing trend-ing northeast-southwest at roughly 32 degrees from the north.We use a subset of the collected data and it covers an approxi-mate area of 4 km by 5 km.

The survey was semi-draped with flight heights ranging from60 to 500 m above the ground surface. The acquired data un-derwent routine proprietary processing and corrections for thecentripetal force and self-gradient, acceleration compensation,and demodulation by the acquisition company. Before datadelivery, the lines were leveled and filtered to attenuate noise.

Figure 2: Observed gravity gradient data. The lower left plotshows topography of the survey area and location of subsetdata.

Each measured component contains information about the ironsource body and has the potential to contribute to character-ize the target ore body. Though the gravity gradient satisfiesLaplace’s equation and there are only five independent com-ponents, six components were measured here.

The extracted data are shown in Figure 2. The geologic featureof interest, the Gandarela Syncline, runs through the middle ofthe data parallel to the long axis of the survey area. The topog-raphy of the survey area is shown in the bottom left with thesubset data location indicated by a black box. The iron forma-tion is coincident with topographic highs in the area, makingthe density value used to remove the terrain effect an importantparameter. To obtain the displayed gradient anomaly, a densityvalue of 2.67 g/cc was used to acceptably remove the terraineffect.

Magnetic DataTotal field magnetic data was collected along with the gravitygradient data and therefore share the same survey parameters.Three tie lines were flown over the 93 km2 survey. Prior todelivery, the service company applied a parallax correction,height correction, removed the diurnal variation and the IGRF.The magnetic observations were upward and downward con-tinued to maintain a constant terrain clearance of 250 m. Toprepare the magnetic data for inversion, it was leveled andgridded at 20 m spacing. The final data used for inversion isshown in Figure 3.

Figure 3: Magnetic anomaly data over the same subset area asthe gravity gradient data after regional-residual separation.

Density contrast modelThe gravity gradient data was inverted utilizing the inversionalgorithm previously described. Six measured components (Txx,Txy, Txz, Tyy, Tyz, and Tzz) were simultaneously inverted to ob-tain a representative density contrast model of the target sub-surface geology (Martinez et al., 2010).

The mesh is composed of rectangular prisms or cells with con-stant density contrast within each cell. The discretization meshhas cell sizes of 25 m in the easting by 25 m in the northing by20 m in depth in the central region of the mesh, with paddingcells beyond the data area and at large depth. The rectangularmesh has dimensions of 156 cells in the easting by 241 cellsin the northing by 45 cells in depth giving a total of 1,691,820cells. The topographic surface is implemented within the in-version, leaving only 979,443 cells after removal of cells above

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Lithologic characterization

the topography.

The density contrast model was obtained by blind inversionof the 18,102 data points. Generic inversion parameters wereused with little a priori information incorporated into the inver-sion. A zero reference model was used with an initial modelof 2.0 g/cc. Lower and upper bounds on the density contrastwere set as 0.0 g/cc and 4.0 g/cc using the knowledge that apositive density contrast is expected from the dense ore bodyin the less dense host rock. The length scales in each directionare two times the cell size such that Lx = Ly = 50 m and Lz =40 m, requiring an equal amount of feature elongation in eachdirection. A volume rendered image of the density contrastdistribution is shown in Figure 4 with model cells below 1.0g/cc removed for clarity.

Figure 4: (a) Density contrast distribution with cells less than1.0 removed; units are g/cc. Distance is in meters. (b) Suscep-tibility distribution with cells less than 0.15 removed; units areSI. Distance is in meters.

Susceptibility modelPrior to obtaining the susceptibility model used for the litho-logic model shown here, removal of the regional field was anecessity. Removal of the regional field took place by imple-menting an inversion methodology. A subset of the magneticdata was inverted using a coarse mesh with cell sizes of 250 min the easting, 250 m in the northing, and 100 m in depth.

Using generalized cross validation, a susceptibility model wasobtained that explains the regional trends in the entire dataset.Since the geologic feature of interest lies near surface, thecoarse 250 m by 250 m by 100 m blocks are insufficient tocapture the variations with the desired detail. From the coarseregional model, we set all the cells between the topographicsurface and an elevation of 919 m within the area of interestto zero and forward model the magnetic anomaly in the areaof interest resulting from the remaining regional sources. Thedata calculated from this altered susceptibility model is nowconsidered the regional trend that we wish to remove from thedata in order to obtain the response of the near surface geology.

The regional trend is subtracted from the observed data andwe use this residual magnetic data within the area of interestshown in Figure 3 to obtain a shallow, near surface susceptibil-ity model. The mesh discretization used for the shallow modelis the same as that of the gravity gradient mesh detailed earlier.

The susceptibility contrast model was obtained by blind in-version of the 12,037 data points. A zero reference modelwas used with an initial model of 0.001 (SI). Lower and up-per bounds of 0.0 and 1.0 were placed on the model to keepthe recovered values within a reasonable range of susceptibili-ties. Coefficients that control the smoothness derivative in eachdirection were 0.0001 for the smallest model and 1.0 for the

easting, northing, and vertical directions. A volume renderedimage of the recovered susceptibility distribution is shown inFigure 4 with model cells below 0.15 (SI) removed for clarity.

LITHOLOGIC MAPPING

Now that we have obtained a density and susceptibility model,it is possible to examine the correlation that the two physi-cal properties have with each other. A cross-plot of the corre-sponding model cells susceptibility versus density is generatedin order to assign lithologic units based on these rock proper-ties. Lithology types are then assigned based on the suscep-tibility and density values according to generally known rockproperties. General density and susceptibility values for rocktypes were taken from Ahrens (1995).

A cross-plot for the susceptibility and density model describedabove is shown in Figure 5. The background density of 2.67g/cc was added back into the density contrast model to restorethe original density range. Note that reference is made to thedensity contrast model. The cross-plot is characterized by adense region of low suscesptibilty, low density values. In ad-dition, we see finger-like clusters extending outward from themain cloud of points.

We next assign colors to collections of points within the cross-plot to better visualize the relationships. With these color as-signments, we are then able to generate a 3D model to seethe lithologic representations. The geologic section given inFigure 6 provides information for evaluating our lithologic as-signments. A cross section through our constructed lithologicmodel, corresponding to the geologic section of Figure 6, isshown in Figure 7. For consistency, we have maintained thesame color scheme for the lithologic units in the cross plot andthe lithologic model. For additional comparison, the corre-sponding cross section from the separate density contrast andsusceptibility models are shown in Figures 9 and 10, respec-tively. From the susceptibility, density, and lithologic modelsit is observed that the high density iron ore within the CaueItabirite is identified by low susceptibility in general.

Figure 5: Left: Cross-plot of susceptibility model versus den-sity with lithologic units color coded. Right: Hematite distri-bution with density and susceptibility constraints.

A cursory look at the cross sections in Figures 7 - 9 may re-sult in the conclusion that density range assignments from thecross-plot are more relevant than susceptibility. This is be-cause the dominant features within the lithologic section (Fig-ure 6) are largely consistent with the density contrast model

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Lithologic characterization

(Figure 8). However, this conclusion is not accurate, and suchan assumption can lead to a gross overestimate of total ore vol-umes. To demonstrate, we first direct our attention to the full3D lithologic volume that the cross section of Figure 7 was ex-tracted from. A volume rendered image of this model is givenin Figure 11, and all of the lithologic units have been removedexcept for the one corresponding to hematite (maroon in boththe upper left part of the cross-plot, and in Figure 7). When weincorporate both density and susceptibility constraints on thelithologic model, as we have done here, the result is a distribu-tion consistent with known hematite from drill records.

For comparison, we next remove the susceptibility constraintson the hematite, and thus define the lithologic unit based solelyon the upper and lower bounds from density. This alternatescenario corresponds to the cross-plot in Figure 10, where ma-roon denotes hematite with no susceptibility constraints. Thevolume rendered image of the resulting 3D lithologic model isshown in Figure 10, as before, with all units removed exceptthe one corresponding to hematite (maroon). The structure ofthe overall lithologic model (Figure 10) is similar to the recov-ered density contrast volume (Figure 4). However, knowledgeof the site’s geology indicates that the total hematite volumesmay be significantly overestimated in this instance. There-fore, both recovered density and susceptibility constraints arerequired to generate a 3D lithologic model of the site.

Figure 6: Geologic cross section generated from bore hole datashowing itabirite in blue and hematite in pink.

Figure 7: Cross section through lithologic model correspond-ing to geologic section of Figure 8 and color scheme identifiedin cross plot

Figure 8: Cross section through density contrast model corre-sponding to geologic cross section of Figure 6; units are g/cc.

Figure 9: Cross section through susceptibility model corre-sponding to geologic cross section of Figure 6 plotted on alogarithmic scale; units are SI.

Figure 10: Left: Cross-plot of susceptibility model versusdensity with no constraints on hematite susceptibility. Right:Overestimate of hematite distribution when no susceptibilityconstraints are applied.

CONCLUSIONS

Susceptibility and density models have been generated fromairborne magnetic and gravity gradient data in the QuadrilteroFerrfero. With the computational power of today’s desktopcomputer, it is possible to obtain models of local subsurfacedetail for interpretation purposes. As a means of further utiliz-ing inversion for interpretation on a local rather than regionalscale, it is possible to combine physical property models. Thetwo physical property distributions can be grouped into geo-logically representative units. These lithologic units can thenbe organized in a model similar to the susceptibility and den-sity distributions in order to help characterize subsurface struc-ture.

Utilizing inverse models has the potential to be a powerful in-terpretation tool, particularly combined with other general ge-ologic information. Preliminary models such as the suscepti-bility distribution, density distribution, and lithologic charac-ter may prove useful in planning further exploration in bothgreenfield and brownfield type areas.

ACKNOWLEDGMENTS

We thank the sponsors of the Gravity and Magnetics ResearchConsortium (GMRC) for supporting this work: Anadarko, BP,BGP, Chevron, ConocoPhillips, Fugro, Marathon Oil, Petro-bras, and Vale.

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