Jeffrey Park | Yale University (original) (raw)

Papers by Jeffrey Park

Geophysical Journal International, Dec 1, 1993

We have developed an expression for the first-order Born waveform perturbation for long-period se... more We have developed an expression for the first-order Born waveform perturbation for long-period seismic records on an aspherical earth, using an anelastic monopole reference model. We have derived both an explicitly anelastic first-order Born term u'(r, t ) and an approximate, but much simpler, expression in which quasi-degenerate modal coupling is represented by secular terms in the time domain. We designate this expression the 'strong' Born approximation to identify the presence of 'strong' quasi-degenerate coupling. Earlier applications of Born theory to surface wave seismograms have typically neglected the coupling between different modal dispersion branches. The strong Born approximation is linear in the aspherical model, but the secular terms restrict its accuracy to 'short' times after event onset, typically fewer than 10 hr. Additional accuracy can be gained by treating the self-coupling of isolated multiplets explicitly by formally summing the Born series using a projection of the aspherical operator 2" onto the multiplet in question. We call this the 'stronger' Born approximation, which is a non-linear functional of the aspherical model. The stronger Born approximation is similar to, but formally less accurate than, the subspace projection algorithm. We verified the accuracy of synthetic seismograms calculated with the 'strong' and 'stronger' Born approximations against Galerkin coupled-mode synthetics using a zonally symmetric, weakly anisotropic upper mantle model. The Born seismograms replicate successfully the 'quasi-Love' waveforms that diagnose spheroidal-toroidal coupling, suggesting that the strong Born approximation is adequate to model the interaction of free-oscillation coupling partners that are closely spaced in the frequency domain, at least for short records. We performed a waveform inversion test using three-component synthetic seismograms from 297 source-receiver pairs. Once spheroidal-toroidal coupling is incorporated in the inverse formulation, the waveform perturbations associated with the anisotropic parameters are clearly distinct from waveform perturbations associated with the isotropic parameters. Although the model space used in this experiment is highly restricted compared to the real Earth, these results suggest that the trade off between anisotropy and isotropic lateral structure may be less problematic in a fully-coupled waveform inversion than in a tomographic inversion of surface wave phase delays.

Geophysical Journal International, Nov 1, 1981

In a very ingenious paper, Forsyth & Uyeda used observed plate shapes and speeds to compute the r... more In a very ingenious paper, Forsyth & Uyeda used observed plate shapes and speeds to compute the ratios of the eight rms torques which eight different types of plate force exert on 12 crustal plates. We describe one resolution of the conceptual problems arising in Forsyth & Uyeda's estimates for the values and uncertainties of those ratios. We confirm Forsyth & Uyeda's conclusion that equilibrium is mainly between the negative buoyancy of descending slabs and the viscous resistance to their descent; the other six kinds of torque are smaller by at least an order of magnitude. We find the combined rms fractional error in the data and theory to lie between 9 and 16 per cent, at the 1 per cent confidence level. This error prevents determination of the other six torque ratios; so the absolute magnitudes of the eight torques cannot be found by multiplying the magnitude of one of them by the torque ratios.

Geophysical Research Letters, Jun 1, 1990

The radial modes •So-•So axe clearly obsetruble on several long-period seismic records from the 5... more The radial modes •So-•So axe clearly obsetruble on several long-period seismic records from the 5/23/89 Macquarie Ridge earthquake. Observations of are weaker, but stacking demonstrates significant excitation. Calculations suggest that, for spherical-earth mode, no simple double couple in the uppermost mantle can explain the excitation amplitudes of x So-•So relative to 0S0. Ca!cuIations suggest that the anomalous axnplitudes of •$0-•$0 can be explained by coupling to other modes induced by plausible levels of deep-earth lateral structure. The coupling of 050 is much weaker, and its observed plitude suggests that roughly 4% of the total moment release inferred from surfax:e wave studies deviated from pure •8 deviastrike-slip geometry. This can be modeled by > ø tions from A = 0 ø, g = 90 ø in a simple double-couple point source, or by thrust sub events within the main shock.

Geophysical Journal International, Sep 1, 2001

P waves from regional-distance earthquakes are complex and reverberatory, as would be expected fr... more P waves from regional-distance earthquakes are complex and reverberatory, as would be expected from a combination of head waves, post-critical crustal reflections and shallow-incident P waves from the upper mantle. Although designed for steeply-incident teleseismic P waves, receiver functions (RFs) can also retrieve information about crustal structure from regional P. Using a new computation method based on multiple-taper spectral analysis, regional-distance RFs for GSN stations RAYN and ANTO show broad agreement with teleseismic RFs. At RAYN the moveout of the Moho-converted Ps phase, relative to direct P, follows the predictions of the IASP91 earth model well. The Moho-converted Ps phase shows complexity associated with the transition-zone triplications near D=20u and constant delay (zero moveout) as Dp0, consistent with conversion from P n . Similar behaviour is seen for ANTO for events that arrive from the west. For eastern backazimuths the ANTO RFs show features whose moveout is negative as Dp0. This moveout is poorly fit by reverberations in flat layers or by direct scattering from a dipping interface, but is consistent with a topographic scatterer 20-30 km eastward of the ANTO site. Regional receiver functions may therefore be useful in judging whether teleseismic RFs at a particular station are suitable candidates for a 1-D velocity structure inversion. Synthetic seismograms of regional P phases, computed with a locked-mode reflectivity approach in a 1-D structure, confirm several gross features of the RAYN and ANTO regional receiver functions.

Physics of the Earth and Planetary Interiors, Nov 1, 1994

The PS wave is radially polarized in an isotropic spherically symmetric Earth owing to the P to S... more The PS wave is radially polarized in an isotropic spherically symmetric Earth owing to the P to SV conversion at the free surface. If we choose stations with weak SKS splitting to minimize the effect of the receiver, we can measure the anisotropy beneath the bounce point of the PS wave. We find that with a deep source and epicentral range of 90°< ~< 125°,the PS phase can be distinguished from other phases. Owing to the limitation of recent large deep events with epicentral range between 90°and 125°,we analyze data from stations in North America and events beneath the Bonin Islands and the Fiji Islands. For events in these two regions, the bounce points of the PS wave are roughly located northwest of the Kuril Islands and near the Nova-Canton Trough in the central Pacific, respectively. Because the first Fresnel zone for the PS wave at this distance range is roughly 700 km across, each PS splitting observation must be interpreted as a local average of anisotropic properties. The average direction of the fast axis of anisotropy below the Nova-Canton Trough region is N104.2°Ewith a standard deviation 12.7°and a typical delay time of 1.8 s. Landward of the Kuril Islands, the average direction of the fast axis is N127.6°Eclockwise from north, and the standard deviation is 11.3°,with a typical delay time of 1.2 s. We have compared the fast axis with the direction of fossil seafloor spreading and with the present-day absolute plate motion. The fast axis of anisotropy at the Nova-Canton Trough agrees well with the direction of absolute plate motion, and poorly with the complex fossil spreading pattern. This suggests that significant upper-mantle shear anisotropy exists in this part of the central Pacific, and is consistent with mineral alignment owing to strain associated with present-day plate motion. Similarly, the fast axis beneath the Kuril Islands parallels the convergent motion of the slab. Coupled-mode synthetics constructed with the 'strong' Born approximation can be used to model the interaction of the PS waves with anisotropic structure that has a horizontal axis of symmetry. We use all free oscillations up to 35 mHz in the calculation. The coupled-mode synthetics show shear-wave splitting with delay time and fast axis consistent with the ray theory prediction.

Journal of Geophysical Research, Oct 20, 1989

The often striking presence of cyclical beddings has frequently been noted in Cretaceous marine s... more The often striking presence of cyclical beddings has frequently been noted in Cretaceous marine sediment deposits. In many instances, these beddings appear to have periodicities similar to those of the Earth's orbit, i.e., its precession, obliquity, and eccentricity. Variations in the primary deposition of ocean sediments are strongly linked to atmosphere‐land‐ocean interactions. We report a set of numerical experiments using an atmospheric general circulation model that are designed to examine the sensitivity of mid‐Cretaceous climate to insolation changes due to the precessional cycle. We restrict attention to a single orbital parameter because most limestone/black shale bedded sequences were deposited at low latitudes, where precessional insolation variations predominate. We varied systematically the precessional index between the maximum positive and negative values calculated over the last 2 m.y. and used mid‐Cretaceous paleogeographic and paleotopographic reconstructions and zonally symmetric sea surface temperatures based on earlier work by Barron and Washington. Surface wetness and albedo values appropriate for grassland were prescribed uniformly over all land regions. To capture the seasonality of precession, we employed both perpetual January and perpetual July simulations. Changes in surface heating due to the imposed insolation anomalies resulted in a strong, basically linear response of monsoonal circulations, dominated by changes over the northern hemisphere. The hydrologic cycle shows a significant response over many regions. The low‐latitude proto‐South Atlantic region varies from a strong net sink for water vapor (excess precipitation) to a strong source (excess evaporation) over the precession cycle. This variation is consistent with an alternation between a stagnant, stratified ocean basin with anoxic bottom water and an evaporative basin that produces bottom water that is warm, saline, and oxygenated. The portion of the Tethys Ocean that overlays the limestone/black shale sequences now found in present‐day Italy does not exhibit comparable behavior, but the reconstruction of orography and basin boundaries in this region is less known. The simulations show, however, that as the monsoonal flow over south proto‐Asia intensifies, water vapor evaporated in this part of Tethys is prevented from crossing the proto‐Alps into the interior of the continent, thereby remaining in the Tethian drainage basin. As a result, central proto‐Asia shifts between arid and moist conditions with precessional variations. The water vapor budget over northeast Africa varies systematically from zero seasonality to a marked wet/dry seasonal cycle. The deposition of eolian material can be inferred from a combination of continental aridity, favorable mean wind directions, and significant wind variances. In our experiments the mean surface and upper winds often show a systematic response to precession, but surface wind variances show a systematic response only in isolated regions. Our simulations do not provide a simple mechanism to explain the cyclicity in eolian deposition that has been reported for north‐central Tethys.

Geophysical Journal International, Sep 1, 1993

We investigate surface wave propagation effects caused by P and S-wave velocity anisotropy and it... more We investigate surface wave propagation effects caused by P and S-wave velocity anisotropy and its orientation in the upper mantle. We compare coupled-mode synthetic seismograms, constructed from sums of free oscillations for different types of upper mantle models, in order to understand better the observable aspects of anisotropy and its fast direction in the earth. Our calculations suggest that upper mantle anisotropy, which is not transversely isotropic, of few per cent can generate significant waveform anomalies in long-period seismic records of 0-20 mHz. Those anomalies are termed 'quasi-Love' waves and are caused by spheroidal-toroidal free-oscillation coupling. Large quasi-Love waveforms are difficult to produce with levels of isotropic heterogeneity consistent with global tomographic models of the mantle. Coupled-mode waveform anomalies in long-period seismic records at a single station can be used to diagnose the presence of anisotropic structure in the upper mantle. Because J, -OT,r coupling pairs have weak sensitivity to aspherical wavenumbers s < I/ -['I, and II -1'1 increases with frequency for f > 4 mHz, smoother/rougher structure generates longer/shorter-period fundamental-branch waveform anomalies. Anisotropy in our models is assumed to have hexagonal symmetry, that is, a single axis of symmetry. However, the symmetry axis can be arbitrarily oriented. The waveform anomalies associated with spheroidal-toroidal coupling are sensitive to the orientation of the fast-velocity direction of upper mantle anisotropy. In particular, for the same level of velocity perturbation, coupled-mode waveform anomalies increase as the fast axis of anisotropic structure rotates from vertical to horizontal. The orientation of the fast axis can influence both phase shifts and coupled-mode waveforms of long-period surface waves. The coupled-mode waveform anomalies predicted by our theoretical calculations are observed in the data and seem to diagnose the presence of upper mantle anisotropy which is not transversely isotropic.

Science, Aug 27, 1993

When deformed, many rocks develop anisotropic elastic properties. On many seismic records, a long... more When deformed, many rocks develop anisotropic elastic properties. On many seismic records, a long-period (100 to 250 seconds), "quasi-Love" wave with elliptical polarization arrives slightly after the Love wave but before the Rayleigh wave. Mantle anisotropy is sufficient to explain these observations qualitatively as long as the "fast" axis of symmetry is approximately horizontal. Quasi-Love observations for several propagation paths near Pacific Ocean subduction zones are consistent with either flow variations in the mantle within or beneath subducting plates or variations in the direction of fossil spreading in older parts of the Pacific plate.

Journal of Geophysical Research, 1994

Lateral variations in azimuthal anisotropy cause significant waveform anomalies in long-period su... more Lateral variations in azimuthal anisotropy cause significant waveform anomalies in long-period surface waves (f < 15 mHz, T•70 s), as a result of coupling between fundamental branch Rayleigh and Love waves. These anomalies, termed "quasi-Love" waves, have elliptical polarization, arrive slightly behind the Love wave but prior to the Rayleigh wave, and are observed on many propagation paths in the Pacific Ocean region. Our observations of quasi-Love waves indicate the existence of strong lateral anisotropic gradients in the western Pacific Ocean, in particular, near Hawaii and seaward of the Tonga-Kermadec, Kurile and Marianas-Izu-Bonin subduction zones. A lack of quasi-Love generation beneath the Phillipthe Sea suggests weak azimuthal anisotropy in the region. In the southwest Pacific Ocean, the long-period quasi-Love waveforms recorded at station SNZO (South Karori, New Zealand) can be fit well with a simple anisotropic Earth model with a 900 rotation in the orientation of the fast P velocity axis near the boundary between the Indo-Australian and the Pacific plates. In this model, 6% P wave velocity anisotropy from the Moho to 210 km depth, with a NNE-SSW fast direction (roughly parallel to the plate boundary), extends 500-1000 km east of the Tonga-Kermadec trench, where it shifts to a WNW-ESE orientation (parallel to fracture zones in the southernmost Pacific plate). This solution is nonunique, however, as a similar lateral variation of 2% $ wave anisotropy at asthenospheric depths (100-300 km) generates similar waveform anomalies. We attribute the laterally varying anisotropy to either (1) flow variations in the asthenosphere, consistent with latera! shear detected in deep Tonga-Kermadec seismicity, (2) variations in fossil spreading direction in the Cretaceous long normal polarity interval, (3) the disturbance of fossil anisotropy caused by the passage of the Louisville Ridge hotspot, and (4) lithospheric compression associated with continental collision along the Alpine Fault. The apparent location of the Love-to-Rayleigh "scatterer" favors options 1 and 3. Gradients in azimuthal anisotropy are inferred in the northwestern Pacific, associated with one or more of these mechanisms. A quasi-Love wave observed on a path from Alaska to PPT (Papeete, Tahiti) is bandlimited to f > 8 mHz, suggesting lateral variations with wavelength twice the spacing of fracture zones in the north central Pacific.

Journal of Geophysical Research, Jun 10, 1986

Variational theory based on self‐adjoint equations of motion cannot fully represent the interacti... more Variational theory based on self‐adjoint equations of motion cannot fully represent the interaction of the earth's seismic free oscillations in the presence of lateral structure, attenuation, and rotation. The more general Galerkin procedure can model correctly the frequencies and attenuation rates of hybrid oscillations. Implementation of either algorithm leads to a generalized matrix eigenvalue problem in which the potential and kinetic energy interactions are separated into distinct matrices. The interaction of the earth's seismic free oscillations due to aspherical structure, attenuation, and rotation is best treated as a matrix eigenvalue problem. The presence of attenuation causes the matrices to be non‐Hermitian and requires the use of a general Galerkin procedure. Physical dispersion, represented as a logarithmic function in frequency, must be represented by a truncated Taylor series about a fiducial frequency in order to be incorporated in the Galerkin formalism in a numerically tractable manner. The earth's rotation introduces an interaction matrix distinct from the potential and kinetic energy matrices, leading to a quadratic eigenvalue problem. A simple approximation leads to an eigenvalue problem linear in squared frequency. Tests show that this approximation is accurate for calculations using modes of frequencies f ≳ 1 mHz, unless interaction across a wide frequency band is modeled. Hybrid oscillation particle motions are represented by matrix eigenvectors that can be significantly nonorthogonal. The degrees of freedom in the low‐frequency seismic system remain distinct, since source excitation is calculated by using dual eigenvectors. Synthetic seismograms that are constructed from Galerkin coupling calculations without reference to this eigenvector nonorthogonality can be disastrously noncausal.

Geophysical Research Letters, Jun 1, 1997

Radial and transverse teleseismic receiver functions (RFs) at GSN station ARU, in central Euraa 1... more Radial and transverse teleseismic receiver functions (RFs) at GSN station ARU, in central Euraa 1-D anisotropic crustal structure. In a broad •b range, the transverse RFs possess a strong phase at • S-sec delay relative to direct P, with a polarity reversal at •b • 50 ø. The radial RFs peak at the transverse-RF polarity reversal for this converted phase. The first motion of the transverse RFs varies with •b also, reversing polarity at •b ,,• 345 ø. The azimuthal variation can be modeled by a 5-layer velocity profile with substantial (15%) seismic anisotropy in both the lowermost crust and a low-velociW surface layer. Assuming hexagonal symmetry, the lowermost crust has a tilted "slow" symmetry axis i.e. an oblate phase velocity surface. The strike of the axis is oblique to the north-south Urals trend, but deviates • 20 ø from the mantle fast-axis inferred from SKS splitting. The magnitude and tilt of the model's anisotropy suggests that fine layering and/or aligned cracks augment mineral-orientation anisotropy near the top and bottom of the crust. Introduction Receiver function (RF) analysis [Burdick •4 Langston, 1977] uses phase conversions that trail the direct P wave to study 1-D isotropic crustal structure. Transversecomponent conversions, and backazimuth (%b) variations in radial-component RFs can suggest lateral heterogeneity [Owens et al., 1984] and/or dipping interfaces [Langston, 1977] beneath the station. Alternatively, an anisotropic 1-D layered medium produces P-SH in addition to the 'P-SV coupling. Kosarev et al. [1984] used long-period P-SH conversions to infer anisotropic layers in the mantle under Europe. Synthetic seismograms, generated using a reflectivity technique [Keith •4 Crampin, 1977; Levin •4 Park, 1997a], indicate that %bdependent radial and transverse P-coda can be generated by a 1-D anisotropic structure, especially for anisotropy with a tilted symmetry axis [Levin •4 Park, 1997b]. As well, transverse P-coda motion may arise from split P-SV converted phases [Herquel et at., 1995]. We explore the potential influence of crustal anisotropy on RFs using the IKIS GSN station ARU (56.4 ø E, 58.2øN) in central Russia (Figure 1). We develop, via forward modeling with reflectivity-based synthetic seis-

Journal of Geophysical Research, Dec 10, 1987

An 8‐m section of a mid‐Cretaceous (Albian) deep‐sea sediment core from Piobbico, Italy contains ... more An 8‐m section of a mid‐Cretaceous (Albian) deep‐sea sediment core from Piobbico, Italy contains ∼2 cycles/m compositional oscillations. As postdepositional chemical migration in the core is weak, the relative amount of carbonate is a primary indicator of Cretaceous paleoclimate variability. We report results of spectral analysis of two series, CaCO3 wt % measurements taken at roughly 2 cm intervals and a more densely sampled photodensitometer record of light‐dark variation. The uncertainty in the age‐depth relation (i.e., unknown fluctuations in sedimentation rate) hampers a detailed assessment of the suggested eccentricity correlation. We fit for long‐term (time scale greater than 75 kyr) fluctuations in sedimentation rate by tracking the local frequency modulation of the dominant harmonic in the data series, assuming the true input signal to be monochromatic. We estimate uncertainty in the observed local frequency by means of a statistical jackknife. We fit a smoothed cubic spline to the set of discrete frequency modulation estimates, specifying a χ2 = N misfit criterion, where N is the number of frequency estimates. From this analysis we infer fluctuations of a factor of two in the sedimentation rate, which occur predominately on a time scale of 400 kyr. We generate “tuned” series using several candidate age‐depth relations from the carbonate and densitometer series. The tuned carbonate series returns greater correlation with the modern Milankovitch periodicities. The 2 cycles/m energy resolves principally into two harmonic components whose frequency ratio corresponds (to an observational accuracy of 1–2%) to that of the 97.0‐ and 127.6‐kyr eccentricity oscillations. At frequencies lower than 2 cycles/m, we find harmonic oscillations whose phase correlates with the “beating” envelope of the 2 cycles/m energy in a manner consistent with the modern Milankovitch insolation. We also observe a sinusoidal oscillation of lower amplitude with period (scaled by those of the presumed eccentricity oscillations) of 39.2 ± 1.1 kyr, which agrees with the period of the modern obliquity cycle after correction for the effects of tidal friction. Oscillations corresponding to Milankovitch precessional frequencies are not established, owing possibly to low signal level and unknown short‐term deposition fluctuations. The tuned densitometer series recovers few new periodic features, although its inferred age‐depth relation correlates well with that of the carbonate series. We calibrate the depth variable downcore to the orbital cycles to estimate r=5.0 ± 0.15 m/m.y. as the effective sedimentation rate.

American Journal of Science, Jun 1, 2011

Large-scale carbon-cycle feedbacks within Earth's climate system can be inferred from the statist... more Large-scale carbon-cycle feedbacks within Earth's climate system can be inferred from the statistical correlation of atmospheric CO 2 and other climate observations. These statistical relationships can serve as validation targets for global carbon-cycle models. Fourier-transform coherence between atmospheric CO 2 measured at Mauna Loa, Hawaii, and Hadley Centre global-average temperatures changed in the late 20th century at interannual frequencies, from a 6-month time lag to a 90°p hase lag that scaled CO 2 fluctuations to a time-integral of the global-average temperature anomaly. Wavelet coherence estimates argue that this change occurred with a recognized ocean-circulation climate transition during the late 1970s. General features of these CO 2 -temperature correlations are confirmed using global-average temperature from other sources and atmospheric CO 2 measured at other locations, though only the Mauna Loa CO 2 record is long enough to resolve well the coherence properties before the 1970s transition. The CO 2 -coherence phase for the globalaverage surface-air temperature time series from NASA-GISS and the lowertroposphere temperature series from the MSU satellite is more complex than for the Hadley-Centre dataset, the only estimate that incorporates sea-surface temperature (SST) observations. Near f ‫؍‬ 0.25 cyc/year, 4-year oscillation period, the CO 2coherence is particularly strong for the Hadley-Centre gridpoint temperature-anomaly time series from low-latitude oceans. This suggests that sea-surface temperature is a primary driver of the correlation, at least for the 0.2 < f < 0.5 cyc/yr bandpass where the El-Nino/Southern-Oscillation (ENSO) climate process dominates. Outside the ENSO bandpass coherence is significant between 14 long-running GLOBALVIEW CO 2 -observing sites and the sea-level-pressure-based Southern Oscillation Index (SOI) and North Atlantic Oscillation (NAO) time series, consistent with wind stress and mixed-layer-thickness influences on ocean-atmosphere CO 2 flux, independent of temperature fluctuations. Evidence for terrestrial biosphere influence is strongest in the leading principal component of GLOBALVIEW CO 2 -variability at f ‫؍‬ 0.25 cpy, where a larger amplitude and a 4-month phase shift distinguish the mid-and highlatitude Northern Hemisphere CO 2 fluctuations from those of the tropics and the Southern Hemisphere. The terrestrial signal we infer, however, coheres more strongly with oceanic-gridpoint temperatures than to continental-gridpoint temperatures.

Tectonophysics, Feb 1, 2020

This study presents observations of Love-to-Rayleigh scattering beneath the eastern North America... more This study presents observations of Love-to-Rayleigh scattering beneath the eastern North American passive margin that place new constraints on seismic anisotropy in the upper mantle. The scattering of Love-wave energy to Rayleigh waves is generated via sharp lateral gradients in anisotropic structure along the source-receiver path. The scattered phases, known as quasi-Love (QL) waves, exhibit amplitude behavior that depends on the strength of the anisotropic contrast as well as the geometrical relationship between the propagation azimuth and the anisotropic symmetry axis. Previous studies of seismic anisotropy in the upper mantle beneath eastern North America have revealed evidence for a mix of lithospheric and asthenospheric contributions, but the interpretation of indicators such as SKS splitting is hampered by a lack of vertical resolution. Complementary constraints on the depth distribution of anisotropy can be provided by surface waves, which have the additional advantage of sampling portions of the margin that lie offshore. Here we present measurements of QL phases using data from several hundred broadband seismic stations in eastern North America, including stations of the USArray Transportable Array, the Central and Eastern U.S. Network, and the MAGIC experiment in the central Appalachians. We find evidence for clear QL arrivals at stations in eastern North America, consistent with a region of particularly strong and coherent scattering inferred just offshore the central portion of the margin. The coherent scattering near the Eastern North American Margin likely reflects lateral transitions in seismic anisotropy in the asthenospheric mantle, associated with locally complex three-dimensional flow, with possible additional contributions from anisotropy in the mantle lithosphere. A second region of strong QL scattering near the southern coast of Greenland is enigmatic in origin, but may be due to pre-existing lithospheric fabric.

Geophysical Research Letters, Nov 1, 1989

A set of inversion experiments is described that tests the ability of global surface wave tomogra... more A set of inversion experiments is described that tests the ability of global surface wave tomography to retrieve long-wavelength upper mantle velocity structure in the presence of a modest level of rough structure. We use upper-mantle model M84A, augmented with randomly-generated lateral structure to s,• = 20, to calculate coupled-mode synthetic seismograms by means of the subspace projection method. The data kernels for path-integral data observables do not belong to the model space of allowable phase velocity perturbations, suggesting that constraints on model roughness in the inversion should lead to a better agreement with the long-wavelength part of the 'true' model than do the commonly-used constraints on model size. Coherence ½ between the inverted and the input model is enhanced by using roughness constraints. Estimation of perturbation size is more stable using roughness constraints, but is subject to a positive bias, especially for periods T > 200 s. We can achieve, with a data set of 672 Ri and R2 phase delays, ½ _> 0.9 only for s <_ 6, suggesting 'leakage' bias caused by the breakdown of the pure-path assumption. Introduction The investigation of the Earth's interior with long-period surface waves often relies on the 'pure-path,' or 'tomographic,' approximation, which expresses data observables as integrals of model properties along the source-receiver great-circle path. This approximation is valid when the scale length of lateral structure is much larger than the wavelength of the observed seismic wave. Inversions of long-period surface wave data have led to models of seismic velocity that correlate with large-scale tectonic features and the angular degree s = 2, 3 components of the geoid (e.g. model M84A of Woodhouse and Dziewonski [1984]). Controversy has centered on the reliability of smaller-scale features and the amplitudes of the inferred velocity perturbations. Both have important implications for the composition and physical properties of the Earth's mantle. Tanimoto [1985] developed Backus-Gilbert resolution kernels and uncertainty bounds for global phase velocity inversions. These analytical tools can be applied if the inverse problem is linear, or readily linearizable. Tomographic inversion is linear where the 'pure-path' assumption is valid i.e. only for smooth lateral structure. Significant 'rough' lateral structure is present in the upper mantle, as is evident from the global population of slabs, ridges and hot spots. Rough structure can bias a lateral Copyright 1989 by the American Geophysical Union. Paper number 89GL03096.

Geophysical Journal International, Jul 1, 1991

We investigate normal mode multiplet coupling along the fundamental spheroidal mode branch using ... more We investigate normal mode multiplet coupling along the fundamental spheroidal mode branch using three different numerical methods. A suite of 300 synthetic vertical accelerograms computed using the great-circle approximation and the first-order subspace-projection algorithm are compared with accurate accelerograms computed using a Rayleigh-Ritz variational method. In each case, the accelerograms are computed by summing the responses of the hybrid multiplets O&-O&; the resulting waveforms correspond to mantle Rayleigh waves with periods between 150 and 600 s. The great-circle approximation correctly represents all but 5 per cent of the waveform variance produced by the degree-8 model of upper mantle heterogeneity M84A, for each of the sequentially arriving wavegroups R1-R6. For a contrived model with a modest amount of additional heterogeneity up to degree 20, the relative great-circle error is substantially greater, approximately 30 per cent. The first-order subspace-projection algorithm requires an order of magnitude more computer time than the great-circle approximation; however it is much more accurate. For the first arriving wavegroup R 1 , it correctly represents all but 2 per cent of the waveform variance produced by model M84A; this relative error decreases for subsequent wavegroups to less than 1 per cent for R 2 and less than 0.2 per cent for R3. For the contrived degree-20 model, the relative subspace-projection error is 6 per cent for R1, 1.5 per cent for R2 and 0.9 per cent for R3; the relative error is less for the later arriving wavegroups because of the increasing effect of the lateral heterogeneity as well as the more rapid attenuation of the higher frequency multiplets that are not as well modelled by the approximation.

Journal of Geophysical Research, 1986

Progress in Earth and Planetary Science, Jan 27, 2021

Following publication of the original article (Karato et al., 2020), the author identified there ... more Following publication of the original article (Karato et al., 2020), the author identified there is a minor typo in Fig. and graphical abstract image. The correct Fig. and graphic abstract image are provided below. The original paper has been updated.

Reviews of Geophysics, 1995

The early 1990s saw many interesting contributions to the field of seismic wave propagation from ... more The early 1990s saw many interesting contributions to the field of seismic wave propagation from a variety of US researchers, even as many wave‐propagation specialists shifted their research focus away from new methods for seismogram synthesis toward data acquisition and inversion. In part, this shift was a natural consequence of the explosive growth in the amount and availability of high‐quality digital seismic data, ready to be processed with interpretation tools developed in previous decades. As a result, observational seismology has recently made dramatic contributions toward imaging global geodynamics, revealing the great variety of crustal structures, and laying the foundation for a collaborative global network of broadband seismometers to monitor earthquakes and other seismic events. However, recent observational studies have brought to light new problems in wave propagation theory, and have made some older problems more difficult to ignore.

Journal of Geophysical Research, 1991

three-component digital seismometers. The crust can be modeled as 34.5 km thick, and with three l... more three-component digital seismometers. The crust can be modeled as 34.5 km thick, and with three layers having linear gradients without midcrust discontinuities. For this model, P-velocities are 6.1-6.2 km/s in the upper crust, and 6.2-6.8 km/s in the lower crust. S-velocities are 3.5-3.7 km/s in the upper crust, and 3.7-3.9 km/s in the lower crust. Because Moho reflections comprise our principal constraints on lower-crustal velocities, there is a tradeoff between lower-crustal velocity and crustal thickness. In particular, an average crustal thickness of 39-40 kin, reported elsewhere in New England, is not precluded by our data. The Poisson's ratio for the crust varies between 0.23-0.26, in the lower range of values reported for crustal minerals. Our dataset is consistent with •2% lateral variation in the upper crust underlying the New Hampshire and White Mountain Plutonic Series, but larger variations deeper than 15 km. If modeled in terms of Moho topography, Prop traveltime residuals and PraP -P residuals suggest thicker crust (36-37 kin) under the White Mountain batholith, with thinner crust (33-34 km) to the east and southwest of the White Mountains. Such topography of the Moho correlates well with both the surface elevation and the Bouguer gravity anomaly in the region. Gravity data do not favor the simplest alternative model: a thick low-velocity granitic lower crust beneath the batholith. Using a simplified density model, roughly 30-35% of the gravity anomaly in the White Mountain region can be modeled as the result of the inferred Moho depression, requiring only a 5 km low-density root for the White Mountain batholith. The short wavelength of the Moho topography is consistent with a very low flexural rigidity for the lithosphere (• 1021 Nt-m), suggesting that the plutons were intruded into a weak lithosphere. A rapid transition from positive to negative PraP residuals falls along a line that parallels the onshore extension of the Kelvin Seamounts, and may correspond to the "line of weakness" hypothesized by Sykes (1978) to have been tectonically active during the opening of the North Atlantic Ocean at 100-200 Ma.