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1.
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.  相似文献   

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A geomagnetic scattering theory for evaluation of earth structure   总被引:1,自引:0,他引:1  
Summary. Structural features of the Earth's lower crust and upper mantle can be mapped by the analysis of temporal geomagnetic fluctuations using the electromagnetic scattering theory developed in this paper. Decomposing geomagnetic field fluctuations at the Earth's surface into an excitation part and a scattered part forms the basis of a power series development. The vertical field component is interpreted as a scattering of the excitation field. The horizontal gradient and geomagnetic depth sounding methods are special cases of the theory developed. The horizontal gradient sounding method has a tensorial aspect which has not been recognized before; it should be included to obtain correct penetration depth parameter evaluations from field data.  相似文献   

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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.  相似文献   

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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 Br , 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.  相似文献   

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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.  相似文献   

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The relation between magnetic range values and spectral power   总被引:1,自引:0,他引:1  
Spectral power is shown to be proportional to the square of the range for variables with a normal distribution. Plots of log power versus log range for 3  hr intervals of data from Canadian magnetic observatories show a close fit to a straight line with a slope of 2. The same results are obtained from all sites in the Canadian magnetic observatory network, which extends from the polar cap to auroral and sub-auroral latitudes. This indicates that a square-law relation between spectral power and range is a general property of magnetic field variations.  相似文献   

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