Guy Masters

A Shear-Velocity Model of the Mantle [and Discussion]

We present a new model of shear velocity structure in the mantle which is designed to fit data-sets of absolute and differential body-wave travel times, surface-wave phase velocities over a broad range of frequencies, and structure coefficients of modes of free oscillation. The model is parametrized laterally by spherical harmonics (truncated at degree 16) and by 30 natural cubic B-splines in radius. Our best model features large-amplitude structure (up to ±6% anomalies in shear velocity) in the topmost 400 km of the mantle and in the lowermost 500 km (up to ±2.5%) with most of the power in the low harmonics (l < 6). The middle of the mantle is characterized by low-amplitude anomalies with a much whiter spectrum. Our models generally show no distinctive changes in structure (in either shape or amplitude) at the 660 km discontinuity supporting the idea that an endothermic phase transition is not a barrier to large-scale flow in the mantle.

An inversion for radial viscosity structure using seismic tomography

Using a uniform velocity/density scaling, we have inverted the seismically inferred 3-dimensional structure of the whole manfie for the radial viscosity structure which best fits the geoid. We are able to obtain 60-72% variance reductions for three different S-wave tomographic models. The resulting viscosity structures are remarkably similar, showing a high viscosity lid, a low viscosity zone in the transition region and a high viscosity lower manfie. A resolution analysis indcates that the viscosity structure in the upper manfie is well resolved by the data, however the resolution in the lower manfie is poorer. Our models axe in general agreement with previous studies except that our inversions prefer a low viscosity layer at 400-670 km as opposed to 100-400 kin.

Global upper mantle structure from long‐period differential travel times

We have made over ten thousand measurements of PP-P and SS - S differential travel times from long-period Global Digital Seismograph Network recordings of all events with mb ≥ 5.5 which occurred during the years 1976 to 1986. We have obtained reasonable global coverage, with very good sampling of several regions of the world. The residuals range from −5 to 5 s for PP-P and −12 to 12 s for SS-S and reveal a large-scale pattern of heterogeneity when plotted at the reflected phases bounce point. Our experiments indicate that lower-mantle structure and source-receiver structure can each contribute approximately ±0.5 s to our measured PP – P residuals so there is considerable signal to be explained. The pattern observed in the PP – P measurements is similar to the pattern observed in the SS-S measurements, with the SS-S residuals 2 to 4 times larger in magnitude. Comparisons of our measured residuals to those predicted by the upper-mantle models of Woodhouse and Dziewonski show that the overall patterns are quite similar but the amplitude of the model residuals is roughly a factor of 2 too small. Comparisons with the predictions of a whole-mantle model of Tanimoto again shows that the predicted pattern of residuals is reasonably consistent with the observations but now the predicted residuals are too large by about a factor of 2. This variation in predicted amplitudes is probably mainly due to differences in the near-surface structure of the models. We have also binned our measurements according to the tectonic regionalization GTR1 of Jordan and find a qualitative correlation of average residual with tectonic region. In particular, Precambrian shields show a strong anomaly, and there is a correlation of residual size with the age of oceanic crust at the bounce point. For all tectonic regions the ratio of SS - S to PP - P residuals is approximately 2. This ratio is consistent with a thermal origin for the observed signal. Finally, our measurements show no compelling evidence for azimuthal anisotropy which might be related to fossil spreading direction or the direction of absolute plate motion. Such a signal is probably overwhelmed by the large signal from three-dimensional structure.

Constraints on global phase velocity maps from long‐period polarization data

Global phase velocity maps of long-period surface waves are an essential ingredient in modeling 3-D shear wave velocity and are capable of particularly good lateral resolution of upper mantle structure. Unfortunately, even recently derived maps disagree for harmonic degrees greater than about 6 so that further improvement is required. The resolution can be dramatically improved by adding both amplitude and polarization data to the inversion process. Both amplitude and polarization depend on the lateral gradients of phase velocity and hence constrain the short-wavelength structure of the resulting models. Amplitude, polarization, and phase are readily determined for each arriving wave packet using multitaper techniques and can be interpreted using linear perturbation theory. The size of our phase and polarization data sets obtained from seismograms of the global seismic broadband networks GEOSCOPE, IDA/IRIS (International Deployment of Accelerometers/Incorporate Research Institutions for Seismology) and IRIS/USGS (U.S. Geological Survey) justifies inversion for phase velocity expanded in spherical harmonics up to l = 24. While the phase data between 3 and 15 mHz do not require structure beyond about l = 8, small-amplitude structure of harmonic degree greater than 8 is needed to fit the polarization data. Checkerboard tests show that the resolution of phase velocity is greatly improved when polarization data are added to the inversion. Since amplitude data also depend on 3-D anelastic structure of the mantle, these data need a more comprehensive interpretation, and we cannot expect to fit them with a purely elastic model. However, in this paper we show that a good fraction of the amplitude signal is consistent with our phase velocity maps and that it is possible to obtain maps which simultaneously explain both amplitude and polarization data.

ATTENUATION IN THE EARTH AT LOW FREQUENCIES

The introduction of global, digitally recording, seismic networks has provided the seismological community with a large quantity of high quality data. At low frequencies the IDA (International Deployment of Accelerometers) network provides the best available data and, in this report, over 500 IDA records have been carefully analysed giving nearly 4000 reliable measurements of centre frequency and apparent attenuation of fundamental spheroidal modes. The attenuation rate of a normal mode of free oscillation of the Earth is measured in terms of its or quality factor and mean Q values for the modes 0S8- 0S46 are presented with standard deviations of 2-9% . Mean centre frequencies have relative standard deviation of 5 x 10-5 to 5 x 10-4. The distribution of the centre frequencies reveals a large-scale aspherical structure in velocity and density but the distribution of the apparent attenuation measurements does not reveal a corresponding structure. A total of 26 new measurements of the mean Q of overtone modes with standard deviations of 5-30 % have also been obtained by using single-record and multiple-record techniques. Combining the new data with reliable Q measurements from the literature gives a total of 71 data with which we can infer the radial structure of attenuation inside the Earth. This structure is not well constrained in detail and very simple models are capable of fitting the data. Experiments with synthetic data show that an improvement of an order of magnitude in both the number and quality of the measurements is required to make detailed inferences about the structure of attenuation. The data do constrain the average shear Q-1 in the inner core to be 1/3500 ( ± 60 %) and the average shear Q-1 the mantle to be 1/250 ( ± 4 %). These values are appropriate for frequencies less than 5 mHz. Comparison with published values at higher frequencies indicates there is a measurable frequency dependence of attenuation between 3 and 30 mHz. Very little can be inferred about bulk dissipation in the Earth beyond that it must exist to satisfy the attenuation of the radial modes. Experiments show that the data can be satisfied if bulk attenuation is an average 1.3%, or more, of the shear attenuation. Constraining bulk attenuation to be no greater than 2 % of the shear attenuation, and constraining the outer core to have no attenuation, forces bulk attenuation to be concentrated in the upper mantle.

Limits on differential rotation of the inner core from an analysis of the Earth's free oscillations

Differential rotation of the Earths inner core has been inferred by several seismic ‘body-wave’ studies which indicate that the inner core is rotating at a rate between 0.2° and 3° per year faster than the Earths crust and mantle. The wide range in inferred rotation rate is thought to be caused by the sensitivity of body-wave studies to local complexities in inner-core structure. Free-oscillation ‘splitting functions’, on the other hand, are insensitive to local structure and therefore have the potential to estimate differential rotation more accurately. A previous free-oscillation study, however, was equivocal in its conclusions because of the relatively poor quality and coverage of the long-period digital data available 20 years ago. Here we use a method for analysing free oscillations which is insensitive to earthquake source, location and mechanism to constrain this differential rotation. We find that inner-core differential rotation is essentially zero over the past 20 years (to within ±0.2° per year), implying that the inner core is probably gravitationally locked to the Earths mantle.

Global lateral variations of shear wave attenuation in the upper mantle

We analyze several thousand high-quality, globally recorded SS - S differential waveforms to constrain the lateral variation of shear wave attenuation (Q β ) in the upper mantle. We use a multitaper frequency domain technique to measure attenuation, parameterized by a t* operator, and implement a robust estimation technique to compute t* and its variance. The differential waveform technique minimizes the effect of factors such as finite source duration and structural complexity near the source and receiver so the differential SS - S waveforms are mainly sensitive to the shear attenuation in the upper mantle under the SS bounce point. We use seismograms recorded at ranges of 45° to 100° and compute the SS - S differential t* from the broadening of the SS waveform relative to the Hilbert transform of the S waveform. A careful choice of fitting windows allows us to reduce the biasing effects of interfering phases which can affect t* by up to 0.5 s. The t* residuals (with respect to preliminary reference Earth model (PREM)) vary by ±1.5 s with an average of 0.24 s. Our study suggests an average Q β value of 112 (most of the lateral variations of Q β are within 30% of this value) in the top 400 km of the mantle, slightly lower than the PREM value of 128. There is a qualitative correlation of t* residual with tectonic region with distinctly higher attenuation observed under young oceans compared to platforms and shields. Also, the lateral variations of the residuals are similar in trend to those observed in studies of the attenuation of ScS multiples. At long wavelengths, the Qp map shows a modest correlation with shear wave attenuation maps computed from surface wave analyses and with the patterns of lateral variations of shear velocities at certain upper-mantle depths predicted by the model S16B30. The correlation with the velocity model is highest at 300-500 km depth indicating that there may be a contribution to long-wavelength attenuation from relatively deep regions. Formal inversion for an upper mantle Q β model shows that while lateral resolution is quite good, depth resolution is poor as might be expected. Better depth resolution must await combined body wave and surface wave inversions.

Travel times of P and S from the global digital seismic networks: Implications for the relative variation of P and S velocity in the mantle

We present new data sets of P and S arrival times which have been handpicked from long-period vertical and transverse component recordings of the various global seismic networks. Using events which occurred from 1976 to 1994 results in ∼38,000 globally well-distributed measurements of teleseismic P and ∼41,000 measurements of S. These data are particularly useful for looking at the relative variation of S and P velocities in the lower mantle. We describe both the measurement techniques and the gross characteristics of the data sets. The size of our data sets allows us to exploit the internal consistency of the data to identify outliers using a summary ray analysis. Since the polarity of each arrival is also known, we can construct fault plane solutions and/or compare with polarities predicted by the Harvard centroid moment tensor solutions to further diagnose phase misidentification. This analysis results in ∼5% of the data being identified as outliers. An analysis of variance indicates that the S residual travel times are dominated by the effects of three-dimensional structure but the P data have comparable contributions from noise and source mislocation effects. The summary ray analysis reveals the basic character of lower mantle structure, and there are large-scale patterns in both the S and P data sets that correlate quite well with each other. This analysis suggests that on average, d In v S /d In v P is an increasing function of depth in the mantle going from a value of ∼1.7 at the top of the lower mantle to an apparent value of 4 near the base of the mantle. This latter extreme value of R seems to result mainly from data which sample one region in the lowermost mantle under the central Pacific, where large positive S residuals are associated with very small P residuals. Such an anomaly cannot be thermal in origin.

Upper mantle anisotropy from long‐period P polarization

We introduce a method to infer upper mantle azimuthal anisotropy from the polarization, i.e., the direction of particle motion, of teleseismic long-period P onsets. The horizontal polarization of the initial P particle motion can deviate by >10° from the great circle azimuth from station to source despite a high degree of linearity of motion. Recent global isotropic three-dimensional mantle models predict effects that are an order of magnitude smaller than our observations. Stations within regional distances of each other show consistent azimuthal deviation patterns, while the deviations seem to be independent of source depth and near-source structure. We demonstrate that despite this receiver-side spatial coherence, our polarization data cannot be fit by a large-scale joint inversion for whole mantle structure. However, they can be reproduced by azimuthal anisotropy in the upper mantle and crust. Modeling with an anisotropic reflectivity code provides bounds on the magnitude and depth range of the anisotropy manifested in our data. Our method senses anisotropy within one wavelength (250 km) under the receiver. We compare our inferred fast directions of anisotropy to those obtained from Pn travel times and SKS splitting. The results of the comparison are consistent with azimuthal anisotropy situated in the uppermost mantle, with SKS results deviating from Pn and Ppol in some regions with probable additional deeper anisotropy. Generally, our fast directions are consistent with anisotropic alignment due to lithospheric deformation in tectonically active regions and to absolute plate motion in shield areas. Our data provide valuable additional constraints in regions where discrepancies between results from different methods exist since the effect we observe is local rather than cumulative as in the case of travel time anisotropy and shear wave splitting. Additionally, our measurements allow us to identify stations with incorrectly oriented horizontal components.

Frequency-dependent polarization measurements of long-period surface waves and their implications for global phase-velocity maps

Abstract Surface-wave dispersion maps provide important constraints on global models of shear-wave velocity structure. Current surface-wave dispersion maps show significant differences from researcher to researcher, and it is clear that further work is required. In addition to dispersion data, polarization measurements obtained from long-period (100 s or more) three-component recordings from the various global networks can also be used to constrain dispersion maps. The off great circle propagation of the surface-wave packets is relatively easy to interpret within a ray-theoretic framework, and provides sensitivity to higher-order structure. The polarization angles as a function of frequency are readily measured using a multi-taper technique, which also has the benefit of providing an error estimate for the measurements. Application of the technique to three-component seismograms from the global GEOSCOPE array reveals large deviations from great circle propagation (up to 15° for low-orbit Love waves and 10° for Rayleigh waves in the frequency band 5–12.5 mHz). On a more regional scale, an analysis of seismograms from the German Regional Seismic Network (GRSN) reveals even larger, strongly frequency-dependent deviations from great circle propagation in the frequency range 10–50 mHz.