GJI Geomagnetism, rock magnetism and palaeomagnetism Spectral and spatial decomposition of lithospheric magnetic field models using spherical Slepian functions
GJI Geomagnetism, rock magnetism and palaeomagnetism Spectral and spatial decomposition of lithospheric magnetic field models using spherical Slepian functions
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GJI 地磁学、岩石磁学和古地磁学 使用球形 Slepian 函数对岩石圈磁场模型进行频谱和空间分解
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发表时间：
2013
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通讯作者：
F. Simons
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作者：
Jarno Saarim;K. Whaler;F. Simons
全球磁场模型通常表示为球谐展开系数。Slepian函数是球谐函数的线性组合，其产生新的基函数，其在所选地理边界之外近似消失，但在感兴趣的空间区域内也保持正交。因此，它们适合于将球谐模型分解为仅在选定区域中具有显著磁场强度的部分。Slepian函数是空间-光谱集中的，平衡空间偏差和光谱泄漏。在这里，我们以它们为基础，将高达72阶的全球岩石圈磁场模型MF 7分解为两个不同的区域。其中一个合成场集中在大陆域的整体内，另一个则局限于其补充物海洋。我们的程序整齐地划分为两个部分的频谱功率在每个谐波度。大陆上的磁场主导着整个地壳磁场，每个区域都有不同的功率谱特征。海洋功率谱近似平坦，而大陆区域的功率谱随着球谐度的增加而增加。我们提供了一个更小的，不重叠的大陆和海洋区域的字段进一步细分，并推测其光谱特征的变化的来源。
SUMMARY Global magnetic field models are typically expressed as spherical-harmonic expansion coefficients. Slepian functions are linear combinations of spherical harmonics that produce new basis functions, which vanish approximately outside chosen geographical boundaries but also remain orthogonal within the spatial region of interest. Hence, they are suitable for decomposing spherical-harmonic models into portions that have significant magnetic field strength only in selected areas. Slepian functions are spatio-spectrally concentrated, balancing spatial bias and spectral leakage. Here, we employ them as a basis to decompose the global lithospheric magnetic field model MF7 up to degree and order 72, into two distinct regions. One of the resultant fields is concentrated within the ensemble of continental domains, and the other is localized over its complement, the oceans. Our procedure neatly divides the spectral power at each harmonic degree into two parts. The field over the continents dominates the overall crustal magnetic field, and each region has a distinct power-spectral signature. The oceanic power spectrum is approximately flat, while that of the continental region shows increasing power as the spherical-harmonic degree increases. We provide a further breakdown of the field into smaller, non-overlapping continental and oceanic regions, and speculate on the source of the variability in their spectral signatures.