Tippers at island observatories: Can we use them to probe electrical conductivity of the Earth's crust and upper mantle?



[1] For decades, time series of hourly-mean values of the geomagnetic field measured on a global network of observatories have been routinely used to recover the electrical conductivity distribution in midmantle depths. Nowadays, most observatories provide data in the form of minute-means. This allows for analysis of short-period geomagnetic variations, which, in principle, contain information about geoelectric structures in the crust and upper mantle. However, so far these data have been ignored for induction studies of the Earth due to a theoretical preconception. In this paper, we demonstrate that short-period responses (tippers) at island observatories, being large owing to the ocean effect, are also sensitive to 1-D structures and thus can be used for probing the Earth. This means that a huge amount of data that was not exploited hitherto for induction studies should be reconsidered as a useful source of information about geoelectric structures in oceanic regions where our knowledge is still very limited.

1 Introduction

[2] Hourly-mean time series of the geomagnetic field measured on a global net of geomagnetic observatories have been routinely used for decades in induction studies that aim to recover mantle electrical conductivity [e.g. Schmucker, 1999; Kelbert et al., 2009]. Bearing in mind the 1 h sampling interval and depending on the period, two global sources are used for these studies: (1) solar quiet (Sq) variations with periods between 4 and 24 h, caused by electric currents flowing in the ionosphere; (2) irregular (Dst) variations with periods longer than 1 day, caused by modulation of the ring current flowing in the magnetosphere. An interpretation of these data yields the recovery of electrical conductivities in the depth range from about 400 km down to about 1600 km. Recent progress in deep electromagnetic (EM) sounding of the Earth is summarized in a review paper by Kuvshinov [2012]. Nowadays, most geomagnetic observatories provide minute-mean data, which gives an opportunity to analyze the variations at shorter periods, namely, in the period range between a few minutes and a few hours. There is common consensus that these variations are generated by an auroral ionospheric current system which is seen at midlatitude observatories as a vertically propagated plane wave of time-varying polarization [cf. discussion in Chave and Jones, 2012, page 10]. These variations can, in principle, provide information about geoelectric structures at crustal and upper mantle depths (<400 km). However, to the best of our knowledge, there have been no attempts yet to use these data (short-period geomagnetic field variations at observatory locations) to infer the conductivity of the Earth. The reason for this seems to be rather intuitive and appears to be as follows. For a given and isolated observatory (and for the considered period range), one can at best determine the one-dimensional (1-D) local conductivity structure beneath the observatory site. Moreover, assuming plane-wave excitation, the only response functions which might be then constructed from geomagnetic data is the first-order tensor of complex-valued and dimensionless tippers, T = (Tx,Ty), which connects the vertical magnetic component Bz with two horizontal components Bx and By

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[3] Here ω = 2π / p is the circular frequency, where p is a period, z points positive downward, x points to geographic north, and y points to geographic east. However, as a consequence of the plane-wave excitation, variations in Bz (and thus T) are nonzero only above non-1-D conductivity structures. In fact, one can interpret T as a measure of the tipping of the magnetic field out of the horizontal plane above non-1-D conductivity structures, which cause anomalous variations in Bz [Parkinson, 1959; Jones and Price, 1970].

[4] This line of reasoning advocates ignoring minute-mean data to probe the Earth's crust in the frame of 1-D models. This is probably true for inland observatories, but it is not for island and coastal sites where the ocean plays a role. Here the horizontal conductivity contrast between resistive continental bedrock and conductive sea water results in large tipper amplitudes even if the crustal structure is essentially 1-D. This is referred to as the ocean (or coast) effect [e.g. Parkinson, 1962]. Note that real and imaginary parts of tippers are often displayed separately as arrows with respective coordinates − (ReTx,ReTy) and − (ImTx,ImTy). Minus sign means that the Parkinson convention is used.

[5] Under the assumption that both the conductivity of the land, σland, and the conductivity of seawater, σsea, are constant with math formula, and considering induction methods as volume sounding techniques, the real part of tippers always points toward the nearest deepest ocean. Furthermore, tippers reach their maximum amplitudes at those periods where conductivity contrast is maximum within the penetrated volume. At roughly the same periods the reversal of the imaginary parts occurs [e.g. Dosso and Chen, 2000]. In this paper, we perform model studies in order to answer the following two questions: (1) Is it possible to reproduce the complex frequency-dependent behavior of the observed tippers at island observatories with rigorous 3-D modeling of the ocean effect? (2) Are these tippers sensitive to 1-D conductivity structures beneath the ocean?

2 Observations

[6] For analysis, we have chosen data consisting of minute-mean time series of the geomagnetic field from three island observatories which are located in the Atlantic, Pacific, and Indian oceans. Their location is shown in Figure  1. The first observatory (TDC) is situated in the northwestern part of Tristan da Cunha island, which is part of the Tristan da Cunha archipelago in the South Atlantic Ocean and consists of a large oceanic shield volcano that rises more than 5000 m from the seafloor to an altitude of 2000 m [Matzka et al, 2009]. The second observatory HON (Honolulu) is located in the south of the volcanic Hawaiian island Oahu, which reaches an altitude of 1200 m and is surrounded by 5000 m deep ocean. Unlike TDC and HON, the third observatory, provisionally acronymed by CKI, is not part of the INTERMAGNET network; it was established very recently on southern Cocos (Keeling) Island and is currently in experimental operation status. Southern Cocos Island is a coral ring atoll in the Indian ocean, and CKI observatory is located on a southwestern island of the atoll. The Cocos Islands are situated on top of seamounts of volcanic origin on Cocos Rise and are also surrounded by 5000 m deep ocean. The maximum altitude of the islands is a few meters only. The tippers were estimated from the data using the BIRRP-code [Chave and Thomson, 2003, 2004] in a period range between 2 min and 1 day. BIRRP stands for Bounded Influence, Remote Reference Processing; the code is based on section-averaging of the time series with a jackknife estimator of the uncertainties. The section length is variable and depends on the period (shorter sections for shorter periods). Before processing, the geomagnetic data were visually preselected, and days with obvious spikes and boxcar offsets were removed. Repetitive processing of data with varying time spans has shown that an approximately 30 day period of geomagnetic data is sufficient to gain stable responses in the considered period range. Figure  2 shows real and imaginary parts of the observed tippers. It is seen that at all observatories, at least the real parts of tippers are substantially larger than 0. Their behavior is smooth, and their uncertainties are small up to periods of 10,000 s  ≈  3 h, with overall tendency for uncertainties to be larger at longer periods. This can be explained as follows: The number of sections used to estimate tippers (and thus the number of degrees of freedom) is smaller for longer periods compared to shorter periods. Since the statistical error is inversely proportional to the number of degrees of freedom, this results in larger uncertainties at longer periods. Another observation is that at periods larger than 3 h, the responses become more scattered, and their uncertainties increase. This is most probably due to Sq source contamination and thereby violation of the plane-wave assumption [e.g. Shimizu et al., 2011]. In the following, we concentrate therefore on analysis of the responses at periods less than 3 h.

Figure 1.

World surface conductance map [Manoj et al. 2006] using a logarithmic scale and location of the observatories TDC, HON, and CKI. The surface conductance is based on contributions from seawater and sediments. Note the large horizontal conductivity contrast along the coasts.

Figure 2.

Plots (from left to right) of observed tippers at TDC, HON, and CKI. In the upper plots, Tx are shown as squares and Ty as triangles. Real and imaginary parts are depicted in blue and red, respectively. In the lower plots, tippers are displayed as arrows in the Parkinson convention, i.e., real parts point toward the most conductive region within the penetrated volume. The length of each arrow signifies the norm of the tippers real part and imaginary part, respectively. Coordinate systems are shown in the plots with the axes having a reference length of 0.5. The orders of periods in the “arrow” plots are the same as in the upper plots.

[7] At all observatories and at periods up to 3000 s, the real tipper component perpendicular to the local coast line dominates; cf. Figure  3. This confirms that the responses are strongly influenced by the ocean effect. Otherwise, the behavior of the tippers at different sites is substantially different. At TDC, real parts of the tipper are maximum (with largest magnitude of 0.6) at short periods and decrease with increasing periods. This is consistent with the fact that here the conductivity contrast within the penetrated volume decreases with period. As for HON, a clearly dominating real Tx component for periods below 1000 s is in agreement with the east-west elongated coast line in the vicinity of the observatory. With increasing period, tipper arrows smoothly change to point westward, then for periods greater than 3000 s real parts of Ty are dominating. This is explained by concentration of the main landmass east of the observatory for larger penetrated volume; cf. Figure  3b. The maximum magnitude of the observed tippers at HON is 0.5. At CKI, the real parts of the tippers point constantly toward southwest over the whole period range. With their southwestern direction, they point away from the center of the ring atoll toward deep ocean as one would expect in this scenario. Real tipper amplitudes are increasing till a period of 2000 s with dominating Tx. The maximum magnitude of the observed tippers at CKI is 0.45.

Figure 3.

(a–c) Interpolated ETOPO1 bathymetry data [Amante and Eakins, 2009] around observatories TDC, HON, and CKI, respectively; the coastline is indicated as a black line. The location of each observatory is marked with a diamond symbol. Zoomed subfigures show coastlines around observatory location in detail. Numbers on the axes stand for the model cell numbers; the total horizontal size of all models is 356 km  ×  356 km.

3 Model Studies

[8] The model studies were performed using the X3D code (Avdeev et al. 2002), which is based on the contracting integral equation technique. This frequency-domain code allows for calculating plane-wave electric and magnetic fields (and thus various response functions, including tippers) in Earth's models with a three-dimensional conductivity distribution. Bathymetry and topography data have been taken from the ETOPO1 Global Relief Model database [Amante and Eakins, 2009]. Models for TDC and HON consist of eight anomalous top layers (three layers account for topography and five for bathymetry); the models for CKI consist of only five anomalous top layers due to absence of topography. Anomalous layers are built based on ETOPO1 data and are followed with depth by a 1-D conductivity section. The shallow 3-D conductivity distribution is derived from ETOPO1 data under the assumption of a sea water conductivity of σsea = 3.2S / m and a land conductivity of σland = 10 − 2S / m. The original one arc-minute data of bathymetry and topography used for estimating conductivity distributions in the anomalous layers were interpolated to a regular Cartesian grid with a horizontal cell size of 1 km  ×  1 km. Based on these assumptions, vertically averaged conductivities for all cells of the anomalous layers were calculated. Interpolated ETOPO1 bathymetry and topography data around TDC, HON, and CKI are shown in Figures  3a– 3c. The total horizontal size for all (TDC, HON, and CKI) models is 356 km  ×  356 km. Note that we performed extensive and systematic model studies to justify the parameters describing the models (cell and mesh sizes, number of anomalous layers, values for sea water and land conductivities). In particular, from these studies, we learned that the effect from varying sea water and land conductivities is less than the effect from varying the 1-D section.

[9] The sensitivity of tippers to conductivity variations in the crust and upper mantle was investigated with respect to three different 1-D conductivity sections. These sections are shown in Figure  4. The section labeled as GLO is a (modified) global conductivity section that has been inferred from satellite magnetic data by Kuvshinov and Olsen [2006]. The modification is assigning a realistic low conductivity value to the upper 100 km as these depths are not resolvable by satellite magnetic data. Sections here denoted as PHS and PAC are sections for Philippine Sea and for North Pacific region, respectively, which have been recovered from the seafloor magnetotelluric data [Baba et al. 2010]. The most significant differences between sections appear at shallow depths, where, integrated over the upper 200 km, PHS is the most conductive and GLO is the most resistive section.

Figure 4.

1-D conductivity sections GLO (green) [Kuvshinov and Olsen, 2006], PAC (blue), and PHS (red) [Baba et al. 2010], which are used in 3-D modeling; see details in the text.

[10] The predicted tippers are shown in Figure  5 in comparison with observed ones. At observatory TDC,the general shape of the observed tipper curves is well reproduced by prediction irrespective of which 1-D section is used. However, all predicted real parts of tippers are shifted to lower values except in the period range above 3000 s. The largest deviations occur in the Tx component whereby predicted real parts of Tx from the model with GLO 1-D section are closest to the observed ones. The variability at a certain period in the predicted tippers, determined as

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appeared to be maximum (0.12) in the real part of Tx at period of 5000 s, which is ∼ 20% of the magnitude of the observed response at this period.

Figure 5.

Plots from left to right: Observed and predicted responses at observatories TDC, HON, and CKI. Upper and lower plots show real and imaginary parts, respectively. Tx are denoted as squares, Ty as triangles. Predicted tippers for GLO, PAC, and PHS 1-D section are plotted in green, blue, and red, respectively. Observed responses and their uncertainties are shown in black. As a whole, the predicted tippers for different 1-D conductivity sections show significant differences.

[11] Predicted tippers for HON show much more variability compared with the results for TDC. The maximum variability in the predicted tippers with respect to three different 1-D sections is in Ty. At a period of 5000 s, the variability in real Ty is ∼ 0.37, which is ∼ 80% of the magnitude of the observed response at this period. The agreement between predictions and observations is worse than at TDC; however, the observed transition from dominating real part of Tx to dominating real part of Ty with increasing period is well reproduced with all 1-D sections. In contrast to TDC, the results for the GLO 1-D section generally show the highest misfit for both real and imaginary parts.

[12] At CKI, the overall behavior is well reproduced by all models, and the maximum variability in the predicted tippers with respect to three different 1-D sections is 0.05 in the real part of Tx, which is ∼ 12% of the magnitude of the observed response. This is the minimum among the three sites, but nevertheless it far exceeds the uncertainty of the observed responses.

4 Conclusions and Outlook

[13] We demonstrate that the overall behavior of tippers at island observatories is well explained by the ocean effect, if topography and bathymetry are adequately modeled.

[14] We also clearly show that tippers at island observatories are sensitive to the 1-D conductivity section underneath. The largest sensitivity is observed at observatory site locations with a high land-to-sea ratio in upper layers.

[15] From the aforementioned conclusions, we can state that a huge amount of data that was not exploited so far for induction studies can be reconsidered as a useful source of information at many (island) observatories. Of particular importance is that these data allow us to, at least partially, surmount an evident lack of knowledge about crustal and upper mantle structures in the oceanic regions.

[16] We observe different levels of agreement between predicted and observed tippers at different island observatories, which suggests a regional difference in conducting structures at crustal and upper mantle depths. In order to quantitatively specify the variability of the underlying conductivities with respect to observatories and regions, we plan to develop a numerical scheme which will allow for inverting for tippers in terms of 1-D conductivity distribution in the presence of a realistic 3-D bathymetry. Finally, we would like to extend our studies to coastal observatories, although our first studies have revealed substantial disagreement between observations and predictions. This is most probably due to inherent 3-D complications in the transition zone between ocean and land that are not easy to account for.


[17] The authors would like to thank Susan Macmillan and an anonymous reviewer for their valuable comments and suggestions to improve the quality of the paper. Furthermore, we thank William Lowrie for help with improving the English presentation of this paper and Thomas Kalscheuer for valuable comments on an initial version of the paper. The results presented in this paper rely on data collected at magnetic observatories. We thank the national institutes that support them and INTERMAGNET for promoting high standards of magnetic observatory practice (www.intermagnet.org). We especially thank Juergen Matzka (DTU Space, Copenhagen) for motivating us to work on TDC observatory data and Geoscience Australia for enabling us to work on CKI data. This work has been supported by ETH grant No. ETH-3010-3.