Journal of Applied Geophysics 69 (2009) 96–102

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Journal of Applied Geophysics

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Virtual Pole from Magnetic Anomaly (VPMA): A procedure to estimate the age of arock from its magnetic anomaly only

Renato Cordani a,⁎, Wladimir Shukowsky b

a Reconsult Geofísica, Brazilb IAG-USP, Brazil

⁎ Corresponding author.E-mail addresses: rcordani@reconsult.com.br (R. Cor

(W. Shukowsky).

0926-9851/$ – see front matter © 2009 Elsevier B.V. Aldoi:10.1016/j.jappgeo.2009.07.001

a b s t r a c t

a r t i c l e i n f o

Article history:Received 14 February 2008Accepted 6 July 2009

Keywords:Magnetic anomaliesPaleomagnetic virtual polesSouth American tectonic plateMesozoic intrusions

Virtual Pole from Magnetic Anomaly (VPMA) is a new multi-disciplinary methodology that estimates the age of asource rock from its magnetic anomaly, taken directly from available aeromagnetic data. The idea is to use thoseanomalies in which a strong remanent magnetic component is likely to occur. Once the total magnetization of theanomaly is computed through any of the currently available methods, the line that connects all virtualpaleogeographic poles is relatedwith the position, on a paleogeographic projection, of the appropriate age fragmentof the APWP curve. We applied this procedure to five (5) well-known magnetic anomalies of the South Americanplate in SE Brazil, all of them associated to alkaline complexes of Mesozoic age. The apparent ages obtained fromVPMAon three of the anomalies where the radiometric age of the source rock is known – Tapira, Araxá and Juquiá –were inside the error interval of the published ages. The VPMA apparent ages of the other two, where the age of thesource rock is not known (Registro andPariqueraçumagnetic anomalies)were geologically coherent.Weexpect thatthe application of the VPMA methodology as a reconnaissance geochronological tool may contribute to geologicalknowledge over continental areas, especially when the source rocks of the magnetic anomalies are unknown orburied below superficial sediments.

© 2009 Elsevier B.V. All rights reserved.

1. Introduction

The determination of magnetic paleopoles from seamount magneticanomalies constitutes the major data source for the Pacific ApparentPolar Wander Path (APWP); Emilia & Massey (1974); Hilderbrand &Parker (1987); Gee et al. (1989); Sager & Koppers (2000); Lee et al.(2003); Kubota & Uchiyama (2005). In these cases the bathymetryprovides an immediate constrain for the geometry of the magneticsources, i.e., the submarine volcanic cones.

This article was motivated by the great success in using seamountmagnetic anomalies for APWP mapping. However, the main difficulty isthat in this case we are dealing with continental magnetic anomalieswhere size and geometry of the sources are usually unknown or verydifficult to characterize.

One of the traditional applications of paleomagnetism consists inisolating the primary natural remanent magnetization (NRM) of a givenrock, and then determining the correspondent paleogeographic pole atthe time of the rock emplacement. This result is then compared tothe APWP. As it will be described later, the Virtual Pole from Magnetic

dani), wladimir@iag.usp.br

l rights reserved.

Anomaly (VPMA) technique proposed here is based on the assumptionthat the remanent component

⇀Jr determined from the anomaly, would

be approximately correspondent to the primary NRM of the sourcerock.

Therefore, this methodology produces an age estimation of the rockswithout need of sampling them. Here we apply this methodology to fiveMesozoic alkaline intrusions in Southeast Brazil, and compare the VPMAage results to theknownradiometric ages obtained fromgeochronologicalstudies.

All themagnetic data used in this work came from CPRM (BrazilianGeological Survey) regional aeromagnetic database. Line spacingvaried from 1000 to 2000m. Application of the VPMAmethodology tohigh-resolution magnetic datasets should yield better results.

2. VPMA methodology description

Themain concept of VPMAmethodology is to isolate the remanentcomponent

⇀Jr of the magnetic anomaly and use it in paleomagnetic

studies. Therefore, first we calculate the total magnetization of themagnetic source using one of the existing methods, and then weremove the induced component using the following vectorial equa-tion.

J→

= J→i + J

→r ð1Þ

Fig. 1. Registro magnetic anomaly. Magnetic data line spacing=1000 m. Flight altitude=150 m. Line direction: N–S.

Table 1Remanent magnetic directions of Registro-SP-Brazil magnetic anomaly, calculatedusing Q Koenigsberger ratio values from minimum to maximum.

Q⇀Jr

Inclination Declination

Q minimum 0.3 −70.80 48.401 −48.83 −3.112 −43.55 −7.063 −41.74 −8.2410 −39.20 −9.7820 −38.65 −10.09

Fig. 2. Paleogeographic Pole coordinates of Registro-SP-Brazil magnetic anomaly, c

97R. Cordani, W. Shukowsky / Journal of Applied Geophysics 69 (2009) 96–102

where

⇀J is total magnetization.⇀Ji is induced magnetization component.⇀Jr is remanent magnetization component.

There are several methods available for the calculation of the totalmagnetic vector

⇀J from a total field magnetic anomaly. In this case we

used Fedi et al. (1994) Maxi-min method, but any other method canbe used too (e.g., Zietz and Andreasen (1967), Schnetzler and Taylor(1984), Medeiros and Silva (1995)). Fedi et al. (1994) Maxi-minmethod is based on the successive application of the reduction-to-the-pole operator on the measured magnetic data for different total

alculated using Q (Koenigsberger ratio) values from minimum to maximum.

Table 2Paleogeographic pole coordinates of Registro-SP-Brazil magnetic anomaly, calculatedusing Q (Koenigsberger ratio) values from minimum to maximum.

Q Paleogeographic poles

Latitude Longitude

Q minimum 0.3 −43.3 −83.71 −84.1 −20.52 −83.5 333 −82.5 44.410 −80.7 55.120 −80.3 56.8

98 R. Cordani, W. Shukowsky / Journal of Applied Geophysics 69 (2009) 96–102

magnetization parameters (inclination I, declination D). The correct(I, D) pair is the one that maximizes the minimum of the magneticanomaly. Once

⇀J is determined, we subtract the induced component

from Eq. (1) and solve for⇀Jr.

The direction of⇀Ji is known, for it is parallel to the known IGRF

direction. However, since the Koenigsberger ratio of⇀Jr to

⇀Ji is unknown,

so is⇀Jimagnitude. In spite of this, we can use all possible Q values from

the minimum (i.e., the closest to zero still honouring Eq. (1)), to themaximum (i.e., the Q value that makes

⇀Jr converge to

⇀J). The key of

VPMA is to solve Eq. (1) and find the different values of⇀Jr in function of

Q. Then calculate the paleogeographic poles corresponding to all valuesof⇀Jr, and plot the locations of the paleogeographic poles in function ofQ.

The resulting plot on a polar stereographic projection diagram is a line-segment related to the studied anomaly.

The final stage is the determination of the crossing point betweenthe VPMA line-segment and the APWP. The crossing point on thepaleogeographic poles diagram is the estimate for the age of the rock.

Summary of the steps and application example (Registro magneticanomaly):

Step 1 — acquire magnetic data, remove IGRF and other regionalsources, and determine the total magnetization (

⇀J) of the anomaly.

Fig. 1 shows the example of magnetic anomaly of Registro.

Fig. 3. Apparent Polar Wander Path for South American plate (Ernesto, 2007) and Paleogeograpmaximum Q values.

The IGRF (Inclination, Declination) of the Registro anomaly (i.e.,⇀Ji) is

(I=−26.92, D=−15.83). Total magnetization⇀J calculated from

Max-min method is (I=−38.1°; D=−10.4°).Step 2 — solve the vectorial equation J

→= J

→i + J

→r and find

values of⇀Jr in function of Q. Table 1 shows the results obtained for

the Registro magnetic anomaly.Step 3 — calculate the corresponding paleopole for each

⇀Jr found,

generating a table of paleopoles in function of Q and plot them inpaleopoles diagram (VPMA line segment). Table 1 and Fig. 2 showthe results on the example of Registro (Table 2).Step 4 — determine the crossing point between VPMA line segmentand the APWP for the anomaly tectonic plate. The next figure showsthe Registro – SP – Brazil anomaly VPMA line segment example overthe APWP of Ernesto (2007).Step 5 — interpret the result and determine the age of the sourcerock.

The VPMA line-segment intercepts the Ernesto (2007) APWP intwo possible positions (Fig. 3). Each intercept gives an associated age-interval for the source-rocks. Q=0.70 yields 25–80 My; Q=0.88yields 80–100 My.

The segment of the APWP for the time beyond 130 My is not re-presented in the above diagram. For this anomaly, the source rock isprobably buried, and was not determined by geological mapping; there-fore VPMA cannot provide a definite answer to the age of the rocks. Wealsoneed to consider the hypothesis that the source rockmaybe still olderthan the mentioned two options. On the other hand, considering theexistence of the known Cretaceous intrusions in the same region(Jacupiranga, Juquiá, Pariqueraçu) that produced similar magneticanomalies, it is reasonable to interpret that the age between 80 and 100My (using Q=0.88) is the probable age of the possible hidden source ofthe Registro anomaly.

hic Pole coordinates of Registro-SP-Brazil magnetic anomaly, calculated using minimum to

Fig. 4. Anomaly location.

Fig. 5. Left: Araxá magnetic anomaly. Right: Tapira magnetic anomaly. Magnetic data line spacing=2000 m. Flight altitude=350 m. Line direction: E–W.

99R. Cordani, W. Shukowsky / Journal of Applied Geophysics 69 (2009) 96–102

Fig. 6. Left: Juquiá magnetic anomaly. Right: Pariqueraçu magnetic anomaly. Magnetic data line spacing=1000 m. Flight altitude=150 m. Line direction: N–S.

100 R. Cordani, W. Shukowsky / Journal of Applied Geophysics 69 (2009) 96–102

3. Results and discussion

We applied the developed VPMAmethodology in five (5)magneticanomalies in Southeast Brazil (Figs. 4, 5, 6, Table 3).

We determined the VPMA line-segments for each anomaly andplotted them in the paleogeographic poles diagram, together with theSouth American APWP (Ernesto, 2007) for the time since theCretaceous. We did not use APWP for earlier periods for two mainreasons: (i) we have good geological control and we know the age ofthree; and (ii) the available APWPs for those ages are in conflictbetween them.

Fig. 7 shows the results. The green circle corresponds to theamplitude of the uncertainty of the paleomagnetic determinations, atthe 95% confidence level:

From Fig. 7, we selected the crossing point of each anomaly (or itsclosest point to the APWP), and finally estimate the age of the rocksources.

Considering the apparent ages obtained by the VPMA method(Table 4), the following conclusions can be made:

• Juquiá: using Q=3, the VPMA apparent age of 130 My is similar tothe measured radiometric age according to Amaral et al. (1967).

• Registro: using Q=0.88, the preferred VPMA apparent age isbracketed between 80 and 110 My. Source rock is unknown.

• Pariqueraçu: using Q=10, the VPMA apparent age was of 125 My.The alkaline rocks of this intrusion have not been dated radio-metrically; but Morbidelli et al. (2000) suggested that based ongeological and petrological comparisons with Jacupiranga andJuquiá, as well as structural context, the intrusion must exhibit anage close to 130 My.

Table 3Site location and induced field direction (IGRF at the survey time) for the anomalies.

Site IGRF

Anomaly Latitude Longitude Inclination Declination

Juquiá −24.41 −47.68 −26.77 −15.88Pariqueraçu −24.73 −47.82 −27.09 −15.71Registro −24.54 −47.71 −26.92 −15.83Araxá −19.66 −46.94 −19.60 −16.50Tapira −19.89 −46.83 −19.40 −16.20

• Araxá: usingQ=0.35, the VPMA apparent age of 70Ma is concordantwith the radiometric dates,whose interval cover80±10Myaccordingto Gomes et al. (1990).

• Tapira: using Q=2, the VPMA apparent age 70 Ma, is close to theradiometric value of 79±8 My according to Hasui and Cordani(1968).

4. Error estimation and method limitations

The main uncertainties of the VPMA methodology are: (i) the totalmagnetic

⇀J calculation method; (ii) the assumption that the entire

anomalycomes froma single rock; (iii) the assumption that theobtained⇀Jr is equivalent to the primary NRM, i.e., there is no presence of relevantsecondary NRM; and (iv) the accuracy of the APWP.

It is possible to at least estimate the error of the total magnetiza-tion direction calculation method using a numerical simulation. Weapplied the Max-min method in anomalies due to fixed direction andvariable directionmagnetization in three different synthetic geometryblocks. The Max-min algorithm estimates the direction of the totalmagnetic moment of the causative body. In the case of fixed directionmagnetization this coincides with the actual direction of magnetiza-tion. For the variable direction magnetization the Max-min estimaterepresents the direction of the average magnetization (Fig. 8).

We ran a total of 1200 simulations using both fixed magnetization(each cubic blockwith samemagnetization) and variablemagnetization(different magnetization for each cubic block). For each simulation wecompared the real magnetization of the geometry block and the totalmagnetization recovered using the Max-min algorithm. Then we plotthe difference between them (Fig. 9).

The numerical simulation results gave an error of less than 5.00° onthe magnetization direction estimation, using the Max-min method(with 95% of confidence interval). Other uncertainties are difficult toestimate numerically, but the accuracy of APWP is obviously a keyfactor.

5. Conclusions

This paper presents the description of VPMA methodology, whichis capable to estimate the age of a rock formation that causes amagnetic anomaly.

We applied the VPMAmethodology to five (5)magnetic anomaliesin Southeastern Brazil. Four of the anomalies (Juquiá, Pariqueraçu,

Fig. 7. South American APWP and VPMA line segments of five magnetic anomalies in Southeastern Brazil.

Table 4Final virtual magnetic pole coordinates estimated for Brazilian anomalies, corresponding to chosen Q value.

Anomaly Latitude Longitude Q Apparent age(from VPMA method)

Radiometric age

Juquiá −86.06 87.86 3.00 130 My 130 My — Amaral et al. (1967)Pariqueraçu −86.79 79.61 10.00 130 My UnknownRegistro −83.20 −34.90 0.88 80 to 110 My UnknownAraxá −73.02 −6.58 0.35 70 My 80±10 My — Gomes et al. (1990)Tapira −78.30 −3.10 2.00 75 My 79±8 My — Hasui & Cordani (1968)

Apparent age of intrusions according to VPMA and radiometric age for previously dated rocks.

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Araxá and Tapira) have the correspondent source rock identified at thesurface. They are Mesozoic alkaline intrusions, whose radiometricages are known in three of them. The fifth anomaly (Registro) does nothave a correspondent geological feature at the surface, but the similarshape of its anomaly indicates that it is due to a similar alkalineintrusive body. For the three cases inwhich the radiometric ages of thesource rocks are known, the VPMA method recovered their apparentages inside the margin of error of both the APWP and radiometricages. We estimated the age for the source of the two other anomaliesas Cretaceous. These do not have an associated radiometric age, but

Fig. 8. Models for numeric simulation, each one containing nine cubic blocks with 1

the anomalies were considered because of the similar shape as theother three magnetic anomalies.

Since the VPMA results are constrained by the tectonic platemovement and the associated APWP, the ideal conditions for itsapplication are: i) noticeable movement of the tectonic plate relativeto the paleomagnetic pole; ii) accurate knowledge of the APWP.

In the future, we understand that the VPMA methodology couldcontribute to future geoscientific knowledge in several ways:

(a) anomalies whose source is unknown could now be studied;

00 m side each. We considered three different spatial orientations (I; II and III).

Fig. 9. Error of the magnetization direction estimation. The blue circle marks the 95% confidence interval. Each dataset comprises 600 simulations. Left: fixed magnetization; Right:variable magnetization.

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(b) the generation of new virtual poles could contribute andimprove the knowledge of the APWP;

(c) quick estimation of the age of a source rock for geoscientistswithout access to geochronological or paleomagnetic labs;

(d) previous analysis of the age of a rock unit, to better find futureareas for paleomagnetic targets;

(e) helping on defining magnetic parameters for magneticinversion.

Acknowledgments

This work was the result of a Ph.D programme at the Institute ofAstronomy and Geophysics of the University of São Paulo — IAG-USP.We would like to thank the entire paleomagnetic group of IAG forsuggestions and corrections. Special thanks are extended to R.Trindade, C. Mendonça, D. Brandt and U. Cordani for discussions andtext reviews.

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