Geophysical Journal International
doi: 10.1111/j.1365-246X.2010.04702.x
Depths to the magnetic layer bottom in the South China Sea area
and their tectonic implications
Chun-Feng Li,1 Xiaobin Shi,2 Zuyi Zhou,1 Jiabiao Li,3 Jianhua Geng1 and Bing Chen1
1 State
Laboratory of Marine Geology, Tongji University, Shanghai 200092, China. E-mail: [email protected]
of Marginal Sea Geology, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou, Guangdong 510301, China
3 2nd Institute of Oceanography, State Oceanic Administration, Hangzhou, Zhejiang 310012, China
2 Laboratory
Accepted 2010 June 15. Received 2010 June 1; in original form 2009 June 8
SUMMARY
The depths to the magnetic layer bottom (Zb ) in the South China Sea (SCS) area are estimated
by computing radially averaged amplitude spectra of total field magnetic anomalies. We test
different sizes of moving windows in which the spectra are calculated to better understand how
window sizes affect the depth estimations. Apart from lowering the resolutions of estimated Zb ,
larger windows do not necessarily incur presumable increases in Zb in the SCS area. Although
the centroid method is taken as our primary technique for estimating Zb , for cross check, the
spectral peak and the non-linear inversion methods are also applied to those windows where
spectral peaks do appear. In a single window we may find discrepancy in Zb estimated from
different techniques, but for all windows showing spectral peaks, the estimated Zb from one
technique are grossly correlated with those from another. Our results show that most parts
of the central SCS ocean basin and the northern continent–ocean transition (COT) zone have
significantly smaller Zb than the surrounding continental blocks. In the surrounding continental
regions Zb are averaged at about 34 km, a depth close to the Moho depth. The average Zb is
about 22 km in the central basin, but this value is much larger than the Moho depth, signifying
that the uppermost 10 km or so of the mantle beneath the central basin is also magnetized. The
strong faulting and recent magmatism within the COT zone can account for the small Zb near
the northern continental margin. The estimated Zb are also found very correlative to surface
heat flow. This observation verifies dominant contributions to surface heat flow from incoming
mantle heat flow due to thermal conduction. The positive correlations observed among Zb
from different techniques as well as the good correlation between surface heat flow and Zb
support the reasoning that our estimated Zb are within an acceptable range of accuracy.
Key words: Fourier analysis; Inverse theory; Magnetic anomalies: modelling and interpretation; Marine magnetics and palaeomagnetics; Heat flow; Continental margins: divergent.
1 I N T RO D U C T I O N
Magnetic anomalies offer invaluable insights into deep crustal structures and physical properties of the Earth, particularly on depths,
magnetizations and geometries of magnetic sources. Different data
reduction and inversion techniques, such as reduction to the Pole,
upward continuation and Euler deconvolution, can be applied targeting on specific research objectives and/or magnetic patterns. In
addition, there is an intimate connection between surface magnetic
anomalies and the Earth’s geothermal field, since rock magnetizations can be strongly affected by temperature variations. Magnetic
layer bottom constitutes an undulating surface in the Earth’s interior,
below which minerals reach their Curie temperatures (about 550 ◦ C
but variable with composition) and lose their ferromagnetism. If
magnetite is the only mineral that characterizes the rock magnetization, the depth to magnetic layer bottom (Zb ) can be taken as the
Curie point depth.
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Journal compilation The surface of Zb is therefore a magnetic as well as a thermal
boundary that reflects the tectonic stability of a geological block,
and is an important parameter in constraining regional geodynamics. However, many factors, such as geothermal field, faulting and
lithology, would affect Zb . Therefore there would be many uncertainties in estimated Curie point depths based on just one single
parameter, for example, surface heat flow. Yet, no matter how these
factors may change, information about variations of Zb is always
imbedded in magnetic anomalies, and direct inversion of surface
magnetic data is a commonly practiced technique in estimating
Zb (e.g. Agrawal et al. 1992; Blakely 1995; Tanaka et al. 1999;
Stampolidis & Tsokas 2002; Aydin et al. 2005; Ross et al. 2006;
Ravat et al. 2007; Li et al. 2009).
Magnetic data acquisition in the South China Sea (SCS) area
(Fig. 1) started in the 1960s, by various institutions from many
countries, using both ship-borne and air-borne instruments (BenAvraham & Uyeda 1973; Bowin et al. 1978; Taylor & Hayes 1980,
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Figure 1. Shaded relief map showing major tectonic regimes in the SCS region. AB, BC, DE and 973G are locations of reflection seismic lines. Two isobaths
shown on the map are 500 and 3000 m, respectively. NT = Nansha Trough; DS = Dongsha Rise; EB = east sub-basin; SWB = southwest sub-basin; NWB =
northwest sub-basin; OT = Okinawa Trough; PT = Palawan Trough; T = Taiwan Island; XT = Xisha Trough; ZB = Zhongsha (Macclesfield) Bank; LB =
Liyue (Reed) Bank; NM = Nansha Massif (Dangerous Grounds). The black arrow points to the location of a listric crustal fault shown in Fig. 13.
1983; He & Chen 1987; Yao et al. 1994). In 1996, a data set of
total field magnetic anomalies (Fig. 2) is compiled by Geological
Survey of Japan and Coordinating Committee for Coastal and Offshore Geoscience Programmes in East and Southeast Asia (CCOP)
(1996). Although the original data are from a variety of different sources, with different time, scales and grid spacings, this new
compilation offers a remarkable coverage and accuracy (Fig. 2).
However, geodynamic studies based primarily on processing and
interpretation of magnetic anomalies in the SCS have been so far
very rare. In the past, magnetic anomalies were used mainly as a
tool for age correlations (e.g. Taylor & Hayes 1980; He & Chen
1987; Briais et al. 1993; Yao et al. 1994; Barckhausen & Roeser
2004; Hsu et al. 2004). Several other attempts have been made to
invert for seamount magnetism that can then be used to infer relative plate movements (Jin et al. 2002). Recently, Li et al. (2008a,b)
carried out a series of data processing procedures on the total field
magnetic anomalies from the SCS to further infer deep structures
and seafloor spreading dynamics. These techniques include reduction to the pole, upward continuation, Euler deconvolution, power
spectrum analysis, analytical signal analysis and depth estimation.
Tanaka et al. (1999) designed a wavenumber-domain technique
to calculate Zb of eastern Asia. Since their study covers a very
large area, their map of estimated Zb in the SCS area is of very low
resolution. In this paper, we compute Zb at relatively high resolutions
through analysing radially averaged amplitude spectra of total field
magnetic anomalies (Connard et al. 1983; Blakely 1995; Tanaka
et al. 1999; Ross et al. 2006; Ravat et al. 2007). We then integrate
Zb with 355 surface heat flow measurements in the area to better
understand crustal geotherms and their tectonic significance.
2 METHODOLOGY
Assuming infinite horizontal extensions of magnetic sources and
much smaller depths than horizontal scales, Blakely (1995) showed
that radially averaged amplitude spectrum AT (|k|) of the total field
magnetic anomalies T is related to radially averaged amplitude
spectrum A M (|k|) of magnetization M by
AT (|k|) = C A M (|k|) e−|k|Z t (1 − e−|k|(Z b −Z t ) ),
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(1)
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Figure 2. Map of total field magnetic anomalies in the SCS area. ZNF = Zhongnan Fault; LRTPB = Luzon-Ryukyu Transform Plate Boundary; DS = Dongsha
Rise; SCMA = offshore south China magnetic anomaly; XS = Xisha; ZB = Zhongsha (Macclesfield) Bank; LB = Liyue (Reed) Bank; NM = Nansha Massif
(Dangerous Grounds). The amplitude spectra and normalized autocorrelations from magnetic anomalies in windows A and B are shown in Fig. 3.
in which β is called spectrum exponent, a parameter related to
correlation lengths between magnetizations of different magnetic
sources, or to magnetization complexities. Substituting eq. (2) into
(1) and taking natural logarithm on both sides, we have
In eq. (3) there are four unknowns, namely, B, Zb , Zt and β. Li
et al. (2009) attempted to simultaneously invert these four unknowns
from radially averaged amplitude spectrum by non-linear inversion
techniques such as the commonly applied Levenberg–Marquardt
method (Levenberg 1944; Marquardt 1963), but found it very difficult to obtain accurate and stable inversions. Ravat et al. (2007) also
noted that it is very difficult to simultaneously invert these unknowns
as they are closely interdependent. To achieve stable inversions of
Zb , we need to either reduce the number of unknowns, or linearize
the model expressed by eq. (3) at different wavenumber bands by
incorporating more assumptions (Tanaka et al. 1999). We can first
assume a special scenario in which magnetizations are completely
random in the two horizontal directions. Under this assumption,
magnetizations from different magnetic sources are not correlated
and β = 0 (Turcotte 1997; Li 2003). Eq. (3) can then be simplified
(Tanaka et al. 1999) at middle- to high-wavenumber band to
ln [ AT (|k|)] = ln B − |k| Z t + ln[1 − e−|k|(Z b −Z t ) ] − β ln |k| ,
ln [AT (|k|)] ≈ ln D − |k| Z t ,
in which k is the wavenumber, C is a constant related to magnetization direction and geomagnetic field direction and Zb and Zt are
depths to the bottom and top bounds of magnetic sources, respectively.
In general, crustal magnetization is not completely uncorrelated
but follows a fractal spatial distribution (Gregotski et al. 1991;
Pilkington & Todoeschuck 1993; Fedi et al. 1997; Maus et al. 1997).
In this case, amplitude spectrum of magnetization has a power-law
relationship with wavenumber, by
A M (|k|) ∝ |k|−β ,
(2)
(3)
in which B is a constant.
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where D is a constant, and at low-wavenumber band to
ln[AT (|k|)/|k|] ≈ ln E − |k| Z 0 ,
(5)
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in which E is a constant, and Z 0 is the centroid depth of the magnetic
source.
Apparently both eqs (4) and (5) are linear models at localized
wavenumber bands, with which stable inversions for Zt and Z 0 can
be guaranteed using least-squares linear regressions. Zb can then be
estimated from
Z b = 2Z 0 − Z t .
(6)
It should be mentioned that, in practice, the radially averaged amplitude spectrum in the above equations is really the area-weighted
radial amplitude spectrum (Cordell et al. 1991), which is favoured
and adopted here. The reason is that in the 2-D wavenumber domain, the area of a given spectral band increases with spectral radius
and, therefore the total amount of energy in a given spectral band is
best characterized by the area-weighted radial amplitude spectrum
rather than the radially averaged amplitude spectrum alone (Cordell
et al. 1991). No other particular filtering has been applied on the
magnetic data before calculating the amplitude spectrum. Weighting by area may tend to reduce the variance of spectral energy at
low wavenumbers, but is mathematically more accurate.
The preceding technique (Tanaka et al. 1999) estimates the top
and centroid depths Zt and Z 0 first before calculating Zb , and belongs
to a group of method called the centroid method (Ravat et al. 2007).
This method is useful when no spectral peaks occur on the amplitude
spectra. In case a peak shows up on a spectrum, we also apply
the spectral peak method by eq. (7) (Connard et al. 1983) and
a non-linear inversion scheme (eqs 8 and 9) for cross-check and
comparison. However, the wavenumber-domain centroid method of
Tanaka et al. (1999) is our primary means of obtaining Zb , for it
can provide stable result within each single window, making 2-D
mapping of Zb possible.
The spectral peak method (Connard et al. 1983) proceeds by
numerically solving the transcendental equation
ln Z b − ln Z t = kpeak (Z b − Z t ) ,
(7)
where k peak is the observed wavenumber of the spectral peak. Ravat
et al. (2007) pointed out the limitations of this method, that the
spectral peak is not always observed and very often the peak is
represented by a single point at a fixed wavenumber. These are
exactly the problems we are facing here. Moreover, the estimation
of Zb is also dependent on the depth to the top Zt , which itself is
often unknown beforehand and must be obtained by other methods.
If we reduce the number of unknowns in eq. (3) down to three by
assuming a random magnetization β = 0, the chance of obtaining
stable inversions of both Zt and Zb simultaneously increases sharply.
We can fit the theoretical radially averaged spectrum curve to the
observed one, either manually by forward modelling, and trial and
error (Ross et al. 2006; Ravat et al. 2007), or directly by nonlinear inversion in the least-squares sense. With the assumption of
random magnetization β = 0, the theoretical magnetization model,
represented by eq. (3) in the wavenumber domain, becomes
ln [AT (|k|)] = ln B − |k| Z t + ln[1 − e−|k|(Z b −Z t ) ].
(8)
Now we have three unknowns left and we are able to write a
mathematical code based on the Levenberg–Marquardt algorithm
(Levenberg 1944; Marquardt 1963) to invert for Zt and Zb simultaneously by finding the minimum of
N
(ln [φ (|ki |)] − ln [ AT (|ki |)])2 ,
(9)
g(Z b , Z t , B) =
i
in which φ(|ki |) stands for the observed radially averaged spectral
amplitude at ith wavenumber from a window, and N is the total
number of points in the amplitude spectrum that are taken into the
inversion. Due to the mutual dependence of Zt and Zb , and the nonuniqueness of inversion or trial and error, it can be difficult to find
the optimal solutions. This method often requires fitting only at the
very low-wavenumber portion of spectra, turning it basically into a
narrow-band and low-wavenumber operation, which we think might
be inappropriate for accurate depth estimation. Narrow-band nonlinear inversion with just a few data points also tends to produce
highly fluctuating results.
3 DEPTHS TO THE BOTTOM
O F M A G N E T I C L AY E R
Total field magnetic data compiled by CCOP (1996) (Fig. 2) are first
projected into Ellipsoidal Transverse Mercator coordinates with the
central meridian equal to 117◦ . The data are then gridded into 998 ×
1226 bins of an equal size of 1.55 × 1.55 km2 , using the minimum
curvature method (Briggs 1974). The bins are then reassembled
into overlapping square windows, in which the amplitude spectra
are subsequently calculated.
The original magnetic data from CCOP are corrupted with highwavenumber noises and track corrugations, as evident on Fig. 2 to
the west of the Dongsha Islands. However the noise can be avoided
in calculating Zt and Z 0 by taking wavelengths larger than ∼10 km
(Fig. 3), and this treatment was also practiced by others (Tanaka et al.
1999; Stampolidis & Tsokas 2002; Lin et al. 2005). Meanwhile,
this treatment can also help avoid detecting top bounds of small,
shallowly buried or isolated magnetic sources. Detected top bounds
of isolated magnetic sources may be shallower, and may not belong
to the same magnetic layers whose bottom bounds are calculated
from radially averaged amplitude spectra.
Magnetic anomalies from the SCS are at low latitudes and are
affected by oblique inductions of the Earth’s magnetic field. Without
reduction to the Pole the observed magnetic anomalies are largely
distorted, but reduction to the Pole at very low latitudes can be tricky.
Additionally, remanent magnetization in the area should be quite
strong as the SCS basin is floored by an oceanic crust. However,
it is found from numerical experiments that there are insignificant
differences between Zb obtained with and without reduction to the
pole (Okubo et al. 1985; Zhou & Thybo 1998), and there is even
no need to assume that magnetizations are induced (Okubo et al.
1985).
If a selected window is too large, it will decrease the spatial
resolution of Zb and local depth anomalies may not be discernible.
On the other hand, if the window is too small, the magnetic signal
may not contain enough information from the deepest magnetization
variations. There have been some discussions about the choice of
window sizes (e.g. Okubo et al. 1985; Maus et al. 1997; Lin et al.
2005; Nuri Dolmaz et al. 2005), and the windows chosen mostly
range from 60 × 90 km2 to 150 × 150 km2 in sizes, but even much
larger windows have also been advocated (Chiozzi et al. 2005;
Ravat et al. 2007). In general, in volcanic areas or other tectonically
or geothermally active areas, it is appropriate to choose smaller
windows as Zb are expected to be small, whereas in tectonically
stable areas, larger windows can improve the computational stability
and accuracy. Our study area around the SCS is a tectonically young
and volcanically active area, and we think a medium-sized window
can be appropriate.
Nevertheless, we try three different of window sizes to better
understand how they would affect the estimated Zb (Table 1). At
first we use a fixed window size of 99.2 × 99.2 km2 . Within each
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Figure 3. (a) Normalized autocorrelation of window A; (b) The amplitude spectrum and estimate of Zt from window A; (c) The wavenumber-scaled amplitude
spectrum and estimate of Z 0 from window A; (d) The estimate of Zt and Zb using the nonlinear inversion method in window A; (e) Normalized autocorrelation
of window B; (f) The amplitude spectrum and estimate of Zt from window B; (g) The wavenumber-scaled amplitude spectrum and estimate of Z 0 from window
B; (h) The distribution of estimated Zb from the centroid method in the study area of Fig. 2.
Table 1. List of parameters in estimating Zb using different window sizes.
Window size (km2 )
Total number of windows
Moving step in horizontal directions (km)
Number and percentage of windows showing spectral peaks
window, the depth to the top bound (Zt ) and the centroid (Z 0 ) of
the magnetic layer is calculated from radially averaged amplitude
spectrum based on eq. (4) and wavenumber-scaled amplitude spectrum according to eq. (5), respectively. Zb is then estimated from
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44 × 54
34.1
144 ∼ 6.1 per cent
99.2 × 99.2
30 × 37
49.6
80 ∼ 7.2 per cent
144.15 × 144.15
30 × 37
48.05
27 ∼ 2.4 per cent
eq. (6). Fig. 3 shows two examples of normalized autocorrelation
functions and amplitude spectra of the total field magnetic anomalies from windows A and B shown in Fig. 2, respectively, along
with a histogram of the estimated Zb . Window A is located in the
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southwest sub-basin of the central SCS Basin, while window B is
located onshore China (Fig. 2). Although magnetic anomalies from
windows A and B are distinctly different, their normalized autocorrelation functions are almost the same, all showing near-circular
autocorrelation coefficients (Fig. 3). This indicates that there are no
strong trends in the data that could modify the slopes of the radially
averaged spectra (Shuey et al. 1977; Ravat et al. 2007). Using a
fixed window size of 99.2 × 99.2 km2 , our calculations show that Zt
ranges from 2.8 to 6.5 km, Z 0 from 10.6 and 28.1 km and Zb from
13.5 to 49.4 km with a mean of 30.4 km (Fig. 3). The map of Zb is
shown in Fig. 4.
Now with a reduced window size of 68.2 × 68.2 km2 , we again
estimate Zb and the result is shown in Fig. 5. Comparison between
Fig. 5 and Fig. 4 shows that the map of Zb estimated using a smaller
window has a higher resolution, but the general pattern and important features of Zb have little changes. There are only minor local
variations. We next test a window of 144.15 × 144.15 km2 and the
estimated Zb is shown in Fig. 6. Again, the general pattern and im-
portant features are kept almost the same despite at a much lower
resolution.
To understand exactly how Zb varies with different window sizes,
we subtract Zb estimated using one window size from that using another. Fig. 7 is one example showing the difference in Zb
between using window sizes of 68.2 × 68.2 km2 and 144.15 ×
144.15 km2 . It is clear that the Zb difference is almost randomly
distributed and averaged almost at zero, and there are no large or
persistent patterns caused by changing windows, although the size
of the moving window is more than doubled from 68.2 × 68.2 to
144.15×144.15 km2 . On statistics, increasing the window size from
68.2 × 68.2 to 99.2×99.2 km2 slightly increases Zb by 0.6478 km on
average, with a standard deviation (σ ) of 2.1338 km in the difference
of Zb (Fig. 8a). Surprisingly, the mean (μ) of the Zb difference even
drops a little when we change the window size from 99.2 × 99.2 to
144.15 × 144.15 km2 , and the σ in Zb difference is now 2.4168 km
(Fig. 8b). A bigger jump in window sizes from 68.2 × 68.2 to
144.15 × 144.15 km2 leads to a larger standard deviation (σ ) of
Figure 4. Map of depths to the magnetic layer bottom (Zb ) estimated using a moving window size of 99.2 × 99.2 km2 . Overlapped on the map are isobath
contours of 1000, 2000 and 3000 m, respectively. D-PU = Dongsha-Penghu Uplift; C-TD = Chaoshan-Tainan depositional system; ZNF = Zhongnan Fault.
The star symbol locates where the listric crustal fault shown in Fig. 13 is identified. A, B and C are areas with abnormal Zb discussed in the text.
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Figure 5. Map of depths to the magnetic layer bottom (Zb ) estimated using a moving window size of 68.2 × 68.2 km2 .
3.0579 km in the Zb difference (Fig. 8c), which is expected; meanwhile, the mean (μ) of Zb difference, which is now 0.6334 km, is
coincidental to the summation of the mean of Zb difference between
window sizes of 68.2 × 68.2 km2 and 99.2 × 99.2 km2 , and that
between 99.2 × 99.2 and 144.15 × 144.15 km2 .
It is therefore suggested from our numerical experiment that,
in the SCS area, the sizes of moving windows have only minor
effects on the estimated Zb . In our study area, while larger windows
could preferentially capture more contributions from deeper local
bottoms of magnetic sources, they could also smear local features
that potentially have deeper bottoms. Furthermore, by enlarging the
window, long wavenumber components and/or spectra of uniformly
magnetized layer could also gain more portions of power enough to
disguise the peak on the amplitude spectrum.
This could have explained why in this study only a very small
fraction of windows show spectral peaks (Table 1), and most windows showing spectral peaks are within the central basin of the
SCS where the bottom of the magnetic layer are expected to be
shallow. 80 out of a total number of 1110 windows show spectral
peaks when the window size is 99.2 × 99.2 km2 , and this amounts
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peaks drops down to about 6.1 and 2.4 per cent when the window size is 68.2 × 68.2 and 144.15 × 144.15 km2 , respectively
(Table 1). This observational fact contradicts our common presumption that more spectral peaks could appear if we enlarge the
window.
Whenever a peak occurs we also automatically estimate Zb using
both the spectral peak method (Connard et al. 1983) and the nonlinear inversion technique (eq. 9). When the spectral peak method is
applied, a priori information for Zt is required. In this study we use
Zt obtained from the centroid method (Tanaka et al. 1999) and then
estimate Zb using eq. (7). This procedure forms a hybrid method and
we obtain Zb in 80 windows. As mentioned earlier, our inversion
scheme can obtain Zt and Zb simultaneously, though the direct nonlinear inversion operation can sacrifice the computational stabilities
and can fail occasionally in some windows. Using this technique
we obtain stable inversions of Zb from 73 windows.
We correlate Zb estimated from different methods in Fig. 9. Zb
from the non-linear inversion technique show the largest variance,
while the variance of Zb estimated using the spectral peak method
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Figure 6. Map of depths to the magnetic layer bottom (Zb ) estimated using a moving window size of 144.15 × 144.15 km2 .
is the smallest. The large Zb variance from the non-linear inversion
technique is understandable, since the inversion technique we applied in this study employs a non-linear scheme that can potentially
produce fluctuating results. Additionally, the goal function of the
non-linear inversion could be trapped at local rather than global
minima. Despite these different variances, the mean of Zb from
different techniques are very close. More importantly, from both
visual inspection and crossplots of Zb , these different groups of Zb
are linearly correlated one with another (Fig. 9), although for each
individual window the three estimates of Zb can differ by many
kilometres. This good correlation offers a strong verification on our
estimated Zb (Figs 4, 5 and 6), which is the basis for our further
analysis in the next section.
4 T E C T O N I C I M P L I C AT I O N S O F Zb
4.1 The central basin
It is shown by Figs 4, 5 and 6 that most parts of the central basin of
the SCS have distinctly small Zb . In the central basin the average Zb is
about 22 km below the sea level whereas in the surrounding regions
Zb are averaged at about 34 km. This large contrast is expected
as the central basin is floored by an oceanic crust formed from
about 32–16 Ma (e.g. Taylor & Hayes 1980; Briais et al. 1993; Yao
et al. 1994; Wang et al. 2003) and has relatively higher surface heat
flow (Shi et al. 2003). Today the central basin undergoes thermal
subsidence. Within the east sub-basin (Fig. 1), it is found that the
northern half has smaller Zb than the southern half across the relict
spreading centre (Figs 4, 5 and 6).
The eastern part of the southwest sub-basin of the SCS (area A in
Fig. 4) shows even smaller Zb than the east sub-basin (Figs 4, 5 and
6). This attests again that, across the Zhongnan Fault (Figs 1 and
2), the two sub-basins differ profoundly in their magnetic patterns
and therefore differ likely in their evolutionary settings and deep
structures (Li et al. 2007b, 2008a). Further studies are needed to
understand whether the difference in Zb could trigger a contrast in
the differences of magnetic anomalies between the two sub-basins.
However, floored with the same oceanic crust as in the eastern part
of the southwest sub-basin, the southwest corner of the southwest
sub-basin (area B in Fig. 4) does not show small Zb . The same is
true with the northwest sub-basin (area C in Fig. 4), which is floored
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Figure 7. The difference in Zb between using a window size of 144.15 × 144.15 km2 and that of 68.2 × 68.2 km2 .
by oceanic crust but shows no anomalies in Zb . We note these two
parts of the ocean basin have common features in that they both
are narrow oceanic crust at the feather edges of the central ocean
basin, and are adjacent to attenuated continental blocks. This type
of tectonic setting may allow rapid lateral thermal conduction and
cooling of the oceanic lithosphere, thereby leading to larger Zb .
An alternative explanation is that there has been no significant
original magmatism and thermal anomalies associated with these
branches of the ocean basin, so that their present-day bottom bounds
of magnetic layer show not much differences in depths to those in
the adjacent continental blocks. Future studies on magmatism and
thermal evolution within these branching oceanic basins may bring
important insights into interactions between continental and oceanic
lithospheres.
In continental regions, it was argued from measured magnetisms
of mantle xenoliths that the magnetic crust in general overlies a
non-magnetic mantle and the Moho represents a magnetic boundary
(Wasilewski et al. 1979; Wasilewski & Mayhew 1992). This seems
to be true for the continental blocks surrounding the central basin
of the SCS, where the estimated average Zb (∼34 km) is close to
the Moho depth (Fig. 10). However for the oceanic lithosphere it
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uppermost part of the mantle has magnetization in some oceanic
regions (e.g. Counil et al. 1989; Chiozzi et al. 2005). Based on the
traditional Parker–Oldenburg algorithm (Parker 1973; Oldenburg
1974), we also estimate the Moho depths in the area (Fig. 10)
from a simple Bouguer gravity data set we obtained earlier with
the assumed correcting density of 2.67 g cm−3 for shallow crustal
materials (Li et al. 2007a). Bouguer gravity anomalies have been
taken routinely to estimate depths to the Moho, owing to the fact that
Moho represents the largest density contrast in the lithosphere and
contributes the most to Bouguer gravity anomalies. We assume that
across the Moho there is a constant density contrast of 0.5 g cm−3 ,
which is a reasonable estimate based both on the global earth model
(Dziewonski & Anderson 1981) and on regional studies. It is found
that the Moho depths in the central basin of the SCS are mostly
less than 15 km below sea level (Figs 10 and 11), and this depth
range is consistent to that estimated from gravity and/or seismic
data by other researchers (Liu et al. 1983; Xu & Jiang 1989; Chen
& Jaw 1996; Xia 1997; Nakamura et al. 1998; Shih 2001). The Zb in
most parts of the central basin, estimated to be about 22 km below
the sea level, is apparently much deeper than the average Moho
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Figure 8. The histograms of the Zb differences between using different window sizes. The solid red curves are normal fits to the histograms. μ and σ are the
mean and standard deviation of the normal fit, respectively.
depth (Fig. 11). This implies that roughly the uppermost 10 km
of the mantle beneath the central basin is also magnetized. Zhang
(2003) also made a similar observation from a study of satelliteand aero-magnetic anomalies in China.
4.2 Northern continental margin and continent–ocean
transition (COT) zone
Structurally the northern continental margin of the SCS is very complicated (Li et al. 2007b, 2008a), but in general the depressions and
uplifts are in NE orientations, subparallel to the present-day continental shelf (Figs 11 and 12). The distribution of Zb in the northern
continental margin also follows the same pattern. We find that the
Dongsha–Penghu Uplift roughly corresponds to a zone with small
Zb (Figs 4, 5 and 6), while to its immediate south the ChaoshanTainan Mesozoic depositional system (Li et al. 2008a) shows large
Zb . An abnormally depressed bottom of the magnetic layer has
also been found beneath another Paleozoic–Mesozoic sedimentary
basin, the southern Yellow Sea Basin located between China and
Korea (Li et al. 2009). It is likely that the hot lithosphere of an active
basin can later cool down to present abnormally large Zb .
Further south on the COT zone, our calculation shows a zone with
reduced Zb (Figs 4, 5 and 6) that is subparallel to the continental
margin and the general trends of depressions and uplifts (Figs 11 and
12). This pattern shows up consistently on the Zb maps estimated
with different window sizes (Figs 4, 5 and 6). The COT zone here
is heavily faulted and accompanies widespread recent magmatism
(Tsai et al. 2004; Li et al. 2007b, 2008a). The small Zb here may
be interpreted as relative to the strong faulting and/or magmatism.
Deep reflection seismic surveys in the area have identified many
landward dipping strong reflectors, which can be interpreted as
crustal faults (Hayes et al. 1995; Li et al. 2008b). Figs 11 and 13
show a thorough-going crustal fault, which bounds a big igneous
body to its south, and a half-graben to its north. This listric fault
and associated graben are important features along the northern
SCS continental margin, and this fault in particular represents the
northern edge of the COT zone (Li et al. 2008b).
From Figs 4, 5 and 6, it is noticed that the thorough-going crustal
fault is spatially located on a belt of small Zb . We can further examine
tectonic events associated with this fault based on seismic stratigraphy from the seismic section (Figs 11 and 13), and see if by any
means can this fault and associated half-graben and magmatic body
be related with small Zb . One particular sequence boundary Tom
can be easily identified from the seismic section shown in Fig. 13.
ODP Leg 184 has confirmed that Tom is the Oligocene–Miocene
boundary, which has strong seismic reflections and coincides with
a zone of tectonic slump and erosion (Wang et al. 2000; Li et al.
2005). Li et al. (2005) interpreted that this unconformity corresponds probably to changes in the rotation of different land blocks
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Figure 9. (a) Zb estimated from the centroid and the nonlinear inversion methods for 73 windows where there are stable nonlinear inversions of Zb . (b) Zb
estimated from the centroid and spectral peak methods for 80 windows which show spectral peaks. (c) A cross plot of Zb estimated from the centroid method
and Zb from the nonlinear inversion method for 73 windows. (d) A cross plot of Zb estimated from the centroid method and Zb from the spectral peak method
for 80 windows. The solid red lines in (c) and (d) are the linear trends of correlations.
and to a ridge jump in the seafloor spreading ridge of the SCS. Tom
found near the COT zone, as seen in Fig. 13, also appears to merge
with a break-up unconformity in the half-garben, where it is likely
underlain by strongly deformed Pre-Miocene syn-rifting sediments.
Tom is apparently diachronous and to the north it can be underlain
directly by Mesozoic metasedimentary rocks. The angular unconformity and the fold structure in the half-graben are evidence that
the seafloor spreading in the SCS accompanied an episode of compression in the northern continental margin. The emplacement of
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the unconformity Tom and younger sediments (Fig. 13). The COT
zone in the northeastern SCS continental margin is characterized by
emplacements of numerous post-spreading intrusive and extrusive
igneous bodies (Tsai et al. 2004; Wang et al. 2006; Yan et al. 2006;
Li et al. 2007b, 2008b).
These widespread and young magmatic emplacements and strong
faulting can explain the small Zb in the northeastern SCS basin and
the COT zone, which are not underlain by typical oceanic crusts
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Figure 10. The Moho topography in the SCS area estimated from Bouguer gravity anomalies using the Parker–Oldenburg algorithm (Parker 1973; Oldenburg
1974).
(Wang et al. 2006; Li et al. 2007b). It has been noted that Zb tend
to be reduced drastically in areas of active volcanism and faulting, such as in the Ryukyu Arc and Japan Island, in the Changbai
Mountain, the Jingbo Lake and the Wudalian Lake of NE China,
and in the volcanic Cheju Island of Korea (Okubo et al. 1985;
Hu et al. 2006; Li et al. 2009). On the northern SCS continental
margin, Shi et al. (2003) identified a high heat flow zone, which
roughly coincides with the zone of small Zb we identified in this
study, and also corresponds very well with a fault zone (Xia &
Zhou 1993; Liu 1994). It seems therefore that heat flow, faulting
and bottom bound of magnetic layer here are strongly coupled in this
zone.
Near the Pearl River Mouth Basin (PRMB) further north, the bottom bound to the magnetic layer and the Moho interface gradually
merge (Fig. 11). This is in line with the argument that, beneath the
continent, the Moho represents a magnetic boundary (Wasilewski
et al. 1979; Wasilewski & Mayhew 1992). Once again from Fig. 11,
we notice that even though Zb estimated with different window
sizes can differ locally by a few kilometres, they overall match
with one another very well and have the same regional trend. It can
also be confirmed from Fig. 11 that increasing window sizes does
not necessarily increase the estimated Zb other than lowering their
resolution.
5 C O R R E L AT I O N S B E T W E E N Zb
A N D S U R FA C E H E AT F L O W
Since magnetic layer bottom Zb constitutes an undulating surface in
the Earth’s interior where minerals reach their Curie temperatures
and lose their ferromagnetism, Zb could offer important insights
into the thermal state of the upper mantle and crust. The Curie
temperature varies with composition, but if magnetite is the only
mineral that characterizes the rock magnetization, the temperature
at Zb can be assumed at about 550 ◦ C.
To better examine the possible correlation between Zb and surface heat flow, we collected 355 surface heat flow measurements
in the area (Fig. 14). Most studies on Curie point depths include
discussions on the likely correlation between Zb and surface heat
flow, and generally, positive correlations between high heat flow and
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Journal compilation Figure 11. (a) Total field magnetic anomaly and Bouguer gravity anomaly along the seismic line AB shown in Fig. 1. (b) The seismic profile AB along with fault interpretations. (c) The depths to the Moho, and
Zb estimated with different window sizes along seismic line AB. TWTT = two way travel time. COT = continent-ocean transition zone. PRMB = Pearl River Mouth Basin. w = the width of moving windows.
Curie-point depths in the South China Sea
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Figure 12. Shaded relief map showing major Mesozoic and Cenozoic tectonic units near the northern SCS continental margin. Two isobaths shown on the
map are 500 and 3000 m, respectively. CD = Chaoshan Depression; COT = continent-ocean transition zone; DS = Dongsha Rise; D-PU = Dongsha-Penghu
Uplift; LRTPB = Luzon-Ryukyu Transform Plate Boundary; TNB = Tainan Basin; The blue rectangular box shows the location of the seismic section in
Fig. 13. The solid black line is a segment of the seismic line AB. The dotted red line indicates the projected trace of the crustal fault shown in Figs 11 and 13.
Figure 13. Seismic section showing a landward-dipping listric crustal fault, which bounds a big igneous body to its south, and a half-graben to its north.
Horizon Tom is the Oligocene–Miocene boundary coincidental with a zone of tectonic slump and erosion (Wang et al. 2000; Li et al. 2005). Tg = basement.
TWTT = two way travel time. COT = continent-ocean transition zone. See Figs 11 and 12 for the location of this seismic section.
small Zb are supported (Okubo et al. 1985; Liu et al. 1996; Tanaka
et al. 1999; Lin et al. 2005; Nuri Dolmaz et al. 2005; Hu et al. 2006).
However in tectonically complex areas and old tectonic domains,
a well-documented correlation may not be the plausible expecta-
tion, since there are many other factors, such as local geothermal
gradient, heat productivity, fault activity and lithology that would
perturb a simple conductive link between surface heat flow and a
deep geotherm (e.g. the Curie point depth).
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Figure 14. Grey-scaled contour map of surface heat flow in the SCS area. Locations of heat flow measurements are also plotted on the map in different colours
and symbols according to their heat flow ranges. The yellow contours mark the 3000 m isobaths. Data are compiled from Taylor & Hayes (1983), Pollack et al.
(1991), Rao & Li (1991), Xiong et al. (1993), Nissen et al. (1995), Shyu et al. (1998), Shi et al. (2003), and Xu et al. (2006).
It occurs that the opening of the SCS is a young tectonic event
and, although the opening mechanism and sequence have yet to be
better understood, the crustal affiliations of different tectonic domains remain tractable in the area. Therefore an overall correlation
between Zb and surface heat flow is expected. Fig. 14 shows that the
central SCS basin in general has higher heat flow than surrounding
regions. This is expected because the central basin is mostly floored
by a young oceanic crust. By comparing the heat flow map (Fig. 14)
with the Zb map (Figs 4, 5 and 6), it is found that most areas with
high heat flow (mostly in the central basin) correspond preferably
with areas showing small Zb . This implies that in our study area the
deep mantle geothermal state has a significant contribution to the
surface heat flow (Shi et al. 2000, 2003).
We can study the correlation more quantitatively by making a
cross plot of Zb versus surface heat flow (Fig. 15). We have grouped
the surface heat flow and Zb in Fig. 15 according to different geological subprovinces. Despite a large scattering in the plotted points,
most of the data points follow a clear trend showing an inverse correlation between surface heat flow and estimated Zb . This relationship
is theoretically sound, since from the solution of heat conduction
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have a simplified steady state relationship (Stüwe 2002; Turcotte &
Schubert 2002)
qs ≈ k
Tc
+ Sr ,
Zb
(10)
in which qs is surface heat flow measurements, k is the bulk average or effective thermal conductivity for the magnetic layer, Tc
is the Curie temperature and Sr represents a term related to heat
contributions from radioactive sources. The SCS is a tectonically
young unit (ca. 32–16 Ma), but ca. 16 Ma ago the seafloor spreading
process completely stopped, thus validating a steady state approximation like eq. (10). When eq. (10) is applied to the crust and
the uppermost mantle, it requires an effective thermal conductivity
representing the average of thermal conductivities of a variety of
lithology at different temperatures and pressures. Thermal conductivities vary significantly with lithology, temperature, pressure, and
therefore depth (Beardsmore & Cull 2001). Thermal conductivities measured at the surface, where the loose sediments can have
very low thermal conductivities less than 1.0 W (m◦ C)−1 , cannot
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Figure 15. Approximately an overall inverse correlation between surface heat flow (qs ) and Zb in the SCS area. Solid lines are theoretical curves based on
eq. (10) for different bulk average thermal conductivities, assuming a constant Curie temperature of 550 ◦ C and an arbitrary radioactive source contribution
of 10 mW/m2 to the surface heat flow. Different types of symbols represent data from different sub-provinces, which are onshore southeast China, northern
SCS continental shelf, the SCS Basin where the water depths are larger than 3000 m, the SCS Basin where the water depths are smaller than 3000 m, offshore
southwest Taiwan, the Sulu Sea, the Western Philippine Sea and the Okinawa Trough.
represent those measured at other depths. In our study area, it is
found that thermal conductivities measured near the seabed are almost constantly below 1.0 W (m◦ C)−1 (Taylor & Hayes 1983; Shyu
et al. 1998), thermal conductivities estimated from drilling holes
on the northern continental shelf are averaged at 1.865 W (m◦ C)−1
(Rao & Li 1991), and rock experiments from onshore China show
that thermal conductivities can be anywhere between 1.85 and 9.06
W (m◦ C)−1 (Xiong et al. 1993). However, it should be remembered that these observed thermal conductivities, measured within
limited lithology, pressure and temperature ranges, can represent
neither regional variations nor averages of thermal conductivities of
the magnetic layer within the crust and uppermost mantle. The lack
of accurate information of depth variations in thermal conductivities
makes it difficult to evaluate geotherms.
On the other hand, it is meaningful to assume an average effective
thermal conductivity for the magnetic layer in a region in a simple
conductive model as shown by eq. (10), despite the difficulties in assessing the exact values of average thermal conductivities. In Fig. 15
we draw theoretical curves of eq. (10) assuming a constant Curie
temperature of 550 ◦ C and an arbitrary radioactive source contribution of 10 mW m−2 to the surface heat flow. It can be noticed that
most data points in the cross plot of qs versus Zb are clustered near
the theoretical curves with average thermal conductivities between
about 3.0 and 4.0 W (m◦ C)−1 . We have grouped the qs and Zb in
Fig. 15 according to different geological subprovinces, and found
insignificant variations in the bulk average thermal conductivity of
the magnetic layer across different subprovinces. Since both the top
and the bottom of the magnetic layer are determined, the thermal
conductivity in eq. (10) represents the bulk average effective thermal
conductivity for a simple two-boundary configuration. Therefore to
understand the general relationship between the surface heat flow
and the lower thermal boundary (the Curie depth), we need not to
invoke a depth variation (whether it is linear or of any other kinds)
in the thermal conductivity but simply to assume a constant bulk
average effective thermal conductivity of the magnetic layer.
6 C O N C LU S I O N
In this paper we estimate depths to the bottom of magnetic layer
(Zb ) in the SCS area by calculating radially averaged amplitude
spectra of total field magnetic anomalies. In estimating Zb , we test
three different window sizes, and find that varying window sizes
from 68.2 × 68.2 to 144.15 × 144.15 km2 has insignificant effect
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Journal compilation Curie-point depths in the South China Sea
on estimated depths and patterns in the magnetic layer bottom but
lowers the resolutions of the map of Zb . Statistically from the histograms, it is found that changing the window size from 68.2 × 68.2
to 99.2 × 99.2 km2 only increases Zb by 0.6478 km on average, and
from 99.2 × 99.2 to 144.15 × 144.15 km2 the average Zb even drops
slightly.
For all the three window sizes, the numbers of windows showing spectral peaks take only very small fractions, and increasing
the window size does not necessarily incur more spectral peaks. It
is possible that while larger windows preferentially capture more
contributions from deeper magnetic sources in the study area,
they could also smear local features that potentially have deeper
bottoms.
Although the centroid method (Tanaka et al. 1999) is our primary
means of estimating Zb since it gives stable result within each single
window, whenever a spectral peak occurs in a window our computer
program automatically applies the spectral peak method (Connard
et al. 1983) and the non-linear inversion method to calculate Zb .
The inversion method we applied using a non-linear least-squares
scheme can invert Zb directly without a priori information of either
Zt (required by the spectral peak method) or Z 0 (required by the
centroid method) for most windows showing spectral peaks, but Zb
from this method have the largest variance, indicating possibly some
inherent instabilities in the non-linear method. Results from the
spectral peak method, on the other hand, have the smallest variance,
partly due to the fact that the peak is found always fixed at the
wavenumber 0.015 km−1 in our calculations. Despite these different
variances, the averages of Zb from different methods are very close,
and Zb estimated with one method are overall linearly correlated
with those from another, although for each single window Zb from
different methods can differ by a few kilometres.
It is found that Zb in most parts of the central SCS oceanic
basin is considerably smaller, by approximately 12 km, than that
of the surrounding continental blocks where Zb are averaged at
about 34 km. Exceptions exist around the western feather edges
of the northwest and the southwest sub-basins, where the oceanic
lithosphere does not accompany local uplifts in the bottom bound of
magnetic layer. These exceptions can be attributed to rapid lateral
thermal conduction and cooling of the oceanic lithosphere, or to a
lack of sufficient original magmatism associated with these narrow
oceanic blocks. The eastern part of the southwest sub-basin shows
slightly smaller Zb than eastern sub-basin (Fig. 5), indicating once
again the sharp contrast between the two sub-basins (Li et al. 2007b,
2008b). Within the east sub-basin, the northern half of the sub-basin
appears to have smaller Zb than the southern half to the south of the
relict spreading centre.
The fact that the estimated Zb in the central SCS basin is larger
than the Moho depths implies that approximately the uppermost
10 km of the mantle here is also magnetized. Magnetization in the
uppermost part of the mantle is also observed beneath some oceanic
crusts (Counil et al. 1989; Chiozzi et al. 2005).
The strongly faulted and magmatically intruded northern COT
zone has overall small Zb . In particular, within the COT there appears to be a shallow Curie-point belt that coincides with a fracture
zone and a high heat flow zone (Xia & Zhou 1993; Liu 1994;
Shi et al. 2003). These observations indicate that strong faulting
and magmatism as well as high surface heat flow within the COT
are coupled with geothermal upwelling at depth. On the northern
continental margin, the NE-striking Chaoshan-Tainan Mesozoic depositional system (Li et al. 2008a) roughly corresponds with a zone
of large Zb while by contrast the NE-striking Dongsha-Penghu uplift
in general matches a zone with small Zb .
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Higher surface heat flow correlates well with the estimated
smaller Zb in the central basin of the SCS, suggesting that surface
heat flow in the area bear significant contributions from mantle via
thermal conduction. The observed inverse correlation between surface heat flow and Zb is conformable to theoretical considerations.
Taken into account the large number of error sources in both heat
flow measurements and Zb estimations, the observable correlation
between heat flow and Zb , as well as linear correlations we found
between Zb from different techniques, all suggest that our estimated
Zb are within an acceptable range of accuracy.
AC K N OW L E D G M E N T S
Seismic data were acquired with vessel ‘Shiyan-2’ by SCS Institute
of Oceanology. We thank the officers and crew for their contributions. Data processing is supported by the USGS potential field
software (Cordell et al. 1993; Phillips 1997), and by GMT (Wessel &
Smith 1995). Critical and constructive comments from two anonymous reviewers have greatly improved the paper. We also thank editors Richard Holme and Michel Diament for their comments and
assistances. This research is funded by Chinese National Basic Research and Development Program (Grant 2007CB411702), National
Science Foundation of China (Grants 40776026 and 40876022), and
by Program for New Century Excellent Talents in University.
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