Shear Velocity Variations Research Articles

Normal-mode and free-Air gravity constraints on lateral variations in velocity and density of Earth's mantle

With the use of a large collection of free-oscillation data and additional constraints imposed by the free-air gravity anomaly, lateral variations in shear velocity, compressional velocity, and density within the mantle; dynamic topography on the free surface; and topography on the 660-km discontinuity and the core-mantle boundary were determined. The velocity models are consistent with existing models based on travel-time and waveform inversions. In the lowermost mantle, near the core-mantle boundary, denser than average material is found beneath regions of upwellings centered on the Pacific Ocean and Africa that are characterized by slow shear velocities. These anomalies suggest the existence of compositional heterogeneity near the core-mantle boundary.

Elasticity of MgSiO3orthoenstatite

The single-crystal elastic moduli of the MgSiO 3 orthoenstatite end-member have been measured by Brillouin spectroscopy at ambient conditions. The aggregate elastic moduli at 1 atm are KS = 107.6(15) GPa and μ = 76.8(7) GPa, for the adiabatic bulk modulus and shear modulus, respectively. These values are in excellent agreement with the results of previous acoustic studies of synthetic MgSiO3. Comparison of our results with pressure-volume ( P-V) measurements do not support the presence of a change in the P-V trajectory of orthoenstatite at ~4 GPa, as suggested previously on the basis of X-ray measurements to 8.5 GPa. The effects of chemical composition on the elasticity of orthopyroxenes are well represented by the variation of compressional and shear velocities with density, which exhibit well defined trends for both synthetic and natural samples.

Simultaneous inversion for 3-D variations in shear and bulk velocity in the mantle

Until recently, most of the seismic tomographic modeling has been addressing the question of lateral heterogeneity either in P- or S-wave velocities. The S-wave velocity variations are larger and hence provide stronger signal on long-period waveforms. The direct P travel times, being the first arrivals, on the other hand, are most frequently reported in the International Seismological Centre (ISC) Bulletins. In mineral physics experiments, the variation in bulk velocity is more often measured. To better understand the differences between δv P and δv P patterns and better link the results from mineral physics to those of seismic tomography, we formulate the inverse problem in terms of relative perturbations in the shear velocity v S = ( μ ϱ ) 1 2 and bulk sound velocity v Φ = ( K ϱ ) 1 2 . We use a large data set which consists of waveforms, waveform-derived travel times and travel times from the ISC Bulletins. The earthquakes are relocated using corrections for lateral heterogeneity. The events which cannot be reliably determined are discarded. The model is defined as spherical harmonics to Degree 12 horizontally and as Chebyshev polynomials to order 13 radially, for both shear and bulk sound velocity. The inversion is performed under smoothness constraint. The resolution tests and bootstrapping analysis indicate that the model is well recovered, particularly at long wavelength. The results indicate a much larger variability of shear than bulk sound velocity. The model explains observations well. The most intriguing result obtained in this study is that the variations in shear velocity and bulk sound velocity are negatively correlated in the lowermost mantle. The explanation is not very clear. From the mineral physics point of view, it is not unlikely that this could be explained in terms of thermal variation, even though we are unwilling to rule out the possibility of large wavelength compositional variations.

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 (Qβ) 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 Qβ value of 112 (most of the lateral variations of Qβ 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 Qβ 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 Qβ 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.

Upper mantle shear structure beneath the Colorado Rocky Mountains

A tomographic inversion of teleseismic shear wave delays has been performed using data collected in the 1992 Program for Array Seismic Studies of the Continental Lithosphere Rocky Mountain Front experiment. The shear wave residuals used as data were corrected for known crustal, sediment and topographic differences and thus were sensitive to mantle shear velocity variations beneath the Colorado array. Large differences in shear wave travel time are observed across Colorado and into western Kansas with a maximum difference of near 5 sec between the central Rockies in Colorado and a station in western Kansas. The shear wave residuals were inverted for shear wave velocity variations in the upper 350 km of the mantle beneath Colorado and Kansas. Large differences in mantle shear velocity are found between the Rockies and the Kansas Great Plains. The average shear velocity in the upper 200 km is about 9% greater beneath Kansas than beneath the Rockies. At greater depths, lateral variations are far smaller and not as well correlated with surface tectonics. In a qualitative sense, there appear to be three mantle structures present beneath the study area. Beneath the Rockies the upper mantle is extremely slow. Both to the west and east of the Rockies we find intermediate mantle shear velocity. There is then an abrupt increase in mantle shear velocity near the Colorado‐Kansas border. We interpret the abrupt increase in mantle shear velocity near the Colorado‐Kansas border to mark the boundary of cratonic lithosphere. The slow velocity zone beneath the Rockies appears to be upwelled asthenosphere as is seen beneath the Rio Grande Rift to the south. To match the seismic contrast between the mantle beneath Kansas and the Colorado Rockies requires a temperature contrast of at least 350° C as well as partial melt beneath the Rockies. The hot mantle beneath the Rockies implies that the mantle density is low and the high topography of the Rockies is at least partially due to buoyant mantle.

Upper-mantle shear velocity beneath eastern Australia from inversion of waveforms from SKIPPY portable arrays

In 1993, the Research School of Earth Sciences of the Australian National University commenced a nationwide seismometry project, SKIPPY, for a comprehensive study of the upper mantle beneath the Australian continent. We applied a waveform inversion technique to broad-band data recorded while the SKIPPY portable arrays were positioned in eastern Australia in order to construct a 3-D model of shear velocity in the upper mantle and transition zone beneath eastern Australia and the adjacent oceanic regions. The SKIPPY data were augmented by data from the permanent seismological observatories in the region. The first step of the waveform inversion used involved the matching of the waveforms of fundamental- and higher-mode Rayleigh waves with waveforms synthesized from radially stratified models; in the second stage the linear constraints on radial variations in shear velocity were combined in a tomographic inversion for aspherical variations in shear velocity. The preferred model reduces the data variance by 90 per cent. Owing to the dense data coverage, structural features with dimensions larger than 250 km laterally and 50 km vertically are resolved. The major structural features inferred from the tomographic images are (1) a substantial increase in the thickness of the high-velocity ‘lid’ from the oceanic region to the Phanerozoic continental and Proterozoic continental regions, (2) a pronounced low-velocity zone centred at 140 km depth beneath the part of eastern Australia often referred to as the Tasman fold belt, which confirms previous inferences from Rayleigh-wave dispersion curves, (3) a prominent zone of low wave speeds beneath the eastern margin of the continent that coincides with locations of Cenozoic volcanism and regions of enhanced heat flow, (4) deep low-wave-speed anomalies beneath both the Coral and Tasman seas, and (5) localized high-wave-speed perturbations in the mantle transition zone (410-660 km depth) beneath eastern Australia, in particular beneath the New England fold belt and the Mount Isa block. From the images we infer that the eastern boundary of the Precambrian shields does not coincide with a sharp seismic contrast, unless this boundary is located further to the east than is commonly assumed. The structure of the upper mantle and transition zone beneath eastern Australia as inferred from the images is more complex than that beneath the Precambrian cratons of central and western Australia, which could be due to subduction beneath the eastern continental margin prior to opening of the Tasman sea. If correct, this interpretation would imply that part of the upper mantle has moved along laterally with the lithosphere during the relatively fast northward motion of the plane.

Normal‐mode constraints on the structure of the Earth

We have analyzed the splitting characteristics of 75 spheroidal free oscillations excited by the Great 1994 Bolivia and Kuril Islands earthquakes. These spheroidal modes may be roughly subdivided in terms of 8 radial modes, 40 mantle modes, and 27 core‐sensitive modes. The splitting of each mode is corrected for the effects of rotation and hydrostatic ellipticity. The remaining signal is due to lateral variations in the mantle and core and may be expressed in terms of so‐called splitting functions, which represent a local radial average of the Earth's even three‐dimensional heterogeneity. In the surface‐wave limit, splitting functions are the equivalent of an even‐degree phase velocity map. Each mode is uniquely sensitive to the Earth's structure. Some modes are predominantly sensitive to compressional velocities in the upper mantle, others to shear velocity variations in the lowermost mantle, and some modes “see” the inner core. As part of our analysis, we determine the center frequency and quality factor of each individual mode; these observations constrain the terrestrial monopole. Collectively, the normal‐mode splitting observations presented in this paper put constraints on the large‐scale, even structure of the entire Earth. We compare the observed splitting functions with predictions from three recent Harvard models: SH12WM13, SKS12WM12, and PS12WM13. These models are constrained by traveltime and waveform data but contain no normal‐mode information. We demonstrate that large‐scale, even structure is quite accurately represented in current Earth models, but that the splitting of some predominantly compressional modes is not satisfactorily explained. Although a distinct mantle signal is observed in the splitting functions of core‐sensitive modes, a characteristic zonal degree 2 pattern is missing. This missing signal is believed to be the result of inner core anisotropy.

Mantle shear structure beneath the Americas and surrounding oceans

Maps of lateral variation in shear velocity within the mantle beneath North and South America, their surrounding oceans, and parts of Africa and Eurasia are produced from inversion of travel times of horizontally polarized shear body waves. The data consist of S and ScS waves as well as multibounce phases SS, SSS and SSSS. Waves that bottom within the upper mantle are modeled using synthetic seismograms in order to estimate travel times for each of the multiple arrivals caused by velocity discontinuities near 400 and 660 km depth. The model consists of blocks with uniform slowness anomalies relative to a one‐dimensional starting model and extends from the surface to the core‐mantle boundary. The blocks have horizontal dimensions of roughly 275 by 275 km and vary in the vertical dimension from 75 to 150 km. The data are inverted using a simultaneous iterative reconstruction technique algorithm. The upper 400 km of the model is dominated by lateral variations that correspond to surface tectonic environments. Three shields on three separate continents have higher than average velocities down to between 320 and 400 km depth. Young tectonically active regions are very slow in the upper 250 km. The transition zone from 400 to 660 km depth is the most poorly resolved region. High velocity beneath western South America in the transition zone is probably associated with subducting slab. The transition zone velocity beneath the western and central part of North America also appears to be slightly faster than average. The lower mantle is dominated by large‐scale sheets of higher than average velocity and more equidimensional regions of slow velocity. From South America to Siberia, sheet‐like high‐velocity anomalies are observed from 750 km depth to the core‐mantle boundary. Another lower mantle high‐velocity anomaly is seen beneath southern Eurasia. The high‐velocity lower mantle anomalies seem to be associated with subduction during the last 150 Ma. Comparing the location of past subduction with the location of lower mantle anomalies, the identification of lower mantle anomalies with old subducted slabs suggests slow sinking of slabs in the lower mantle (about 1 to 2 cm/yr). If this interpretation is correct then high velocity in the deepest mantle off the west coast of South America through the western United States requires significant subduction from 120 to 150 Ma a few thousand kilometers off the coast of the Americas. The slowest deep region found in this study is at the base of the mantle beneath the eastern Atlantic Ocean and may be associated with hotspots in that region. Other hotspots do not appear to be associated with slow lower mantle velocity.

3-D wave propagation in the Los Angeles basin for the Whittier-Narrows earthquake

Abstract Elastic wave propagation within and around the Los Angeles basin during the Whittier-Narrows earthquake in 1988 is simulated with a 3-D finite difference method. The model consists mainly of a sedimentary layer over the basement, but lateral variations inside the sedimentary basin is also included to approximate observed variations in surface shear velocity. The minimum shear velocity is 1 km/sec on the surface and fairly reliable results are obtained up to 0.75 Hz. The total simulation lasts 26 sec. Our simulation can reproduce the general amplification pattern: small east of the epicenter and large in the L.A. basin and the San Fernando Valley, due to thick sediments of low velocity in these areas. Surface waves are generated by the primary S wave and trapped inside the basins. In the southern part of the L.A. basin, a distinct later phase, delayed by 5 to 6 sec relative to the primary S wave, is produced in our simulation, which matches some strong motion records.

A spectral method for seismic wave propagation in elastic media

We present am algorithm forward modelling of seismic waves in a 2D isotropic linearly elastic medium with arbitrary density, compressional (or P-wave) velocity and shear (or S-wave) velocity variations in both horizontal and vertical directions. The modelling algorithm directly solves the elastic wave equation with the displacements as unknowns through highly accurate approximations of spatial and temporal derivatives. Spatial derivatives are calculated by the pseudospectral Fourier method on a rectangular grid. Time stepping is performed with a spectral method based on a Chebyshev expansion of the formal evolution operator to the spatially discretized wave equation. The modelling scheme is implemented on an Amdahl VP 1100 vector processor. The large main memory of the Amdahl (128 MByte) and extensive use of vectorization enable calculations on meaningfully sized models within minutes. Results from a model with plane interfaces are tested against analytical solutions, showing that the combination of spectral methods in both space and time produces very accurate results. Application of the logarithm is demonstrated on a geologic model with curved interfaces by combining global snapshots of wavefields and time series of displacement velocities in selected points.

The upper mantle degree 2: Constraints and inferences from global mantle wave attenuation measurements

We present the results of an analysis of global lateral variations in anelasticity of the upper mantle, as measured from very long period Rayleigh waves observed on the GEOSCOPE network. Four consecutive wave trains are used on each record to eliminate uncertainty on the amplitude at the source and to take into account, in a linear manner, focussing effects due to lateral variations in elastic parameters. Local estimates of attenuation are obtained using an inversion method based on the introduction of a correlation length, as an alternative to spherical harmonics expansion. Comparison of phase velocity and attenuation maps obtained at various periods shows a strong correlation of high‐Q and high‐velocity regions (respectively low Q and low velocity) both for great circle and minor arc data, at periods around 200 s. The detailed analysis of the degree 2 pattern, well resolved in the attenuation maps around this period, shows that it originates in the depth range 250–500 km and indicates that of the upper mantle degree 2 pattern observed in shear velocity is likely to be of thermal origin, possibly related to the topmost part of the large‐scale convective system. Corrections for dispersion due to anelastic attenuation in degree 2 lead to significant decrease of corresponding lateral variations in shear velocity and a better agreement in phase and amplitude of the upper mantle degree 2 pattern with that observed in the geoid. This study shows that it is important to consider correcting presently available upper mantle tomographic models for the effects of intrinsic attenuation at long periods, before performing any comparison with short‐period data or other geophysical parameters.

A model of passive settlement by planktonic larvae onto bottoms of differing roughness

A simple, one-dimensional, advection-diffusion model was developed that predicts rates of settlement by larvae transported passively within turbulent boundary layers onto bottoms of differing roughness. The model describes depth-limited boundary layers and considers variation in boundary shear velocity, larval fall velocity, and the height and areal density of bottom-roughness features. Larvae were allowed to settle onto the bottom but not onto roughness features. The model predicts that rates of settlement should increase monotonically with areal density of roughness features. Relatively flat bottoms should experience rates of settlement 2–4 times higher than bottoms with low densities of roughness features, but 1–2 orders of magnitude lower than bottoms with relatively high densities of roughness. Whereas roughness density defines the direction of differences in settlement expected, the degree of difference is also affected by the height of roughness features and the ratio of larval fall velocity to shear velocity.

The anisotropic structure of the upper mantle in the Pacific

Anisotropic inversions of surface wave data show that the variations in vertical shear velocity, βv, and anisotropy of the oceanic upper mantle in the Pacific are much smoother and more systematic functions of the age of the seafloor than has been reported in previous studies. The data used in this analysis are the pure-path results of previous studies on the lateral distribution of fundamental-mode Love and Rayleigh wave phase velocities (Nishimura & Forsyth 1985, 1988). The pure-path models include parameters which describe the variations with age, azimuthal anisotropy and residual depth anomalies. The calculated velocity models of the upper mantle are constrained to vary smoothly with depth and to represent the minimum deviation from an isotropic starting model. Inversions were performed using the method of Tarantola & Valette (1982). The two best resolved parameters of the computed transversely isotropic model are the shear wave velocity terms, βv and ξ. The results indicate that βv above 200 km progressively increases as a function of the age of the seafloor with the pattern qualitatively mimicking isotherms of theoretical thermal cooling models. If one selects the depth to the maximum negative gradient in shear velocity as being the best available indicator of lithospheric thickness, then the thickness increases from about 15–35 km beneath 0–4 Myr old seafloor to 70–110 km in the oldest seafloor. The magnitude of the shear wave anisotropy term, ξ, rapidly increases in the first 20 Myr until some apparent constant value is reached in the older regions. A more realistic upper mantle structure is calculated using a priori information on the correlation between changes in shear and compressional wave velocities and the expected nature of the anisotropy. The general results are the same as the previous inversion without a priori constraints. Finally, the effect of attenuation is included, the primary result being an overall increase in βv. The maximum change occurs at around 150 km depth, which reduces the velocity contrast between the lithosphere and asthenosphere. It is therefore more difficult to make a distinction between the plate and low-velocity zone when the effect of attenuation is included. An estimate of the azimuthal anisotropic structure is obtained by inverting for the Rayleigh wave cos 2ψ coefficients using derivatives calculated by the method of Montagner & Nataf (1986). The reference frame used to constrain the azimuthal effect is that of fossil seafloor spreading direction. The results indicate that in regions of the Pacific less than 80 Myr in age, there is significant anisotropy down to 200 km depth. In regions older than 80 Myr, azimuthal anisotropy is confined to the upper 50 km. The transverse and azimuthal anisotropy structures can be explained by an oceanic upper mantle containing olivine with different orientations.

Three‐dimensional elastic modeling by the Fourier method

Earlier work on three‐dimensional forward modeling is extended to elastic waves using the equations of conservation of momentum and the stress‐strain relations for an isotropic elastic medium undergoing infinitesimal deformation. In addition to arbitrary compressional (or P‐wave) velocity and density variation in lateral and vertical directions, elastic modeling permits shear (or S‐wave) velocity variation as well. The elastic wave equation is solved using a generalization of the method for the acoustic case. Computation of each time step begins by computing six strain components by performing nine spatial partial differentiation operations on the three displacement components from the previous time step. The six strains and two Lamé constants are linearly combined to yield six stress components. Nine spatial partial differentiation operations on the six stresses, three body forces, and density are used to compute second partial time derivatives of the three displacement components. Time stepping to obtain the three displacement components for the current time step is performed with second‐order difference operators. The modeling includes an optional free surface above the spatial grid. An absorbing boundary is applied on the lateral and bottom edges of the spatial grid. This modeling scheme is implemented on a four‐processor CRAY X‐MP computer system using the solid‐state storage device (SSD). Using parallel processing with four CPUs, a reasonable geologic model can be computed within a few hours. The modeling scheme provides a variety of seismic source types and many possible output displays. These features enable the modeling of a wide range of seismic surveys. Numerical and analytic results are presented.

Scales of heterogeneity near the core‐mantle‐boundary

We have mapped shear velocity variations near the base of the mantle with ScS‐S differential travel times. Beneath the North Atlantic, there is a systematic variation in velocity over a distance of 1500 km or more, with a pronounced low velocity anomaly centered roughly beneath Madeira island. Beneath the northern Indian Ocean, there is no similar long‐wavelength anomaly. The average ScS‐S residual beneath the Indian Ocean is 3.6 ± 0 .7 s more negative than the Atlantic residual, indicating faster average velocities near the base of the mantle.

Synthetic seismograms from coupled free oscillations: Effects of lateral structure and rotation

Synthetic seismograms from coupled free oscillations are calculated for a regionalized continent‐ocean model of the upper mantle and a recently proposed spherical harmonic lateral structure model. Spectral correlation analysis of these synthetic records, containing Rayleigh waves with period T ≳ 160 s, reveals the size of departures from the assumption that the waveform perturbation can be explained by just the structure under the great circle between source and receiver. Arrival azimuth deflections of up to 10° are observed on horizontal synthetics using a 2.3% variation in shear velocity between continents and oceans. Among the M84A synthetics, the great circle travel times R3–R1, R4–R2, R5–R3 vary on average by 3–5 s for 3 ≲ f ≲ 6 mHz surface wave motion. Comparison between synthetics, calculated to be sensitive to even‐order structure or to both even‐ and odd‐order structure, gives a 5‐s average time delay attributable to odd‐order structure. Significant Rayleigh wave packet amplitude anomalies are common in the synthetic records and are nearly as common in synthetics calculated for the even‐order structure as in those sensitive to all structure. Examples suggest that model M84A does not consistently reproduce the amplitude anomalies observed in International Deployment of Accelerometers (IDA) and Global Digital Seismographic Network (GDSN) data. Lastly, we demonstrate the effect of Coriolis coupling in the time domain. Visible precursors to Rayleigh wave packets are predicted in cases of favorable source‐receiver geometry. These precursors are caused by the spheroidal component of the hybrid, predominantly toroidal, low‐frequency (f ≲ 4.2 mHz) Love wave, whose arrival precedes that of the Rayleigh wave. We present examples of this anomalous waveform in IDA data from a large strike‐slip earthquake in New Guinea, showing a qualitative fit to the coupled‐mode prediction.

Propagation of 0.7-2.5 Hz Rayleigh waves in Scotland

Summary. Rayleigh waves in the frequency range 0.7–2.5 Hz are recorded at stations on the Scottish LOWNET array, from local underwater explosions in the Kirkcaldy Bay region of the Firth of Forth. The fundamental mode is identified by comparing theoretical and observed particle motion plots derived from seismograms at the Edinburgh station, this being used as a guide for selection at the other stations. The selected signals are then analysed to obtain estimates of the group velocity dispersion characteristics along isolated event-station paths, and this information is interpreted in two ways: (a) The group velocity curves are inverted to obtain shear velocity profiles of each path, these penetrating to depths of between 1.2 and 3 km into the crust. The models show an increase of shear velocity with depth. Shear velocity in the upper 400 m of the crust, which includes the surface weathering, lies between 1.4 and 2.1 km s−1. The regional variation of shear velocity correlates with the surface geology, which consists of Carboniferous sediments, Old Red Sandstone and Dalradian rocks. There are wide differences in the velocities of the deepest layer, ranging from 1.9 to 3.5 km s−1. (b) The variation of group slowness with the geological expression is utilized in a linear scheme to obtain pure-provincial group velocities for several geological provinces. The dispersion curves corresponding to the Carboniferous sediments and the Firth of Forth regions decrease smoothly from 1.6 km s−1 at 0.7 Hz to 1.2 km s−1 at 1.8 Hz. The group velocities for the Old Red Sandstone formation are about 0.5 km s−1 faster. These results also demonstrate that the water layer and seabed sediments do not have a significant effect on the surface wave propagation.

Shear‐Induced Secondary Currents in Channel Flows

A simple, analytical model is proposed for the description of flow and stress characteristics in an open-channel flow with nonuniform distribution of bed-shear stress. The model describes the relationship between the secondary current and the transverse variation in bed-shear stress. The streamwise velocity profile is obtained by superposition of a power law and a second-order defect law. The model simulates the flow behavior measured in a laboratory channel with artificially induced transverse variation of shear velocity.

Frequency-Domain Inversion of Receiver Transfer Functions For Crustal Structure

A linearized frequency domain inversion of receiver transfer functions is investigated as a means for determining crustal structure. The forward problem is solved using a Thomson-Haskell method which includes the effects of attenuating layers. The function to be fit consists of the deconvolved radial component of teleseismic P waves (to remove source effects) which is sensitive mainly to variations in shear velocity and density. Compressional velocity and attenuation are adjusted by assuming a Poisson solid. Complex partial derivatives are computed with respect to the complex shear velocity in each layer using a finite difference approach. Thus, it is possible to simultaneously invert for shear velocity and shear attenuation. Test cases show that for short path lengths, the effects of attenuation are relatively small compared to the effects of velocity contrasts at layer interfaces. Test cases utilizing synthetic and real data demonstrate the impressive resolving power of the technique for the determination of crustal thickness and the importance of density on the calculated receiver functions. Examination of partial derivatives for the receiver transfer functions with respect to various layer parameters further demonstrates that the effect of density is nearly as important as that due to shear velocity. The test cases also bring out the importance of an accurate trial solution, especially in the presence of noise. Thus, in actual practice it is necessary to combine the inversion with trial and error calculations.

Multimode Rayleigh wave attenuation and Qβ in the crust of the Barents Shelf

The multimode method of Cheng and Mitchell [1981] is used to study the attenuation properties of the crust throughout the Barents shelf. The sensitivity of the spectra to various source factors and to propagation factors which might characterize a shelf region are thoroughly studied. For plane‐layered models, the method is very sensitive to Qβ in the upper crust and to Qβ of sedimentary layers if those layers are thick and highly attenuating. It is far less sensitive to Qβ in the lower crust and to Qα. The spectra, for shallow strike slip earthquakes, are very insensitive to changes in strike, slip, and dip angles of the fault throughout the entire period range of interest but are very sensitive to variations in focal depth except in the long‐period range of the fundamental mode and the short‐period range of the higher modes. The fundamental mode, but not the higher mode, spectra for one path across the Barents shelf are, apparently, distorted at short periods by lateral heterogeneities along the travel path. Simple two‐layer, trial‐and‐error inversions yield a model of the Barents shelf with an upper crustal Qβ value of about 80. Three‐layer inversions with a sedimentary layer, however, yield an upper crustal Qβ of about 250, if the sediments are 1 km thick and are characterized by Qβ values of 40. Shear velocity models for the Barents shelf show variations between about 3.0 and 3.6 km/s in the upper crust along different paths. The lower crust shows smaller regional differences, but velocities vary between 3.5 and 4.0 km/s through the depth range 25–35 km. The variation of shear velocities in the upper mantle may correlate with those of the upper crust and vary regionally between about 4.3 and 4.8 km/s.