By Renata Dmowska, Barry Saltzman
This sequence presents a venue for longer stories of present advances in geophysics. Written at a degree obtainable to graduate scholars, the articles serve to expand wisdom of varied fields and should be worthy in classes and seminars.
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Additional info for Advances in Geophysics, Vol. 41
In the PCA decomposition, the propagating phase structure in the signals cannot be correctly 26 MICHAEL E. MANN AND JEFFREY PARK described by the empirical eigenvectors. Rather, the eigendecomposition must artiﬁcially describe such phase information in terms of multiple standing waves. Nonetheless, a variety of generalizations of PCA have been developed which attempt to ameliorate several of the problems noted above, through various modiﬁcations or alternative spatiotemporal variance decompositions.
Y fŽ1. 1 .. y fŽ1. N 1 y fŽ2. 1 2 y fŽ1M . 1 y fŽ2. N 1 . Ž 10. A PCA is then performed in the transformed frequency domain, N Y Ý n u n†vn , n Ž 11. 1 where n in this context runs over the N distinct frequencies of the discrete Fourier transform of a data set of length N samples. The empirical orthogonal function ŽEOF. vm describes the complex spatial pattern in amplitude and phase of the nth eigenvector, and the N-vector u m now describes the combinations of pure harmonic components of variability that describe the relatively smooth time-evolution of the nth eigenvector.
In the case of MTM-SVD, a corresponding alternative linear transformationᎏthe Fourier transformᎏis in fact speciﬁable a priori. The MTM-SVD procedure assumes that a signal has a very speciﬁc narrowband frequency-domain structure, and under that assumption assures quite high spatial signal-to-noise ratios in signal reconstruction. While there is considerable power in the synthetic data Žsignalplus-noise. at all gridpoints at all frequencies, the regional as well as the large-scale spatial structure of the reconstructed signals were shown above to be quite faithful to their true counterparts.
Advances in Geophysics, Vol. 41 by Renata Dmowska, Barry Saltzman