Teleseismic P waves are followed by a series of scattered waves, particularly P-to-S converted phases, that form a coda. The sequence of scattered waves on the horizontal components can be represented by the receiver function (RF) for the station and may vary with the approach angle and azimuth of the incoming P wave. We have developed a frequency-domain RF inversion algorithm using multiple-taper correlation (MTC) estimates, instead of spectral division, using the pre-event noise spectrum for frequency-dependent damping. The multitaper spectrum estimates are leakage resistant, so low-amplitude portions of the P-wave spectrum can contribute usefully to the RF estimate. The coherence between vertical and horizontal components can be used to obtain a frequency-dependent uncertainty for the RF. We compare the MTC method with two popular methods for RF estimation, timedomain deconvolution (TDD), and spectral division (SPD), both with damping to avoid numerical instabilities. Deconvolution operators are often biased toward the frequencies where signal is strongest. Spectral-division schemes with constant waterlevel damping can suffer from the same problem in the presence of strong signalgenerated noise. Estimates of uncertainty are scarce for TDD and SPD, which impedes developing a weighted average of RF estimates from multiple events. Multiple-taper correlation RFs are more resistant to signal-generated noise in test cases, though a "coherent" scattering effect, like a strong near-surface organ-pipe resonance in soft sediments, will overprint the Ps conversions from deeper interfaces. The MTC RF analysis confirms the broad features of an earlier RF study for the Urals foredeep by Levin and Park (1997a) using station ARU of the Global Seismographic Network (GSN), but adds considerable detail, resolving P-to-S converted energy up to f ס 4.0 Hz.
S U M M A R YP-SH conversion is commonly observed in teleseismic P waves, and is often attributed to dipping interfaces beneath the receiver. Our modelling suggests an alternative explanation in terms of flat-layered anisotropy. We use reflectivity techniques to compute three-component synthetic seismograms in a 1 -D anisotropic layered medium. For each layer of the medium, we prescribe values of seismic velocities and hexagonally symmetric anisotropy about a common symmetry axis of arbitrary orientation. A compressional wave in an anisotropic velocity structure suffers conversion to both SVand SH-polarized shear waves, unless the axis of symmetry is everywhere vertical or the wave travels parallel to all symmetry axes. The P-SV conversion forms the basis of the widely used 'receiver function' technique. The P-SH conversion occurs at interfaces where one or both layers are anisotropic. A tilted axis of symmetry and a dipping interface in isotropic media produce similar amplitudes of both direct ( P ) and converted (Ps) phases, leaving the backazimuth variation of the P-Ps delay as the main discriminant. Seismic anisotropy with a tilted symmetry axis leads to complex synthetic seismograms in velocity models composed of just a few flat homogeneous layers. It is possible therefore to model observations of P coda with prominent transverse components with relatively simple 1 -D velocity structures. Successful retrieval of salient model characteristics appears possible using multiple realizations of a geneticalgorithm (GA) inversion of P coda from several backazimuths. Using GA inversion, we determine that six P coda recorded at station ARU in central Russia are consistent with models that possess strong (> 10 per cent) anisotropy in the top 5 km and between 30 and 43 km depth. The symmetry axes are tilted, and appear aligned with the seismic anisotropy orientation in the mantle under ARU suggested by SKS splitting.
Using 100 years of global temperature anomaly data, we have performed a singular value decomposition of temperature variations in narrow frequency bands to isolate coherent spatio‐temporal “modes” of global climate variability. Statistical significance is determined from confidence limits obtained by Monte Carlo simulations. Secular variance is dominated by a globally coherent trend, with nearly all grid points warming in phase at varying amplitude. A smaller, but significant, share of the secular variance corresponds to a pattern dominated by warming and subsequent cooling in the high latitude North Atlantic with a roughly centennial timescale. Spatial patterns associated with significant peaks in variance within a broad period range from 2.8 to 5.7 years exhibit characteristic El Niño‐Southern Oscillation (ENSO) patterns. A recent transition to a regime of higher ENSO frequency is suggested by our analysis. An interdecadal mode in the 15‐to‐18 years period range appears to represent long‐term ENSO variability. This mode has a sizeable projection onto global‐average temperature, and accounts for much of the anomalous global warmth of the 1980s. A quasi‐biennial mode centered near 2.2‐years period and a mode centered at 7‐to‐8 years period both exhibit predominantly a North Atlantic Oscillation (NAO) temperature pattern. A potentially significant “decadal” mode centered on 11‐to‐12 years period also exhibits an NAO temperature pattern and may be modulated by the century‐scale North Atlantic variability.
Spectral estimation procedures which employ several prolate spheroidal sequences as tapers have been shown to yield better results than standard single‐taper spectral analysis when used on a variety of engineering data. We apply the adaptive multitaper spectral estimation method of Thomson (1982) to a number of high‐resolution digital seismic records and compare the results to those obtained using standard single‐taper spectral estimates. Single‐taper smoothed‐spectrum estimates are plagued by a trade‐off between the variance of the estimate and the bias caused by spectral leakage. Applying a taper to reduce bias discards data, increasing the variance of the estimate. Using a taper also unevenly samples the record. Throwing out data from the ends of the record can result in a spectral estimate which does not adequately represent the character of the spectrum of nonstationary processes like seismic waveforms. For example, a discrete Fourier transform of an untapered record (i.e., using a boxcar taper) produces a reasonable spectral estimate of the large‐amplitude portion of the seismic source spectrum but cannot be trusted to provide a good estimate of the high‐frequency roll‐off. A discrete Fourier transform of the record multiplied by a more severe taper (like the Hann taper) which is resistant to spectral leakage leads to a reliable estimate of high‐frequency spectral roll‐off, but this estimate weights the analyzed data unequally. Therefore single‐taper estimators which are less affected by leakage not only have increased variance but also can misrepresent the spectra of nonstationary data. The adaptive multitaper algorithm automatically adjusts between these extremes. We demonstrate its advantages using 16‐bit seismic data recorded by instruments in the Anza Telemetered Seismic Network. We also present an analysis demonstrating the superiority of the multitaper algorithm in providing low‐variance spectral estimates with good leakage resistance which do not overemphasize the central portion of the record.
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