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Virtual Pole from Magnetic Anomaly (VPMA): A procedure to estimate the age of a rock from its magnetic anomaly only
Journal of Applied Geophysics 69 (2009) 96–102
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Journal of Applied Geophysics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j a p p g e o
Virtual Pole from Magnetic Anomaly (VPMA): A procedure to estimate the age of a rock from its magnetic anomaly only Renato Cordani a,⁎, Wladimir Shukowsky b a b
Reconsult Geofísica, Brazil IAG-USP, Brazil
a r t i c l e
i n f o
Article history: Received 14 February 2008 Accepted 6 July 2009 Keywords: Magnetic anomalies Paleomagnetic virtual poles South American tectonic plate Mesozoic intrusions
a b s t r a c t Virtual Pole from Magnetic Anomaly (VPMA) is a new multi-disciplinary methodology that estimates the age of a source rock from its magnetic anomaly, taken directly from available aeromagnetic data. The idea is to use those anomalies in which a strong remanent magnetic component is likely to occur. Once the total magnetization of the anomaly is computed through any of the currently available methods, the line that connects all virtual paleogeographic poles is related with the position, on a paleogeographic projection, of the appropriate age fragment of the APWP curve. We applied this procedure to five (5) well-known magnetic anomalies of the South American plate in SE Brazil, all of them associated to alkaline complexes of Mesozoic age. The apparent ages obtained from VPMA on 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 the source rock is not known (Registro and Pariqueraçu magnetic anomalies) were geologically coherent. We expect that the application of the VPMA methodology as a reconnaissance geochronological tool may contribute to geological knowledge over continental areas, especially when the source rocks of the magnetic anomalies are unknown or buried below superficial sediments. © 2009 Elsevier B.V. All rights reserved.
1. Introduction The determination of magnetic paleopoles from seamount magnetic anomalies constitutes the major data source for the Pacific Apparent Polar 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 bathymetry provides an immediate constrain for the geometry of the magnetic sources, i.e., the submarine volcanic cones. This article was motivated by the great success in using seamount magnetic anomalies for APWP mapping. However, the main difficulty is that in this case we are dealing with continental magnetic anomalies where size and geometry of the sources are usually unknown or very difficult to characterize. One of the traditional applications of paleomagnetism consists in isolating the primary natural remanent magnetization (NRM) of a given rock, and then determining the correspondent paleogeographic pole at the time of the rock emplacement. This result is then compared to the APWP. As it will be described later, the Virtual Pole from Magnetic
⁎ Corresponding author. E-mail addresses: [email protected] (R. Cordani), [email protected] (W. Shukowsky). 0926-9851/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jappgeo.2009.07.001
Anomaly (VPMA) technique proposed here is based on the assumption ⇀ that the remanent component Jr determined from the anomaly, would be approximately correspondent to the primary NRM of the source rock. Therefore, this methodology produces an age estimation of the rocks without need of sampling them. Here we apply this methodology to five Mesozoic alkaline intrusions in Southeast Brazil, and compare the VPMA age results to the known radiometric ages obtained from geochronological studies. All the magnetic data used in this work came from CPRM (Brazilian Geological Survey) regional aeromagnetic database. Line spacing varied from 1000 to 2000 m. Application of the VPMA methodology to high-resolution magnetic datasets should yield better results. 2. VPMA methodology description The main concept of VPMA methodology is to isolate the remanent ⇀ component Jr of the magnetic anomaly and use it in paleomagnetic studies. Therefore, first we calculate the total magnetization of the magnetic source using one of the existing methods, and then we remove the induced component using the following vectorial equation. → → → J = Ji+ Jr
ð1Þ
R. Cordani, W. Shukowsky / Journal of Applied Geophysics 69 (2009) 96–102
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Fig. 1. Registro magnetic anomaly. Magnetic data line spacing = 1000 m. Flight altitude = 150 m. Line direction: N–S.
Table 1 Remanent magnetic directions of Registro-SP-Brazil magnetic anomaly, calculated using Q Koenigsberger ratio values from minimum to maximum. ⇀ Jr
Q Q minimum 0.3 1 2 3 10 20
Inclination
Declination
− 70.80 − 48.83 − 43.55 − 41.74 − 39.20 − 38.65
48.40 − 3.11 − 7.06 − 8.24 − 9.78 − 10.09
where ⇀ J ⇀ Ji ⇀ Jr
is total magnetization. is induced magnetization component. is remanent magnetization component.
There are several methods available for the calculation of the total ⇀ magnetic vector J from a total field magnetic anomaly. In this case we used Fedi et al. (1994) Maxi-min method, but any other method can be used too (e.g., Zietz and Andreasen (1967), Schnetzler and Taylor (1984), Medeiros and Silva (1995)). Fedi et al. (1994) Maxi-min method is based on the successive application of the reduction-to-thepole operator on the measured magnetic data for different total
Fig. 2. Paleogeographic Pole coordinates of Registro-SP-Brazil magnetic anomaly, calculated using Q (Koenigsberger ratio) values from minimum to maximum.
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Table 2 Paleogeographic pole coordinates of Registro-SP-Brazil magnetic anomaly, calculated using Q (Koenigsberger ratio) values from minimum to maximum. Q
Paleogeographic poles
Q minimum 0.3 1 2 3 10 20
Latitude
Longitude
− 43.3 − 84.1 − 83.5 − 82.5 − 80.7 − 80.3
− 83.7 − 20.5 33 44.4 55.1 56.8
magnetization parameters (inclination I, declination D). The correct (I, D) pair is the one that maximizes the minimum of the magnetic ⇀ anomaly. 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 Ji magnitude. 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 the ⇀ ⇀ maximum (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 values ⇀ of Jr, and plot the locations of the paleogeographic poles in function of Q. The resulting plot on a polar stereographic projection diagram is a linesegment related to the studied anomaly. The final stage is the determination of the crossing point between the VPMA line-segment and the APWP. The crossing point on the paleogeographic poles diagram is the estimate for the age of the rock. Summary of the steps and application example (Registro magnetic anomaly): Step 1 — acquire magnetic data, remove IGRF and other regional ⇀ sources, and determine the total magnetization ( J) of the anomaly. Fig. 1 shows the example of magnetic anomaly of Registro.
⇀ 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 in paleopoles diagram (VPMA line segment). Table 1 and Fig. 2 show the results on the example of Registro (Table 2). Step 4 — determine the crossing point between VPMA line segment and the APWP for the anomaly tectonic plate. The next figure shows the Registro – SP – Brazil anomaly VPMA line segment example over the APWP of Ernesto (2007). Step 5 — interpret the result and determine the age of the source rock.
The VPMA line-segment intercepts the Ernesto (2007) APWP in two possible positions (Fig. 3). Each intercept gives an associated ageinterval for the source-rocks. Q = 0.70 yields 25–80 My; Q = 0.88 yields 80–100 My. The segment of the APWP for the time beyond 130 My is not represented in the above diagram. For this anomaly, the source rock is probably buried, and was not determined by geological mapping; therefore VPMA cannot provide a definite answer to the age of the rocks. We also need to consider the hypothesis that the source rock may be still older than the mentioned two options. On the other hand, considering the existence of the known Cretaceous intrusions in the same region (Jacupiranga, Juquiá, Pariqueraçu) that produced similar magnetic anomalies, it is reasonable to interpret that the age between 80 and 100 My (using Q=0.88) is the probable age of the possible hidden source of the Registro anomaly.
Fig. 3. Apparent Polar Wander Path for South American plate (Ernesto, 2007) and Paleogeographic Pole coordinates of Registro-SP-Brazil magnetic anomaly, calculated using minimum to maximum Q values.
R. Cordani, W. Shukowsky / Journal of Applied Geophysics 69 (2009) 96–102
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.
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Fig. 6. Left: Juquiá magnetic anomaly. Right: Pariqueraçu magnetic anomaly. Magnetic data line spacing = 1000 m. Flight altitude = 150 m. Line direction: N–S.
3. Results and discussion We applied the developed VPMA methodology in five (5) magnetic anomalies in Southeast Brazil (Figs. 4, 5, 6, Table 3). We determined the VPMA line-segments for each anomaly and plotted them in the paleogeographic poles diagram, together with the South American APWP (Ernesto, 2007) for the time since the Cretaceous. We did not use APWP for earlier periods for two main reasons: (i) we have good geological control and we know the age of three; and (ii) the available APWPs for those ages are in conflict between them. Fig. 7 shows the results. The green circle corresponds to the amplitude of the uncertainty of the paleomagnetic determinations, at the 95% confidence level: From Fig. 7, we selected the crossing point of each anomaly (or its closest point to the APWP), and finally estimate the age of the rock sources. 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 to the measured radiometric age according to Amaral et al. (1967). • Registro: using Q = 0.88, the preferred VPMA apparent age is bracketed 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 radiometrically; but Morbidelli et al. (2000) suggested that based on geological and petrological comparisons with Jacupiranga and Juquiá, as well as structural context, the intrusion must exhibit an age close to 130 My.
Table 3 Site location and induced field direction (IGRF at the survey time) for the anomalies. Site
• Araxá: using Q = 0.35, the VPMA apparent age of 70 Ma is concordant with the radiometric dates, whose interval cover 80 ± 10 My according to Gomes et al. (1990). • Tapira: using Q = 2, the VPMA apparent age 70 Ma, is close to the radiometric 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 total ⇀ magnetic J calculation method; (ii) the assumption that the entire anomaly comes from a single rock; (iii) the assumption that the obtained ⇀ Jr is equivalent to the primary NRM, i.e., there is no presence of relevant secondary NRM; and (iv) the accuracy of the APWP. It is possible to at least estimate the error of the total magnetization direction calculation method using a numerical simulation. We applied the Max-min method in anomalies due to fixed direction and variable direction magnetization in three different synthetic geometry blocks. The Max-min algorithm estimates the direction of the total magnetic moment of the causative body. In the case of fixed direction magnetization this coincides with the actual direction of magnetization. For the variable direction magnetization the Max-min estimate represents the direction of the average magnetization (Fig. 8). We ran a total of 1200 simulations using both fixed magnetization (each cubic block with same magnetization) and variable magnetization (different magnetization for each cubic block). For each simulation we compared the real magnetization of the geometry block and the total magnetization recovered using the Max-min algorithm. Then we plot the difference between them (Fig. 9). The numerical simulation results gave an error of less than 5.00° on the magnetization direction estimation, using the Max-min method (with 95% of confidence interval). Other uncertainties are difficult to estimate numerically, but the accuracy of APWP is obviously a key factor. 5. Conclusions
IGRF
Anomaly
Latitude
Longitude
Inclination
Declination
Juquiá Pariqueraçu Registro Araxá Tapira
− 24.41 − 24.73 − 24.54 − 19.66 − 19.89
− 47.68 − 47.82 − 47.71 − 46.94 − 46.83
− 26.77 − 27.09 − 26.92 − 19.60 − 19.40
− 15.88 − 15.71 − 15.83 − 16.50 − 16.20
This paper presents the description of VPMA methodology, which is capable to estimate the age of a rock formation that causes a magnetic anomaly. We applied the VPMA methodology to five (5) magnetic anomalies in Southeastern Brazil. Four of the anomalies (Juquiá, Pariqueraçu,
R. Cordani, W. Shukowsky / Journal of Applied Geophysics 69 (2009) 96–102
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Fig. 7. South American APWP and VPMA line segments of five magnetic anomalies in Southeastern Brazil.
Table 4 Final 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 Pariqueraçu Registro Araxá Tapira
− 86.06 − 86.79 − 83.20 − 73.02 − 78.30
87.86 79.61 − 34.90 − 6.58 − 3.10
3.00 10.00 0.88 0.35 2.00
130 My 130 My 80 to 110 My 70 My 75 My
130 My — Amaral et al. (1967) Unknown Unknown 80 ± 10 My — Gomes et al. (1990) 79 ± 8 My — Hasui & Cordani (1968)
Apparent age of intrusions according to VPMA and radiometric age for previously dated rocks.
Araxá and Tapira) have the correspondent source rock identified at the surface. They are Mesozoic alkaline intrusions, whose radiometric ages are known in three of them. The fifth anomaly (Registro) does not have a correspondent geological feature at the surface, but the similar shape of its anomaly indicates that it is due to a similar alkaline intrusive body. For the three cases in which the radiometric ages of the source rocks are known, the VPMA method recovered their apparent ages inside the margin of error of both the APWP and radiometric ages. We estimated the age for the source of the two other anomalies as Cretaceous. These do not have an associated radiometric age, but
the anomalies were considered because of the similar shape as the other three magnetic anomalies. Since the VPMA results are constrained by the tectonic plate movement and the associated APWP, the ideal conditions for its application are: i) noticeable movement of the tectonic plate relative to the paleomagnetic pole; ii) accurate knowledge of the APWP. In the future, we understand that the VPMA methodology could contribute to future geoscientific knowledge in several ways: (a) anomalies whose source is unknown could now be studied;
Fig. 8. Models for numeric simulation, each one containing nine cubic blocks with 100 m side each. We considered three different spatial orientations (I; II and III).
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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.
(b) the generation of new virtual poles could contribute and improve the knowledge of the APWP; (c) quick estimation of the age of a source rock for geoscientists without access to geochronological or paleomagnetic labs; (d) previous analysis of the age of a rock unit, to better find future areas for paleomagnetic targets; (e) helping on defining magnetic parameters for magnetic inversion. Acknowledgments This work was the result of a Ph.D programme at the Institute of Astronomy and Geophysics of the University of São Paulo — IAG-USP. We would like to thank the entire paleomagnetic group of IAG for suggestions and corrections. Special thanks are extended to R. Trindade, C. Mendonça, D. Brandt and U. Cordani for discussions and text reviews. References Amaral, G., Bushee, J., Cordani, U.G., Kawashita, K., 1967. Potassium-argon ages of alkaline rocks from southern Brazil. Geochimica Cosmochimica Acta 31, 117–142. Emilia, D.A., Massey, R.L., 1974. Magnetization estimation for nonuniformly magnetized seamounts. Geophysics 39, 223–231.
Ernesto, M., 2007. Drift of South America platform since Early Cretaceous: reviewing the apparent polar wander path. Geociências (São Paulo) 25, 83–90, 2007. Fedi, M., Florio, G., Rapolla, A., 1994. A method to estimate the total magnetization direction from a distortion analysis of magnetic-anomalies. Geophys. Prospect. 42 (3), 261–274. Gee, J., Staudigel, H., Tauxe, L., 1989. Contribution of induced magnetization to magnetization of seamounts. Nature 342, 170–173. Gomes, C.B., Ruberti, E., Morbidelli, L., 1990. Carbonatite complexes from Brazil: a review. J. South Amer. Earth Sci. 3, 51–63. Hasui, Y., Cordani, U.G., 1968. Idade Potássio-Argônio de rochas eruptivas Mesozóicas do Oeste Mineiro e sul de Goiás. In: Congresso Brasileiro de Geologia, 22, Belo Horizonte, 1968. Anais, Belo Horizonte, SBG, p. 139–143. Hilderbrand, J.A., Parker, R.L., 1987. Paleomagnetism of cretaceous Pacific seamounts revisited. JGR, 92, 12695–12712. Kubota, R., Uchiyama, A., 2005. Three-dimensional magnetization vector inversion of a seamount. Earth Planets Space 57, 691–699. Lee, T.G., Lee, S.M., Moon, J.W., Lee, K., 2003. Paleomagnetic investigation of seamounts in the vicinity of Ogasawara Fracture Zone northwest of the Marshall Islands, western Pacific. Earth Planets Space 55, 355–360. Medeiros, W.E., Silva, J.B., 1995. Simultaneous estimation of total magnetization direction and 3-D spacial orientation [J]. Geophysics 60, 1365–1377. Morbidelli, L., Gomes, C.B., Brotsu, P., D'Acquarica, S., Garbarino, C., Ruberti, E., Traversa, G., 2000. The Pariquera-Açu K-alkaline complex and Southern Brazil lithospheric mantle source characteristics. J. Asian Earth Sci. 18, 129–150 2000. Sager, W.W., Koppers, A.A.P., 2000. Late Cretaceous polar wander of the Pacific Plate: evidence of a rapid true polar wander event. Science 287, 455–459. Schnetzler, C.C., Taylor, P.T., 1984. Evaluation of an observational method for estimation of remanent magnetization. Geophysics 49, 282–290. Zietz, I., Andreasen, G.E., 1967. Remanent. Magnetization and aeromagnetic interpretation. Mining. Geophysics 2, 569–590.
Contents lists available at ScienceDirect
Journal of Applied Geophysics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j a p p g e o
Virtual Pole from Magnetic Anomaly (VPMA): A procedure to estimate the age of a rock from its magnetic anomaly only Renato Cordani a,⁎, Wladimir Shukowsky b a b
Reconsult Geofísica, Brazil IAG-USP, Brazil
a r t i c l e
i n f o
Article history: Received 14 February 2008 Accepted 6 July 2009 Keywords: Magnetic anomalies Paleomagnetic virtual poles South American tectonic plate Mesozoic intrusions
a b s t r a c t Virtual Pole from Magnetic Anomaly (VPMA) is a new multi-disciplinary methodology that estimates the age of a source rock from its magnetic anomaly, taken directly from available aeromagnetic data. The idea is to use those anomalies in which a strong remanent magnetic component is likely to occur. Once the total magnetization of the anomaly is computed through any of the currently available methods, the line that connects all virtual paleogeographic poles is related with the position, on a paleogeographic projection, of the appropriate age fragment of the APWP curve. We applied this procedure to five (5) well-known magnetic anomalies of the South American plate in SE Brazil, all of them associated to alkaline complexes of Mesozoic age. The apparent ages obtained from VPMA on 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 the source rock is not known (Registro and Pariqueraçu magnetic anomalies) were geologically coherent. We expect that the application of the VPMA methodology as a reconnaissance geochronological tool may contribute to geological knowledge over continental areas, especially when the source rocks of the magnetic anomalies are unknown or buried below superficial sediments. © 2009 Elsevier B.V. All rights reserved.
1. Introduction The determination of magnetic paleopoles from seamount magnetic anomalies constitutes the major data source for the Pacific Apparent Polar 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 bathymetry provides an immediate constrain for the geometry of the magnetic sources, i.e., the submarine volcanic cones. This article was motivated by the great success in using seamount magnetic anomalies for APWP mapping. However, the main difficulty is that in this case we are dealing with continental magnetic anomalies where size and geometry of the sources are usually unknown or very difficult to characterize. One of the traditional applications of paleomagnetism consists in isolating the primary natural remanent magnetization (NRM) of a given rock, and then determining the correspondent paleogeographic pole at the time of the rock emplacement. This result is then compared to the APWP. As it will be described later, the Virtual Pole from Magnetic
⁎ Corresponding author. E-mail addresses: [email protected] (R. Cordani), [email protected] (W. Shukowsky). 0926-9851/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jappgeo.2009.07.001
Anomaly (VPMA) technique proposed here is based on the assumption ⇀ that the remanent component Jr determined from the anomaly, would be approximately correspondent to the primary NRM of the source rock. Therefore, this methodology produces an age estimation of the rocks without need of sampling them. Here we apply this methodology to five Mesozoic alkaline intrusions in Southeast Brazil, and compare the VPMA age results to the known radiometric ages obtained from geochronological studies. All the magnetic data used in this work came from CPRM (Brazilian Geological Survey) regional aeromagnetic database. Line spacing varied from 1000 to 2000 m. Application of the VPMA methodology to high-resolution magnetic datasets should yield better results. 2. VPMA methodology description The main concept of VPMA methodology is to isolate the remanent ⇀ component Jr of the magnetic anomaly and use it in paleomagnetic studies. Therefore, first we calculate the total magnetization of the magnetic source using one of the existing methods, and then we remove the induced component using the following vectorial equation. → → → J = Ji+ Jr
ð1Þ
R. Cordani, W. Shukowsky / Journal of Applied Geophysics 69 (2009) 96–102
97
Fig. 1. Registro magnetic anomaly. Magnetic data line spacing = 1000 m. Flight altitude = 150 m. Line direction: N–S.
Table 1 Remanent magnetic directions of Registro-SP-Brazil magnetic anomaly, calculated using Q Koenigsberger ratio values from minimum to maximum. ⇀ Jr
Q Q minimum 0.3 1 2 3 10 20
Inclination
Declination
− 70.80 − 48.83 − 43.55 − 41.74 − 39.20 − 38.65
48.40 − 3.11 − 7.06 − 8.24 − 9.78 − 10.09
where ⇀ J ⇀ Ji ⇀ Jr
is total magnetization. is induced magnetization component. is remanent magnetization component.
There are several methods available for the calculation of the total ⇀ magnetic vector J from a total field magnetic anomaly. In this case we used Fedi et al. (1994) Maxi-min method, but any other method can be used too (e.g., Zietz and Andreasen (1967), Schnetzler and Taylor (1984), Medeiros and Silva (1995)). Fedi et al. (1994) Maxi-min method is based on the successive application of the reduction-to-thepole operator on the measured magnetic data for different total
Fig. 2. Paleogeographic Pole coordinates of Registro-SP-Brazil magnetic anomaly, calculated using Q (Koenigsberger ratio) values from minimum to maximum.
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Table 2 Paleogeographic pole coordinates of Registro-SP-Brazil magnetic anomaly, calculated using Q (Koenigsberger ratio) values from minimum to maximum. Q
Paleogeographic poles
Q minimum 0.3 1 2 3 10 20
Latitude
Longitude
− 43.3 − 84.1 − 83.5 − 82.5 − 80.7 − 80.3
− 83.7 − 20.5 33 44.4 55.1 56.8
magnetization parameters (inclination I, declination D). The correct (I, D) pair is the one that maximizes the minimum of the magnetic ⇀ anomaly. 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 Ji magnitude. 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 the ⇀ ⇀ maximum (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 values ⇀ of Jr, and plot the locations of the paleogeographic poles in function of Q. The resulting plot on a polar stereographic projection diagram is a linesegment related to the studied anomaly. The final stage is the determination of the crossing point between the VPMA line-segment and the APWP. The crossing point on the paleogeographic poles diagram is the estimate for the age of the rock. Summary of the steps and application example (Registro magnetic anomaly): Step 1 — acquire magnetic data, remove IGRF and other regional ⇀ sources, and determine the total magnetization ( J) of the anomaly. Fig. 1 shows the example of magnetic anomaly of Registro.
⇀ 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 in paleopoles diagram (VPMA line segment). Table 1 and Fig. 2 show the results on the example of Registro (Table 2). Step 4 — determine the crossing point between VPMA line segment and the APWP for the anomaly tectonic plate. The next figure shows the Registro – SP – Brazil anomaly VPMA line segment example over the APWP of Ernesto (2007). Step 5 — interpret the result and determine the age of the source rock.
The VPMA line-segment intercepts the Ernesto (2007) APWP in two possible positions (Fig. 3). Each intercept gives an associated ageinterval for the source-rocks. Q = 0.70 yields 25–80 My; Q = 0.88 yields 80–100 My. The segment of the APWP for the time beyond 130 My is not represented in the above diagram. For this anomaly, the source rock is probably buried, and was not determined by geological mapping; therefore VPMA cannot provide a definite answer to the age of the rocks. We also need to consider the hypothesis that the source rock may be still older than the mentioned two options. On the other hand, considering the existence of the known Cretaceous intrusions in the same region (Jacupiranga, Juquiá, Pariqueraçu) that produced similar magnetic anomalies, it is reasonable to interpret that the age between 80 and 100 My (using Q=0.88) is the probable age of the possible hidden source of the Registro anomaly.
Fig. 3. Apparent Polar Wander Path for South American plate (Ernesto, 2007) and Paleogeographic Pole coordinates of Registro-SP-Brazil magnetic anomaly, calculated using minimum to maximum Q values.
R. Cordani, W. Shukowsky / Journal of Applied Geophysics 69 (2009) 96–102
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.
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Fig. 6. Left: Juquiá magnetic anomaly. Right: Pariqueraçu magnetic anomaly. Magnetic data line spacing = 1000 m. Flight altitude = 150 m. Line direction: N–S.
3. Results and discussion We applied the developed VPMA methodology in five (5) magnetic anomalies in Southeast Brazil (Figs. 4, 5, 6, Table 3). We determined the VPMA line-segments for each anomaly and plotted them in the paleogeographic poles diagram, together with the South American APWP (Ernesto, 2007) for the time since the Cretaceous. We did not use APWP for earlier periods for two main reasons: (i) we have good geological control and we know the age of three; and (ii) the available APWPs for those ages are in conflict between them. Fig. 7 shows the results. The green circle corresponds to the amplitude of the uncertainty of the paleomagnetic determinations, at the 95% confidence level: From Fig. 7, we selected the crossing point of each anomaly (or its closest point to the APWP), and finally estimate the age of the rock sources. 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 to the measured radiometric age according to Amaral et al. (1967). • Registro: using Q = 0.88, the preferred VPMA apparent age is bracketed 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 radiometrically; but Morbidelli et al. (2000) suggested that based on geological and petrological comparisons with Jacupiranga and Juquiá, as well as structural context, the intrusion must exhibit an age close to 130 My.
Table 3 Site location and induced field direction (IGRF at the survey time) for the anomalies. Site
• Araxá: using Q = 0.35, the VPMA apparent age of 70 Ma is concordant with the radiometric dates, whose interval cover 80 ± 10 My according to Gomes et al. (1990). • Tapira: using Q = 2, the VPMA apparent age 70 Ma, is close to the radiometric 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 total ⇀ magnetic J calculation method; (ii) the assumption that the entire anomaly comes from a single rock; (iii) the assumption that the obtained ⇀ Jr is equivalent to the primary NRM, i.e., there is no presence of relevant secondary NRM; and (iv) the accuracy of the APWP. It is possible to at least estimate the error of the total magnetization direction calculation method using a numerical simulation. We applied the Max-min method in anomalies due to fixed direction and variable direction magnetization in three different synthetic geometry blocks. The Max-min algorithm estimates the direction of the total magnetic moment of the causative body. In the case of fixed direction magnetization this coincides with the actual direction of magnetization. For the variable direction magnetization the Max-min estimate represents the direction of the average magnetization (Fig. 8). We ran a total of 1200 simulations using both fixed magnetization (each cubic block with same magnetization) and variable magnetization (different magnetization for each cubic block). For each simulation we compared the real magnetization of the geometry block and the total magnetization recovered using the Max-min algorithm. Then we plot the difference between them (Fig. 9). The numerical simulation results gave an error of less than 5.00° on the magnetization direction estimation, using the Max-min method (with 95% of confidence interval). Other uncertainties are difficult to estimate numerically, but the accuracy of APWP is obviously a key factor. 5. Conclusions
IGRF
Anomaly
Latitude
Longitude
Inclination
Declination
Juquiá Pariqueraçu Registro Araxá Tapira
− 24.41 − 24.73 − 24.54 − 19.66 − 19.89
− 47.68 − 47.82 − 47.71 − 46.94 − 46.83
− 26.77 − 27.09 − 26.92 − 19.60 − 19.40
− 15.88 − 15.71 − 15.83 − 16.50 − 16.20
This paper presents the description of VPMA methodology, which is capable to estimate the age of a rock formation that causes a magnetic anomaly. We applied the VPMA methodology to five (5) magnetic anomalies in Southeastern Brazil. Four of the anomalies (Juquiá, Pariqueraçu,
R. Cordani, W. Shukowsky / Journal of Applied Geophysics 69 (2009) 96–102
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Fig. 7. South American APWP and VPMA line segments of five magnetic anomalies in Southeastern Brazil.
Table 4 Final 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 Pariqueraçu Registro Araxá Tapira
− 86.06 − 86.79 − 83.20 − 73.02 − 78.30
87.86 79.61 − 34.90 − 6.58 − 3.10
3.00 10.00 0.88 0.35 2.00
130 My 130 My 80 to 110 My 70 My 75 My
130 My — Amaral et al. (1967) Unknown Unknown 80 ± 10 My — Gomes et al. (1990) 79 ± 8 My — Hasui & Cordani (1968)
Apparent age of intrusions according to VPMA and radiometric age for previously dated rocks.
Araxá and Tapira) have the correspondent source rock identified at the surface. They are Mesozoic alkaline intrusions, whose radiometric ages are known in three of them. The fifth anomaly (Registro) does not have a correspondent geological feature at the surface, but the similar shape of its anomaly indicates that it is due to a similar alkaline intrusive body. For the three cases in which the radiometric ages of the source rocks are known, the VPMA method recovered their apparent ages inside the margin of error of both the APWP and radiometric ages. We estimated the age for the source of the two other anomalies as Cretaceous. These do not have an associated radiometric age, but
the anomalies were considered because of the similar shape as the other three magnetic anomalies. Since the VPMA results are constrained by the tectonic plate movement and the associated APWP, the ideal conditions for its application are: i) noticeable movement of the tectonic plate relative to the paleomagnetic pole; ii) accurate knowledge of the APWP. In the future, we understand that the VPMA methodology could contribute to future geoscientific knowledge in several ways: (a) anomalies whose source is unknown could now be studied;
Fig. 8. Models for numeric simulation, each one containing nine cubic blocks with 100 m side each. We considered three different spatial orientations (I; II and III).
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R. Cordani, W. Shukowsky / Journal of Applied Geophysics 69 (2009) 96–102
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.
(b) the generation of new virtual poles could contribute and improve the knowledge of the APWP; (c) quick estimation of the age of a source rock for geoscientists without access to geochronological or paleomagnetic labs; (d) previous analysis of the age of a rock unit, to better find future areas for paleomagnetic targets; (e) helping on defining magnetic parameters for magnetic inversion. Acknowledgments This work was the result of a Ph.D programme at the Institute of Astronomy and Geophysics of the University of São Paulo — IAG-USP. We would like to thank the entire paleomagnetic group of IAG for suggestions and corrections. Special thanks are extended to R. Trindade, C. Mendonça, D. Brandt and U. Cordani for discussions and text reviews. References Amaral, G., Bushee, J., Cordani, U.G., Kawashita, K., 1967. Potassium-argon ages of alkaline rocks from southern Brazil. Geochimica Cosmochimica Acta 31, 117–142. Emilia, D.A., Massey, R.L., 1974. Magnetization estimation for nonuniformly magnetized seamounts. Geophysics 39, 223–231.
Ernesto, M., 2007. Drift of South America platform since Early Cretaceous: reviewing the apparent polar wander path. Geociências (São Paulo) 25, 83–90, 2007. Fedi, M., Florio, G., Rapolla, A., 1994. A method to estimate the total magnetization direction from a distortion analysis of magnetic-anomalies. Geophys. Prospect. 42 (3), 261–274. Gee, J., Staudigel, H., Tauxe, L., 1989. Contribution of induced magnetization to magnetization of seamounts. Nature 342, 170–173. Gomes, C.B., Ruberti, E., Morbidelli, L., 1990. Carbonatite complexes from Brazil: a review. J. South Amer. Earth Sci. 3, 51–63. Hasui, Y., Cordani, U.G., 1968. Idade Potássio-Argônio de rochas eruptivas Mesozóicas do Oeste Mineiro e sul de Goiás. In: Congresso Brasileiro de Geologia, 22, Belo Horizonte, 1968. Anais, Belo Horizonte, SBG, p. 139–143. Hilderbrand, J.A., Parker, R.L., 1987. Paleomagnetism of cretaceous Pacific seamounts revisited. JGR, 92, 12695–12712. Kubota, R., Uchiyama, A., 2005. Three-dimensional magnetization vector inversion of a seamount. Earth Planets Space 57, 691–699. Lee, T.G., Lee, S.M., Moon, J.W., Lee, K., 2003. Paleomagnetic investigation of seamounts in the vicinity of Ogasawara Fracture Zone northwest of the Marshall Islands, western Pacific. Earth Planets Space 55, 355–360. Medeiros, W.E., Silva, J.B., 1995. Simultaneous estimation of total magnetization direction and 3-D spacial orientation [J]. Geophysics 60, 1365–1377. Morbidelli, L., Gomes, C.B., Brotsu, P., D'Acquarica, S., Garbarino, C., Ruberti, E., Traversa, G., 2000. The Pariquera-Açu K-alkaline complex and Southern Brazil lithospheric mantle source characteristics. J. Asian Earth Sci. 18, 129–150 2000. Sager, W.W., Koppers, A.A.P., 2000. Late Cretaceous polar wander of the Pacific Plate: evidence of a rapid true polar wander event. Science 287, 455–459. Schnetzler, C.C., Taylor, P.T., 1984. Evaluation of an observational method for estimation of remanent magnetization. Geophysics 49, 282–290. Zietz, I., Andreasen, G.E., 1967. Remanent. Magnetization and aeromagnetic interpretation. Mining. Geophysics 2, 569–590.