Control of smoothness in non-linear filtering of geomagnetic data by a one-pass method with a piecewise cubic polynomial

A smoother realized by a one-pass method with a piecewise cubic polynomial and a modified Powell criterion is termed a PCP filter. Since its action is data-adaptive, the PCP filter is non-linear. Furthermore, this filler is also non-causal and in practice causes little phase shift in the output and/or residual data as long as the input data has no dominant components with frequencies within its transition band. An average amplitude response of the PCP filter for sinusoidal inputs is determined numerically for each value of the parameter μ, which appears in the modified Powell criterion and controls the smoothness in output of the filter. An objective criterion for the selection of μ in the practical application of the PCP filter is then obtained from this response. Furthermore, the cut-off frequency of the PCP filter is defined as the first frequency at which the attenuation of the average amplitude response becomes 3 dB. It is found that the cut-off frequency is a good measure of the smoothness in output of the PCP filter. This frequency decreases with increasing μ, meaning that the output of the PCP filter becomes smoother and the oscillations with longer periods can be separated as residuals as μ grows large. As μ increases, the average number of sample points between two adjacent knots becomes larger and the computational cost increases for data processing by the PCP filter.     

Bootstrapped discrete scale invariance analysis of geomagnetic dipole intensity

The technique of bootstrapped discrete scale invariance allows multiple time-series of different observables to be normalized in terms of observed and predicted characteristic timescales. A case study is presented using the SINT2000 time-series of virtual axial dipole moment, which spans the past 2 Myr. It is shown that this sequence not only bears a clear signature of a preferred timescale of about 55.6 Ka, but additionally predicts similar features (of shorter and longer duration) that are actually observed on the timescales of historical secular variation and dipole reversals, respectively. In turn, the latter two empirical sources both predict the characteristic timescale found in the dipole intensity sequence. These communal scaling characteristics suggest that a single underlying process could be driving dynamo fluctuations across all three observed timescales, from years to millions of years.     

Maximum entropy regularization of the geomagnetic core field inverse problem

The maximum entropy technique is an accepted method of image reconstruction when the image is made up of pixels of unknown positive intensity (e.g. a grey-scale image). The problem of reconstructing the magnetic field at the core–mantle boundary from surface data is a problem where the target image, the value of the radial field B_r , can be of either sign. We adopt a known extension of the usual maximum entropy method that can be applied to images consisting of pixels of unconstrained sign. We find that we are able to construct images which have high dynamic ranges, but which still have very simple structure. In the spherical harmonic domain they have smoothly decreasing power spectra. It is also noteworthy that these models have far less complex null flux curve topology (lines on which the radial field vanishes) than do models which are quadratically regularized. Problems such as the one addressed are ubiquitous in geophysics, and it is suggested that the applications of the method could be much more widespread than is currently the case.     

Curie-temperature depth estimation using a self-similar magnetization model

The Earth's crust is magnetized down to the Curie-temperature depth at about 10 to 50 km. This limited depth extent of the crustal magnetization is discernible in the power spectra of magnetic maps of South Africa and Central Asia. At short wavelengths, the power increases as rapidly towards longer wavelengths as expected for a self-similar magnetized crust with unlimited depth extent. Above wavelengths of about 100 km the power starts increasing less rapidly, indicating the absence of deep-seated sources. To quantify this effect we derive the theoretical power spectrum due to a slab carved out of a self-similar magnetization distribution. This model power spectrum matches the power spectra of South Africa and Central Asia for a self-similarity parameter of β = 4 and Curie temperature depths of 15 to 20 km.     

11 million years of Oligocene geomagnetic field behaviour

An 11 million year long record of the Oligocene geomagnetic field has been obtained from pelagic sediments of DSDP Hole 522 An average sample spacing of 4 cm yielded approximately one specimen per 4 to 8 kyr. The rock magnetics are remarkabh consistent across the entire interval. Previous work demonstrated a magnetic mineralogy dominated by magnetically stable magnetite. The natural remanent magnetism (NRM) carries an Oligocene polarity timescale that is in excellent agreement with the Oligocene reversal record as determined from marine magnetic anomalies (MMAs), including many of the so-called 'crypto-chrons'. Normalized NRM intensities from the undisturbed portions of the record yield a time series of variations with features consistent with a number of other palaeointensity time series derived from both sedimentary and lava sequences. These features include consistent, major decreases in palaeointensity (DIPs) at reversal boundaries, and occasional DIPs between reversal boundaries that could correspond to lineated 'tiny wiggles' in the MMA records. The data set suggests that the overall field strength was 40 per cent higher in the first half of the Oligocene when the average reversal frequency was 1.6 Myr^-1 than in the second half when the reversal frequency was 4 Myr^-1. There is also a weak dependence of average field strength on length of polarity interval. Finally, in the three cores suited to spectral analysis (of coherent polarity and relative intensity independent of lithological contamination), there is a persistent ca. 30–50ka periodicity in the variations of the relative intensity, suggesting that the geomagnetic field 'pulses' at about this frequency, not only during the Brunhes (as demonstrated by Tauxe & Shackleton 1994), but in the Oligocene as well.     

Long-term features of drifting and standing non-dipole fields as determined from Holocene palaeomagnetic secular variations

Geomagnetic field motions of Holocene secular variations are investigated using a separation method. The palaeomagnetic secular variations from Britain, North America and Australia have been subjected to maximum-entropy method analyses. Based on the results of spectral analyses, the secular variations are separated by band-pass filters into low-frequency components, generally including the period band 1800-3600 yr, and high-frequency components, generally including the period band 1000-1200 yr. There is an interval, from 4200 to 1700 yr BP, which shows clockwise rotational motions in the low-frequency components of all three sites. Westward drifting of geomagnetic fields may be globally dominant. Swinging or elliptical looping motions constrained to a certain direction were observed in the low-frequency components of the British data. The time duration for the persistence of the swinging motion constrained to a certain direction was 3500 years or so, which could be the lifetime of an oscillating stationary field. The duration of the transitional motion was 1000-1300 years, which may indicate the recurrence time of a stationary field.     

南极布兰斯菲尔德海峡沉积物的地磁场长期变与定年

对位于布兰斯菲尔德海峡东北部的沉积物岩心D1-7进行了初步环境磁学和古地磁研究,获得了连续的相对地磁场强度和方向。沉积物岩性总体为灰色软塑性粘土,中下部出现一层黑色火山灰层。结合该孔沉积物和有孔虫AMS¹⁴C测年结果（王汝建等未发表资料）,相对地磁场强度及其方向提供了12 ka以来连续的定年标尺,其中相对地磁场强度与具有相似沉积速率的南美Laguna Potrok Aike湖泊记录对比提供了六个对比点;同时特征剩磁倾角和磁偏角提供了另外六个对比点。磁化率各向异性分析揭示了全新世早、中和晚期岩心所在位置底流（南极深层水~1000 m）发生了阶段性显著变化,同时磁性矿物含量、粒度、沉积物湿密度等也发生了相应的变化。这些环境磁学和沉积学的变化主要受控于南极相应纬度处的太阳辐射量以及与辐射量相关的夏季季风降水量的变化,降水量增加导致磁性矿物粒度变细。D1-7也记录了一些千年尺度旋回变化,但是南极地区目前缺乏与之相似分辨率的气候参数记录,无法进一步探讨这些气候事件的缘起和分布范围。对比发现,地磁场长期变产生的年龄与沉积物全样有机碳AMS¹⁴C测年结果之间存在系统的差异,在6 ka以来比有机碳年龄年轻,在6 ka之前则比有机碳年龄老。南极布兰斯菲尔德海峡内各种不同水体的混合以及在全新世全球升温背景下冰川的动态变化和由此引起的中、深层水变化,都是造成水体性质复杂的原因。而地磁场强度和方向变化则不受水体性质的影响,因此可以提供更合理的年龄信息。自12 ka至今,25 cm/ka的平均沉积速率表明南极布兰斯菲尔德海峡地区整个全新世内稳定和丰富的沉积物供应。     

Centennial to millennial geomagnetic secular variation

A time-varying spherical harmonic model of the palaeomagnetic field for 0–7 ka is used to investigate large-scale global geomagnetic secular variation on centennial to millennial scales. We study dipole moment evolution over the past 7 kyr, and estimate its rate of change using the Gauss coefficients of degree 1 (dipole coefficients) from the CALS7K.2 field model and by two alternative methods that confirm the robustness of the predicted variations. All methods show substantial dipole moment variation on timescales ranging from centennial to millennial. The dipole moment from CALS7K.2 has the best resolution and is able to resolve the general decrease in dipole moment seen in historical observations since about 1830. The currently observed rate of dipole decay is underestimated by CALS7K.2, but is still not extraordinarily strong in comparison to the rates of change shown by the model over the whole 7 kyr interval. Truly continuous phases of dipole decrease or increase are decadal to centennial in length rather than longer-term features. The general large-scale secular variation shows substantial changes in power in higher spherical harmonic degrees on similar timescales to the dipole. Comparisons are made between statistical variations calculated directly from CALS7K.2 and longer-term palaeosecular variation models: CALS7K.2 has lower overall variance in the dipole and quadrupole terms, but exhibits an imbalance between dispersion in   g ¹₂  and   h ¹₂  , suggestive of long-term non-zonal structure in the secular variations.     

Invariants in toroidal and tangentially geostrophic frozen-flux velocity fields

We derive two new types of invariant that must be obeyed by the radial magnetic field at the core-mantle boundary if the hypothesis of frozen flux is valid and the fluid motion is either toroidal or tangentially geostrophic there. These general invariants incorporate specific invariants that are already known and can, in principle, be tested using magnetic data that cover an interval of time.