Summary

It has long been challenging to identify magnetic anomalies due to seafloor spreading in the equatorial Pacific. Here we show that Project Magnet vector aeromagnetic profiles from the equatorial Pacific record magnetic anomalies due to seafloor spreading much more clearly than do shipboard total intensity profiles. The anomalies are reliably recorded at wavelengths between ≈20 and ≈150 km in the vertical and east components, which have high coherence, differ in phase by ≈90°, and resemble synthetic magnetic anomaly profiles. From an analysis of a single near-equatorial vector aeromagnetic profile we infer that the magnetic lineations strike ≈8°–10° counter-clockwise of north and that magnetic anomaly 7 is located ≈400 km further east than previously estimated. The newly estimated location of anomaly 6 is consistent with a tentative estimate by Wilson from a low-amplitude shipboard magnetic profile. Because the skewness of profiles over the seafloor formed near the paleoequator changes rapidly with paleolatitude and paleostrike, a skewness analysis of these data may provide useful bounds on the location of Pacific Plate paleomagnetic poles, and indicate that this seafloor has had little, if any, northward motion relative to the spin axis since it formed.

Introduction

It has long been challenging, if not impossible, to identify magnetic anomalies due to seafloor spreading in the equatorial Pacific because the amplitude of the anomalies is small compared with the magnetic noise. Most marine magnetic surveys measure only the total intensity of Earth’s magnetic field and not its vector components. The amplitude of the magnetic field produced by the geodynamo (≈30 000–50 000 nT) is much larger than the amplitude of magnetic anomalies due to seafloor spreading (≈50–1000 nT). Thus the total field intensity is in effect the component of the crustal field that is parallel to the field produced by the geodynamo. It follows that the component of the crustal magnetic field recorded in total intensity magnetic profiles near the equator is nearly horizontal and nearly due north. A magnetized seafloor produces a magnetic field with a negligible horizontal component parallel to the strike of the magnetic lineations. Thus the peak-to-trough total intensity anomaly (i.e. the observed field minus the appropriate reference field) over the near-equatorial seafloor with magnetic lineations striking nearly north–south is small (≈150 nT at the sea surface), where interpretable (Petronotis 1994; Petronotis & Gurden 1999) and presumably smaller elsewhere.

In contrast, the diurnal variation of the magnetic field intensity (due to time-varying currents in the ionosphere) near the equator has a peak-to-trough amplitude of up to ≈200 nT when the effect of the electrojet is included (Sager 1983). A typical ship speed while collecting magnetic data is ≈18 km h−1 or ≈430 km d−1. The width of constant-polarity seafloor formed in the equatorial Pacific during the longer geomagnetic polarity chrons can span 100 km or more. A ship travelling above a single magnetic stripe would take ≈6 h to cross it. At crossing times this long, the diurnal variation of the geomagnetic field interferes with the magnetic anomalies due to seafloor spreading (Fig. 1), resulting in a low signal-to-noise ratio of the latter.

Figure 1

The shipboard total intensity magnetic anomaly profile from the DOLP02HO cruise from 135°W to 105°W is plotted versus time. The reference field has been removed. The vertical dashed lines show the time of maximum daily residual, which is near midday local time. The elapsed time in hours (Δt) between the peaks indicated by the vertical dashed lines is shown at the top of the figure. The mean Δt is 24.09 ± 1.6 h. Numerals beneath the profile indicate magnetic anomaly identifications. The largest features of the profile appear to be produced by diurnal variation enhanced by the electrojet.

Figure 1

The shipboard total intensity magnetic anomaly profile from the DOLP02HO cruise from 135°W to 105°W is plotted versus time. The reference field has been removed. The vertical dashed lines show the time of maximum daily residual, which is near midday local time. The elapsed time in hours (Δt) between the peaks indicated by the vertical dashed lines is shown at the top of the figure. The mean Δt is 24.09 ± 1.6 h. Numerals beneath the profile indicate magnetic anomaly identifications. The largest features of the profile appear to be produced by diurnal variation enhanced by the electrojet.

Vector aeromagnetic data minimize these problems.

First, because the airplane flies at high speed, the diurnal variation is mapped into wavelengths much longer than those of anomalies due to seafloor spreading. A typical aerial survey speed is ≈630 km h−1, 35 times faster than a typical ship survey speed. Thus the diurnal variation is mapped into wavelengths of ≈15 000 km, about 100–1000 times greater than the key wavelengths for anomaly identification, effectively eliminating the noise due to diurnal variation.

Secondly, because the vector aeromagnetic data have three components, they contain more information than is contained in the total intensity data. Both useful components of the field, the horizontal component perpendicular to the strike of the magnetic anomalies due to seafloor spreading and the vertical component, are obtained. For the equatorial Pacific, the former component is nearly due east. Moreover, the solar quiet variation component of diurnal variation is largest in the north component (≈100 nT peak-to-trough), smaller in the vertical (up to 40 nT peak-to-trough, but vanishing at the equator), and negligible in the east component (Sager 1983). Thus, solar quiet variation (and its enhancement by the electrojet) should have little effect on the useful vertical and east components. This set of advantages is shared with vector magnetic data collected with a surface-towed magnetometer (Gee & Cande 2002).

Thirdly, the magnetometer travels ≈7 km above the sea surface for Project Magnet flights, resulting in a smaller peak-to-trough total intensity residual of ≈60 nT near the paleoequator versus 100–150 nT from shipboard surveys. The vector component residuals can be as large as ≈100 nT. The moderate diminution of the signal amplitude due to the higher altitude of vector aeromagnetic data, combined with the practical elimination of the noise due to diurnal variation, give a high signal-to-noise ratio.

Here we show that Project Magnet vector aeromagnetic data can be readily interpreted both for the identification of magnetic anomalies due to seafloor spreading and for paleomagnetic skewness analysis. Below we first discuss the aeromagnetic data and our interpretation of it. Next, we apply spectral and cross-spectral analysis to test our interpretation that the observed anomalies are due to seafloor spreading, to gain further information on what wavelengths contain useful information concerning the anomalies produced by the oceanic crust, and to estimate the depth to the source of the anomalies. We then infer the age of the seafloor from our anomaly identifications and compare it with independent observations. Finally, we examine the paleolatitude of the oceanic crust that we infer from the shape of the anomalies.

Aeromagnetic Data

That Project Magnet vector aeromagnetic data record Pacific equatorial anomalies due to seafloor spreading, can be demonstrated in several ways. First, we do so by visual inspection. For example, Fig. 2 shows part of profile NAV4138, which is National Geophysical Data Center profile 0550-047, collected on 1989 June 28. The largest vector component along the profile is north (≈30 600– 31 100 nT), with an amplitude nearly as large as the total field intensity (≈31 600–31 800 nT) (Fig. 2a). The amplitudes of the east (≈4800–5000 nT) and vertical (≈4000–6500 nT) components are smaller (Fig. 2b). The decrease in east component amplitude along the profile indicates a decrease in declination from the west to the eastern end of the profile. The vertical component is positive (down), which indicates that the profile was collected north of the magnetic (dip) equator. The amplitude of the vertical component increases to the east, suggesting that the distance of the profile from the magnetic equator increases to the east. This is consistent with the reference field, which has a smaller positive inclination at the western end than at the eastern end of the profile.

Figure 2

Components of the magnetic field before and after several processing steps are plotted versus distance along track for an east–west Pacific equatorial segment of Project Magnet Flight 0550-047. The flight path is west to east from 130°W to 110°W with a latitude range of 0.0106°N to 0.0291°S, similar in location to the shipboard profile shown in Fig. 1. The time elapsed during the collection of this section of profile was 3.38 h (12 169.16 s) from 11:04:29.24 GMT to 14:27:18.40 GMT on 1989 June 28. Sunrise at the eastern end of the profile was at 13:20 GMT. (a) Raw total field and north vector component. (b) Raw east and vertical vector components. (c) Airplane altitude. (d) Total intensity residual (reference field removed). (e) North component residual. (f) East component residual. (g) Vertical component residual. (h) Deskewed residual north component, phase shift 236°. (i) Deskewed residual east component, phase shift 186°. (j) Deskewed residual vertical component, phase shift 99°. (k) Three synthetic magnetic anomaly profiles. The middle profile has zero phase shift (ZPS), which is equivalent to assuming vertical downward magnetization and vertical downward ambient magnetic field. The synthetic profiles above and below the ZPS profile are phase shifted by +30° and −30°, respectively. At the bottom of the figure is the block model assumed to calculate the synthetic profiles: black regions indicate normal polarity, numerals indicate the normal polarity chron numbers. The synthetic magnetic anomaly profiles are calculated using the timescale of Cande & Kent (1995), while assuming a variable spreading half rate, which averages 100 mm yr−1, vertical boundaries between polarity reversals, downward vertical magnetization of the seafloor, a downward vertical ambient field, north–south lineation azimuth and a 0.5 km thick vertically magnetized source layer located 4.25 km below sea level. To simulate the finite distance over which the polarity changes sign, a Gaussian transition-width filter (Blakely 1976) of 6 km is used in calculating the synthetics. The phase shifts applied to the profiles were estimated from the phase spectra between the residual north, east and vertical components, on the one hand, and the ZPS synthetic, on the other. Each deskewed residual is shown twice. The thick grey curves show unfiltered deskewed residuals. The thin black curve on top of each grey curve shows the same deskewed residual after a low-wavenumber bandpass filter (eq. 1) has been applied.

Figure 2

Components of the magnetic field before and after several processing steps are plotted versus distance along track for an east–west Pacific equatorial segment of Project Magnet Flight 0550-047. The flight path is west to east from 130°W to 110°W with a latitude range of 0.0106°N to 0.0291°S, similar in location to the shipboard profile shown in Fig. 1. The time elapsed during the collection of this section of profile was 3.38 h (12 169.16 s) from 11:04:29.24 GMT to 14:27:18.40 GMT on 1989 June 28. Sunrise at the eastern end of the profile was at 13:20 GMT. (a) Raw total field and north vector component. (b) Raw east and vertical vector components. (c) Airplane altitude. (d) Total intensity residual (reference field removed). (e) North component residual. (f) East component residual. (g) Vertical component residual. (h) Deskewed residual north component, phase shift 236°. (i) Deskewed residual east component, phase shift 186°. (j) Deskewed residual vertical component, phase shift 99°. (k) Three synthetic magnetic anomaly profiles. The middle profile has zero phase shift (ZPS), which is equivalent to assuming vertical downward magnetization and vertical downward ambient magnetic field. The synthetic profiles above and below the ZPS profile are phase shifted by +30° and −30°, respectively. At the bottom of the figure is the block model assumed to calculate the synthetic profiles: black regions indicate normal polarity, numerals indicate the normal polarity chron numbers. The synthetic magnetic anomaly profiles are calculated using the timescale of Cande & Kent (1995), while assuming a variable spreading half rate, which averages 100 mm yr−1, vertical boundaries between polarity reversals, downward vertical magnetization of the seafloor, a downward vertical ambient field, north–south lineation azimuth and a 0.5 km thick vertically magnetized source layer located 4.25 km below sea level. To simulate the finite distance over which the polarity changes sign, a Gaussian transition-width filter (Blakely 1976) of 6 km is used in calculating the synthetics. The phase shifts applied to the profiles were estimated from the phase spectra between the residual north, east and vertical components, on the one hand, and the ZPS synthetic, on the other. Each deskewed residual is shown twice. The thick grey curves show unfiltered deskewed residuals. The thin black curve on top of each grey curve shows the same deskewed residual after a low-wavenumber bandpass filter (eq. 1) has been applied.

Removing the reference field from the observed field leaves the residual total field intensity and the residual vector component amplitudes shown in Figs 2(d)–(g). The residual total field intensity and residual north component amplitude are small and unsurprisingly similar to one another. The residual east and residual vertical component amplitudes are larger and similar in size. There is little evident correlation between the residual total field intensity and residual north component on the one hand and the residual east component on the other, except possibly at the western end of the profile. The relative amplitudes and lack of correlation are consistent with the interpretation that the residual field is mainly due to seafloor-spreading anomalies that strike nearly north–south.

Skewness

One test of whether these anomalies are due to seafloor spreading has two parts. (1) Do the residual east and residual vertical components resemble one another when one residual component is phase shifted by an amount that differs by 90° from the phase shift applied to the other? (2) When appropriately reduced to the pole do each of the residual components resemble a zero-phase-shifted (ZPS) synthetic magnetic anomaly profile, as is appropriate for the north pole?

The shape of a seafloor-spreading magnetic anomaly changes with its location because the shape depends on the remanent inclination and declination, the azimuth of the anomaly lineation, and the inclination and declination of the present magnetic field—all of which vary over the Earth’s surface (Blakely & Cox 1972; Schouten & McCamy 1972). The residual east and residual vertical components of profile 0550-047 from 130°W to 110°W near the equator show fluctuations that could be seafloor-spreading anomalies (Figs 2f and g), but do not match a ZPS synthetic seafloor-spreading magnetic anomaly profile (Fig. 2k). Phase shifting the residual magnetic profiles facilitates identification of magnetic anomalies.

Because we wished to estimate the phase shifts as objectively as possible, we used the cross-spectra between the ZPS synthetic magnetic anomaly profile and each residual vector component magnetic profile to estimate the phase shift that deskews each vector component profile. We use the mean phase of the lowest wavenumber band over which the coherence between the residual observed anomaly and the synthetic anomaly is high (between 0.0069 and 0.0125 km−1, corresponding to wavelengths of 80–145 km). The residual east component is best deskewed by a 186° phase shift and the residual vertical component is deskewed by a 99° phase shift. These phase shifts differ by 87°, which is near the expected value of 90°.

The deskewed profiles (grey curves in Figs 2i and j) illustrate the excellent agreement of the residual east component with the residual vertical component. Both agree reasonably well with the ZPS synthetic magnetic anomaly profile, although not nearly as well as they agree with one another (Fig. 2k). The agreement with the synthetic profile is, however, as good as that for any observed seafloor spreading profile of which we are aware. The good agreement between the synthetic magnetic anomalies and the observed profiles, and between the deskewed residual east and vertical profiles, convincingly shows that the vector aeromagnetic profile records equatorial seafloor-spreading anomalies.

Spectral Analysis, Depth To Basement and Power-Sum Rule

That these profiles record anomalies due to seafloor spreading can be further tested using spectral analysis. Parker & O’Brien (1997) developed a method of spectral analysis of residual vector magnetic profiles to determine the noise content of the data and to extract, if present, the signal of the crustal magnetic fields. We adopt the coordinate system of Parker & O’Brien (1997): let X be the residual horizontal along-track component of the vector field (east in this case), Z is the residual vertical (positive up) component and Y is the residual horizontal component required to form a right-handed coordinate system (north in this case). Let T be the total field magnetic residual.

Over the smallest wavenumbers the spectrum for T displayed on a linear wavenumber (k), log power spectral density (PSD) plot (Fig. 3a) is, to a first approximation, a downward-trending straight line with slope ≃−4πh, where h is the height of the magnetometer above the source (Spector & Grant 1970; Parker & O’Brien 1997). The slope (−145.7 ± 3.8 nT2 km per km−1; numbers following ± signs herein are 95 per cent confidence limits) indicates that the magnetic source is at an approximate depth of 11.6 ± 0.3 km below the airplane. Given an average altitude of 6.5 km for this section of profile 0550-047 and a mean water depth of 4.3 km, the magnetic source is at an approximate depth of 0.8 ± 0.3 km below the seafloor. The sediment thickness at nearby DSDP Sites 79 and 80 ranges from 410 to 200 m, respectively (Hays 1972a,b). Thus, the magnetic source layer is indicated to be at an approximate depth of 0.4–0.6 ± 0.3 km below the top of the basaltic crust, consistent with our assumption of a crustal source for the anomalies.

Figure 3

Spectra for an east–west equatorial segment of Project Magnet Flight 0550-047. All spectra were calculated using Thomson’s multitaper method (Thomson 1982) using a time–bandwidth product of 6, i.e. the same method as used by Parker & O’Brien (1997). We then smoothed the spectra and cross-spectra by averaging the estimate at each wavenumber with itself and the estimates at the 10 adjacent wavenumbers (five above and five below). (a) Power spectral density of residual total intensity PSDT and residual vector components PSDX, PSDY, PSDZ. For consistency with Parker & O’Brien (1997), we refer to the wavenumber band over which the power sum rule holds as band A and that over which correlated instrument-orientation noise dominates as band B. The edges of bands A and B are shown with heavy dotted lines. (b) The power sum rule. The difference between log(PSDZ) and log(PSDX+ PSDY) is shown. The heavy dotted lines are the edges of bands A and B. (c) Coherence between residual components of the profile. The XZ coherence is shown with a solid line, the XY coherence with a dotted line and the YZ coherence with a dashed line. The dark grey and light grey shaded regions correspond to wavenumber bands A and B. (d) Phase spectra corresponding to the coherences shown in (c).

Figure 3

Spectra for an east–west equatorial segment of Project Magnet Flight 0550-047. All spectra were calculated using Thomson’s multitaper method (Thomson 1982) using a time–bandwidth product of 6, i.e. the same method as used by Parker & O’Brien (1997). We then smoothed the spectra and cross-spectra by averaging the estimate at each wavenumber with itself and the estimates at the 10 adjacent wavenumbers (five above and five below). (a) Power spectral density of residual total intensity PSDT and residual vector components PSDX, PSDY, PSDZ. For consistency with Parker & O’Brien (1997), we refer to the wavenumber band over which the power sum rule holds as band A and that over which correlated instrument-orientation noise dominates as band B. The edges of bands A and B are shown with heavy dotted lines. (b) The power sum rule. The difference between log(PSDZ) and log(PSDX+ PSDY) is shown. The heavy dotted lines are the edges of bands A and B. (c) Coherence between residual components of the profile. The XZ coherence is shown with a solid line, the XY coherence with a dotted line and the YZ coherence with a dashed line. The dark grey and light grey shaded regions correspond to wavenumber bands A and B. (d) Phase spectra corresponding to the coherences shown in (c).

A test of the self-consistency of the data is whether the PSD of the residual vertical component equals the sum of the PSDs of the two residual horizontal components at every wavenumber for a vector magnetic profile along a horizontal straight line above a statistically stationary source (Parker & O’Brien 1997). We applied this ‘power sum rule’ to the residual components of profile 0550-047 and found excellent agreement for wavenumbers between 0.0064 and 0.0541 km−1, corresponding to wavelengths between 18.5 and 156.3 km (Fig. 3b). For consistency with Parker & O’Brien, we refer to this wavenumber band as ‘band A’. For wavenumbers less than 0.0064 km−1, the residual vertical component PSD is a factor of ≈2.5 times larger than the sum of the residual east and north component PSDs. For wavenumbers exceeding 0.0541 km−1 (wavelengths less than 18.5 km) the power sum rule also fails, as is further discussed below, because of instrument orientation error.

Profile 0550-047 has three altitude shifts (Fig. 2c): between 276 and 309 km the altitude increased 399 m from 5971 to 6370 m, between 719 and 724 km the altitude increased 61 m from 6370 to 6431 m, and between 1404 and 1438 km the altitude increased 579 m from 6431 to 7010 m. The noise in the amplitude of the magnetic vector components increases during each climb to a higher altitude and decreases once the plane levels off. The first ascent appears to cause an extra peak to the left of anomaly 11 and the second ascent appears to cause a spike in anomaly 8 (Fig. 2). The altitude increases may add long-wavelength noise to the signal and may contribute to the violation of the power sum rule at low wavenumbers.

In summary, the spectral analysis shows that the main source of the magnetic anomalies recorded by the vector component and total field magnetometers is in the upper part of the oceanic crust and that the PSDs of the residual vector components are consistent with the power sum rule over wavelengths of the scale of seafloor-spreading magnetic anomalies. Thus the spectral analysis is consistent with our interpretation of these equatorial magnetic anomalies as being due to seafloor spreading.

Cross Spectra and Lineation Strike

Additional tests of our interpretation of these profiles as recorders of seafloor-spreading anomalies can be obtained from cross-spectra (Parker & O’Brien 1997). We find that the mean coherence between the X and Z components over wavenumber band A (0.0064 < kx < 0.0541 km−1), the wavenumber band over which the power sum rule holds, is 0.82 ± 0.038 (Fig. 3c). The XZ coherence exceeds 0.8 over the wavenumber range 0.0025–0.0394 km−1 and 0.9 over the wavenumber range 0.0051–0.0381 km−1. The XZ phase spectrum over band A closely follows 90° (Fig. 3d), but rises near the large wavenumber end of the band where the coherence drops below 0.4. The mean phase over band A is 91.1°± 1.2°. The mean phases over the shorter intervals where the coherence is above 0.8 and 0.9, respectively, are 89.3°± 0.8° and 89.2°± 0.5°. The high coherence and the consistent phase angle over wavenumber band A are consistent with our interpretation that the anomalies are mainly due to a crustal magnetization and with our assumption of approximately north–south magnetic striping.

The coherence between X and Y components and between Y and Z components should vanish for all wavenumbers if the profile is exactly perpendicular to prominent lineations in the magnetic field (Parker & O’Brien 1997). We believe that the west to east profile we examine lies nearly but not exactly perpendicular to the Pacific–Farallon seafloor spreading magnetic lineations. The XY and YZ coherences for band A are low and variable, averaging 0.18 ± 0.02 and 0.22 ± 0.02, respectively, consistent with this interpretation. The XY and YZ phase spectra lack the stability of the XZ phase spectrum in band A. The YZ phase spectrum averages 75.9°± 5.5° and fluctuates up to ≈80° from this value. The XY phase spectrum averages −6.5°± 12.4° but fluctuates up to ≈170° from this value. These cross-spectral results seem plausible for magnetic lineations that strike nearly but not exactly perpendicular to the profile. When we take this result together with the low amplitudes of the total intensity and north component residuals, the lack of recognizable anomalies in those residuals, and the good correlation of the X (east) and Z (vertical) residual components of the observed anomalies with the synthetic anomalies, the evidence is convincing that the profile is recording seafloor-spreading anomalies from nearly north–south magnetic lineations.

We more precisely estimated the orientation of the magnetic lineations using two simple approaches. First, we estimated the mean coherence between the residual vertical (Z) and horizontal (X) components over wavenumber band A for all possible orientations of horizontal (Fig. 4). The minimum mean coherence should occur when the horizontal orientation is parallel to the strike of the anomalies and the maximum mean coherence should occur when the horizontal orientation is perpendicular to the strike of the anomalies. The orientation of minimum mean coherence (0.0953) is 8° counter-clockwise of north and the orientation of maximum mean coherence (0.9181) is 78° clockwise of north. Subtracting 90° from the lineation-perpendicular orientation to find the lineation-parallel direction results in a strike of 12° counter-clockwise of north.

Figure 4

Plot of 0550-047 XZ coherence for X azimuths of 0°–360° The dashed white vertical lines are the boundaries of band A. The coherence is high throughout most of the azimuth range within band A and low outside band A. The two narrow bands of low coherence within band A near azimuths 170° and 350° indicate the magnetic lineation strike.

Figure 4

Plot of 0550-047 XZ coherence for X azimuths of 0°–360° The dashed white vertical lines are the boundaries of band A. The coherence is high throughout most of the azimuth range within band A and low outside band A. The two narrow bands of low coherence within band A near azimuths 170° and 350° indicate the magnetic lineation strike.

Secondly, we calculated the summed squared variance in the two residual horizontal components after bandpassing to remove all but band A and found that this was minimized for a residual horizontal component striking 10.1° counter-clockwise of north. This result is in good agreement with the results indicated by the cross-spectral methods. Our unpublished magnetic anomaly correlations between the Galapagos fracture zone and the Clipperton fracture zone to the north suggest that the magnetic lineations strike ≈18° counter-clockwise of north. North of the Clipperton fracture zone, where anomaly correlations are better constrained, however, the strike is only 4° counter-clockwise of north. Thus, the lineation strike that we estimate from the single aeromagnetic profile is consistent with other observations and may be the best available estimate of the strike.

Effect of Instrument Orientation Error

The linear wavenumber, log PSD graph approximately follows a downward-trending straight line between wavenumbers of 0.0064 and 0.0602 km−1 for a residual total field intensity and between wavenumbers of 0.0064 to 0.0541 km−1 for the three residual vector components (Fig. 3a). Thus the spectra for the residual vector components flatten out at a smaller wavenumber than does the spectrum for the residual total field intensity. This difference in behaviour between the PSD of the residual total field intensity and that for residual vector components is known from prior work to be caused by errors in the alignment of the vector magnetometer at wavenumbers exceeding that at the break in slope in the component spectra (Blakely 1973; Parker & O’Brien 1997), as seen in Fig. 3(a). In the vector component data considered here, useful information concerning the magnetization of the oceanic crust is consequently only contained in wavelengths of 18.5 km or greater, with wavelengths smaller than 18.5 km being contaminated by instrument orientation error (Fig. 3a).

For the profile segment they analysed, Parker & O’Brien (1997) found that the XZ coherence was high (mainly above 0.6) with a phase near 180° for wavenumbers between 0.033 and 0.18 km−1. They referred to this range of wavenumbers as band B. They convincingly argued that these results are the consequence of vibrational rotation of the airplane about a horizontal axis perpendicular to the airplane path (pitch), which causes a 180° phase variation in magnetic field strength between their residual along-track (X) and residual vertical (Z) components.

Unlike the results of Parker & O’Brien (1997), our cross-spectra indicate no band of high XZ coherence at wavenumbers higher than those in band A, but there is a band of wavenumbers with high XY coherence. We define band B in our spectra to begin at the high wavenumber limit of band A, that is, at the wavenumber above which spectra are inconsistent with the power sum rule. This boundary between bands A and B approximately coincides with the break in slope in the PSDs of the X, Y and Z components. Beginning at wavenumbers slightly larger than this boundary, XY coherence is high, averaging 0.562, and has a mean phase of 179.2°. The XY coherence is clearly greater in band B than in band A (over which the mean XY coherence is 0.194). We define the upper wavenumber limit of band B to be the upper limit of high XY coherence (0.2695 km−1). The high XY coherence in our profile is presumably due to vibrational rotation of the airplane about a vertical axis (yaw).

The XZ coherence over our wavenumber band B (0.0541 < kx < 0.2695 km−1, Fig. 3c) has a mean value of 0.18, lower than the XZ coherence (>0.6) found by Parker & O’Brien (1997). As in Parker & O’Brien’s band B, the XZ phase is near 180° (mean of 175.6°) but our XZ phase fluctuates considerably more than does theirs (Fig. 3d). We know of no reason why the airplane would vibrate significantly less on the flight segment that we analysed than on the segment they analysed, although we can by no means rule this out. A more likely explanation, however, is that the effect of the along-track and vertical components of the field of the geodynamo are much larger on their south to north southern hemisphere profile than on our west to east equatorial profile. In our band B the YZ coherence is small and has a phase near 0°. Although the XZ and YZ coherences are low in band B, their phase spectra suggest to us that they too are dominated by correlated noise due to vibration of the magnetometer.

In agreement with Blakely (1973) and Parker & O’Brien (1997), our cross-spectral analysis indicates that more than 96.7 per cent of the wavenumber range of the residual measured vector data is noise. It is important to check how well the observed anomalies match the synthetic anomalies to ensure that noise has not caused an error in anomaly identification. We bandpass filtered the deskewed residuals to reject contributions at wavenumbers greater than 0.0541 km−1 (wavelengths less than 18.5 km). The bandpass filter of Blakely (1973) was applied by multiplication in the wavenumber domain by the function 

1
formula
where k2 is the high end of the wavenumber range to be bandpassed and k1 equals k2 minus 5 per cent of the width of the wavenumber range to be bandpassed. We used this filter on the wavenumber range 0 ≤kx < 0.0541 km−1, resulting in a value for k2 of 0.0541 km−1 and for k1 of 0.0514 (=k2− 0.05(0.0541 − 0.0)).

The bandpass-filtered residual profiles are shown as thin black lines superimposed on the thick grey lines of the unfiltered residual profiles (Figs 2h–j). The slight smoothing that results from rejecting these high wavenumbers has no effect on the identification of the magnetic anomalies recorded in the east and vertical components. In particular, the interpretation of the short-wavelength wiggles identified on the eastern end of the profile, i.e. anomalies 5B, 5AD, 5AC, 5AB, 5AA, and other nearby wiggles, is unaffected by the filtering. Thus, this analysis provides strong support for our interpretation of these anomalies as being due to seafloor spreading, even if 96.7 per cent of the wavenumber range is noise.

It may seem surprising that the anomalies are so little changed by the removal of 96.7 per cent of the wavenumbers, but not so if one considers what fraction of the power is in the rejected high wavenumbers (kx > 0.0541 km−1), which is 0.05 per cent for the residual X component, 0.20 per cent for the residual Y component and 0.05 per cent of the residual Z component. Thus removing 96.7 per cent of the wavenumbers that contain noise removes less than 0.2 per cent of the power of the residual components.

Age of the Seafloor

We used the same approach on other aeromagnetic profiles near the equator and have identified or revised the locations of anomalies in the eastern equatorial Pacific (Fig. 5). In particular, the locations of magnetic anomalies 6 and 7 near the equator differ from those of Cande (1989). Our new locations for magnetic anomalies 6 and 7 are, respectively, 530 and 400 km further east than the locations of Cande (1989). The new location for anomaly 6 is consistent, however, with a tentative correlation made by Wilson (1996). Fig. 2 of Wilson (1996) gives an updated analysis (relative to Cande 1989) of the northeast quadrant of our Fig. 5. Our new anomaly correlations agree with Wilson’s (1996) correlations where there is overlap (i.e. anomalies 5B and 5C). If his correlations of the anomaly 5A to 5B sequence are extrapolated southward to the equator they are also consistent with our new correlations. Both our correlations and Wilson’s (1996) correlations of the sequence 5A to 5C are consistent with age dates obtained by deep sea drilling (Hays 1972c; Mayer 1985; Wilson 1996).

Figure 5

New map of the eastern equatorial Pacific showing magnetic anomaly identifications and deskewed residual vector aeromagnetic profiles from Project Magnet. Profile 0550-047 is shown along the equator. The residual magnetic anomalies are shown by a solid line, the path of the airplane by a dotted line. DSDP/ODP sites that reached basement are shown by open diamonds and identified by site number. (Mercator projection, 5° tick marks.)

Figure 5

New map of the eastern equatorial Pacific showing magnetic anomaly identifications and deskewed residual vector aeromagnetic profiles from Project Magnet. Profile 0550-047 is shown along the equator. The residual magnetic anomalies are shown by a solid line, the path of the airplane by a dotted line. DSDP/ODP sites that reached basement are shown by open diamonds and identified by site number. (Mercator projection, 5° tick marks.)

Our locations for anomalies 6 and 7 can also be compared with ages inferred from deep sea drilling results. The baked sediments at the sediment/basement interface at DSDP Sites 79 and 80 are in the Globorotalia kugleri planktonic foraminifera zone (Hays 1972a,b), which has an age range of 23.8–21.5 Myr (chrons C6Cn.2n–C6Ar) (Berggren 1995). The top of this zone occurs 26 and 30 m above the basalt at DSDP Sites 79 and 80, respectively, which suggests that the ages of the basalts are ≈1.6 and ≈2.7 Myr older, respectively, using the estimated sedimentation rates for each site (Hays 1972a,b). In Fig. 5 Site 79 appears to be on magnetic anomaly 6C (24.12–23.35 Myr), assuming a 350° lineation strike and extrapolating northward the position of anomaly 6C on profile 0550-047. Both biostratigraphic (23.8–21.5 Ma) and estimated basalt (25.4–23.1 Ma) ages of Site 79 are consistent with its projected location on magnetic anomaly 6C. Site 80 appears to be in magnetic anomaly 6Cr (24.73–24.12 Ma) based on profiles 0550-047 and 0480-271. The biostratigraphic age (23.8–21.5 Ma) of Site 80 is slightly younger than, but the estimated age of the basalt (26.5–24.2 Ma) is consistent with, the age based on its location on magnetic anomaly 6Cr.

The proposed existence of a fossil spreading ridge north of the equator at 115°W (Herron 1972; Mammerickx & Klitgord 1982) with asymmetric magnetic anomaly 5B locations is not supported by our magnetic anomaly identifications or by satellite-derived gravity values (Sandwell & Smith 1995). The only aeromagnetic profiles through this region, however, are immediately south of the proposed fossil ridge and may miss it. In any event, our new interpretation of the age of the eastern Pacific equatorial seafloor is consistent with the available independent age dates.

Paleolatitude

The vertical component profiles across nearly north–south-striking magnetic lineations require phase shifts of ≈180° in the southern hemisphere and ≈0° in the northern hemisphere to match a ZPS synthetic profile. In contrast, the horizontal component profiles require phase shifts of ≈270° in the southern hemisphere and ≈90° in the northern hemisphere. Only when a profile lies near the paleomagnetic equator does the required phase shift change rapidly with location. When traversing the paleomagnetic equator from south to north, phase shifts for vertical component profiles decrease from 180° to 0° and phase shifts for horizontal component profiles decrease from 270° to 90°.

To convert the phase shifts of residual vector profiles to apparent effective remanent inclinations, we use the relation ea=−Δθ−e+ 180°, where ea is the apparent effective remanent inclination, Δθ is the phase shift and e is the ambient effective inclination at the profile location (e= tan−1[tan(I)/sin(AD)], where I= inclination, D= declination, A= lineation azimuth that is 90° clockwise from the direction in which seafloor gets younger) (Blakely & Cox 1972; Schouten & McCamy 1972; Gordon & Cox 1980). For a horizontal residual profile, e is 0° and ea=−Δθ+ 180°. For a vertical residual profile, e is 90° and ea=−Δθ+ 90°. Thus, ea estimated from residual vector data is independent of the azimuth of the magnetic lineation. In contrast, ea estimated from residual total intensity data depends on the lineation azimuth (through its dependence on e). This dependence is strong for nearly north–south lineations near the equator. Thus, the value of ea estimated from residual total intensity data is sensitive to the uncertainty in the lineation azimuth, but ea estimated from residual vector data is not.

The phase shifts of the east (186°± 2.5°) and vertical (99°± 3.0°) residual profiles indicate apparent effective remanent inclinations (ea) of −6°± 2.5° and −9°± 3.0°, respectively, with a mean ea of −7.5°± 3.9°. Assuming a dipole field and neglecting any anomalous skewness (Cande 1976), this shallow inclination would indicate a paleolatitude of 3.8°S ± 2.0° if the paleostrike of the East Pacific Rise were east–west (90° clockwise of north). This paleolatitude is an upper bound because any other paleostrike would produce a smaller magnitude of south latitude. The present strike of the magnetic anomalies is 170° and the strike of the anomalies with respect to a 32 Myr old pole (Horner-Johnson & Gordon 2003) is 173°. Therefore, the strike was probably between 170° and 173°, respectively, indicating smaller magnitudes of south latitude, 0.7°S ± 2.0° and 0.5°S ± 2.0°. Therefore, the observed skewness of the anomalies observed in the vector aeromagnetic data indicate little, if any, northward motion of this seafloor in the 13–33 Myr since it formed.

Prior studies have indicated that anomalous skewness is insignificant at spreading rates as fast as those recorded in the equatorial profile we investigate here (Dyment 1994). If the anomalous skewness were non-zero, however, it would tend to cause the apparent effective remanent inclination (i.e. that inferred from the shape of the magnetic anomaly) to be less than the effective remanent inclination (i.e. that corresponding to the actual direction of magnetization in the permanently magnetized portion of the lithosphere) (Petronotis 1992). If we hypothetically assume a nominal value of anomalous skewness of 10°, the effective remanent inclination would be positive (instead of the negative value inferred above), indicating that the seafloor formed just north of, instead of just south of, the paleoequator. In this case small and insignificant southward motion, instead of small and insignificant northward motion, would be indicated since 13–33 Ma. In any event, no significant northward motion of the plate would be indicated.

Conclusions

The smaller amplitudes of the residual total intensity and residual north component compared with the residual east and vertical components are consistent with the interpretation that the residual field is mainly due to seafloor-spreading magnetic anomalies that strike nearly north–south. The lack of correlation between the residual north component, on the one hand, and the residual east and vertical components, on the other, is also consistent with this interpretation. The residual east and vertical component profiles are deskewed by phase shifts that differ by 87°, close to the 90° expected if the anomalies in the profiles are due to seafloor spreading or any other stationary stochastic crustal source. The good agreement between the synthetic magnetic anomalies and the observed profiles, and between the deskewed residual east and vertical profiles, is strong evidence that the vector aeromagnetic profile records equatorial seafloor-spreading anomalies. The approximate depth of the magnetic source layer is 0.4–0.6 km below the top of the oceanic crust, consistent with our assumption of a crustal source for the anomalies. The wavenumbers that contribute to the observed magnetic anomalies pass the test provided by the spectral power sum rule, consistent with a crustal source for anomalies.

As has been found in prior studies of residual vector aeromagnetic data, the high-wavenumber portion of the power spectrum is noise. In this case the power spectrum for wavenumbers exceeding 0.0541 km−1, amounting to 97 per cent of the range of wavenumbers in the power spectrum, is noise. The fraction of power in that 97 per cent of the spectrum, however, is less than 0.2 per cent. Filtering out the high wavenumbers has negligible visual effect on the observed magnetic anomalies and on our interpretation of them.

From the XZ coherence, we infer that the magnetic lineations strike 8°–12° counter-clockwise of north. From the XY variance, we infer that the magnetic lineations strike about 10° counter-clockwise of north. Our revised locations of anomalies 6 and 7 are, respectively, 530 and 400 km to the east of the locations of anomalies 6 and 7 of Cande (1989). Our new interpretation of the age of the eastern Pacific equatorial seafloor is consistent with the available independent age dates and with Wilson’s (1996) identifications of anomalies 5A to 6 northeast of, and slightly overlapping, the region we investigate here.

The value of ea estimated from equatorial residual total intensity data is sensitive to uncertainty in the lineation azimuth, but ea estimated from equatorial residual vector data is not. The observed skewness of the anomalies observed in the vector aeromagnetic data indicate little, if any, northward motion of this seafloor in the 13– 33 Myr since it was created.

Acknowledgments

This work was supported by NSF grant EAR9814673 to Rice University. The figures were prepared using GMT (Wessel & Smith 1998).

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