Seismic Modelling of Lateral Heterogeneity At the Base of the Mantle

Summary. Results from several recent studies suggest that there are lateral heterogeneities of up to a few per cent in the lowermost 150–200 km of the mantle (Bullen's D " region). Inferred anomaly sizes span the range from less than 50 km to greater than 1000 km.
In this study differences in the velocity structure among regions at the base of the mantle were inferred from an analysis of amplitude ratios of PKPAB and PKPDF for given earthquake-station pairs at distances greater than 155° (Sacks, Snoke & Beach). We distinguish two kinds of regions: A (anomalous) regions in which the mean, median and spread in AB/DF amplitude ratios are significantly higher (> 50 per cent) than for a reference radial earth model and N (normal) regions in which the distribution of the amplitude ratios is as expected.
The AB branch has near-grazing incidence to the core and therefore maximum sensitivity to velocity structure compared to the near-normal incident DF phases. Using an iterative, forward-modelling approach, we have determined general characteristics of the velocity structure for regions at the base of the mantle which can produce amplitude-ratio distributions similar to those for an A region. Agreement between model and data is obtained over the period range from 0.5 s to greater than 10 s using a laterally heterogeneous model for the D " region. the model consists of cells which are 200 km in lateral extent with velocity variations of up to ±1 per cent. This structure is modulated by a region-wide (1000km) perturbation which increases smoothly from zero at the edges of the region to a negative 1 per cent at the centre. Small cells (∼40 km) cannot produce anomalously large amplitude, long-period AB arrivals, and larger cells (∼1000km) cannot match the observed scatter. the ∼200 km scale anomalies could be small-scale convection cells confined to the D " region.     

Travel-time anomalies in the mantle under the North Atlantic

Summary. Lateral heterogeneity exists in the Earth's mantle, and may result in seismic velocity anomalies up to several per cent. If convection cells and plumes extend down to the core, then these features may be associated with local inhomogeneities observed in the lower mantle.
Published data for direct and core-reflected P -wave residuals are used to delineate velocity anomalies in the middle—lower mantle under the North Atlantic. Differential ( PcP — P ) residuals indicate travel-time anomalies near the core—mantle transition, and may be due to core topography or lateral variations in velocity. It is assumed that the anomalies occur near the midpoints of the ray paths. The main source of error in the data set may arise from phases which have been identified incorrectly. Hence trend-surfaces are fitted to the residual data to show only the large-scale trends in anomaly values, with wavelengths of the order of 1000 km.
The Azores and Colorado hot spots occur in a region covered by the data. A possible interpretation of the trend maps is that an anomalous zone extends from a relatively fast region at the core boundary at 35° N, 50° W up to these hot spots, at about 30 degrees from the vertical. This may agree with the suggestion of Anderson that plumes are chemical rather than thermal in origin. If inclⁱned plumes do exist, the deviation from the ideal vertical plume or convection cell boundary may imply that lateral shear or other distortion effects exist in the mantle.     

Geophysical model of the dynamical flattening of the Earth in agreement with the precession constant

The dynamical flattening of the Earth, as observed by geodetic techniques, is different by about 1 per cent from the value associated with the PREM density profile with hydrostatic equilibrium. In this paper, we compute a new dynamical flattening H induced by PREM mean density with hydrostatic equilibrium, to which we add lateral heterogeneities associated with (1) seismic velocity variations observed by tomography and (2) internal boundary topographies. First, we compute mantle circulation associated with the density anomalies derived from a tomography model. The flow-induced boundary deformations are then converted into additional mass anomalies which are added to the tomography model for computing the associated perturbation to the Earth's inertia tensor. Finally, we show that it is possible to obtain a dynamical flattening from the total inertia tensor (i.e. the sum of the PREM inertia tensor and of the perturbation) in agreement with that observed.     

Some effects of lateral heterogeneities in the upper mantle on postglacial land uplift close to continental margins

We investigate the effects of lateral heterogeneities in the upper mantle on the calculation of postglacial land uplift. For the model calculations we use a commercial finite-element code, which enables us to solve the equations governing a layered, isotropic. incompressible, Maxwell-viscoelastic half-space with laterally varying layer thicknesses and physical properties. Following previous investigations performed by Sabadini. Yuen & Portney (1986) and Gasperini & Sabadini (1989), we extend their results using a more realistic loading history and different earth models. We then focus our attention on the question whether lateral heterogeneities in the upper mantle can be modelled correctly using a set of homogeneous earth models. To this end, a comparison of model calculations using both laterally homogeneous and heterogeneous earth models is performed.
We find that lateral heterogeneities in the upper mantle significantly influence the calculated postglacial land uplift. The resolving power of relative sea-level observations for the prescribed lateral heterogeneities used in this study is mainly focused on observations around the load margin and outside the glaciated areas, where differences in predicted land uplift between individual models are large enough to be resolved by observations.
We can qualitatively determine lateral heterogeneities in the upper mantle using a set of laterally homogeneous earth models, if the geological structure, for example a continental margin, is known. However, in order to infer the correct values of lithospheric thickness and asthenospheric viscosity, we need to use laterally heterogeneous models.     

Seismic structure of the upper mantle beneath the United States by three-dimensional inversion of body wave arrival times

Summary. Teleseismic P and S arrival times to North American stations are obtained from the ISC bulletins for the 10-yr period 1964–73, and relative travel-time delays are calculated with respect to standard tables. Station anomalies as well as variations of the delays with azimuth and epicentral distance from station are analysed, and the location of the velocity anomalies responsible for them is discussed. Inversion of the P delays to infer upper mantle velocity structure down to a depth of 700 km is obtained using three-dimensional blocks, as proposed by Aki, Christofferson & Husebye. Three layers can be resolved in this depth range. It is found that the heterogeneities responsible for the travel-time delays are primarily located in the first 250 km of the upper mantle, and that they correlate with surface features. Significant heterogeneities subsist to depths of at least 700 km and their broad scale pattern also correlates with the surface features: in the third layer (500 to 700 km depth) there is an increase of velocity from the West to the East of the United States, while the second layer (250 to 450 km depth) exhibits a reversed pattern. A tentative interpretation of these deeper anomalies is made, as being due mainly to topography of the major upper mantle discontinuities, near 400 and 650 km depth.     

A lower mantle S-wave triplication and the shear velocity structure of D"

Summary. A lower mantle S-wave triplication detected with short- and long-period WWSSN and CSN recordings indicates a substantial shear velocity discontinuity near 280 km above the core–mantle boundary. The triplication can be observed in rotated SH seismograms from intermediate and deep focus events throughout the distance range from 70° to 95°. Three distinct source region–receiver array combinations that have been investigated in detail demonstrate consistent travel time and relative amplitude behaviour of the triplication, with slight systematic shifts in the triplication indicating up to 40 km variations in the depth of the discontinuity. Modelling of the observations with synthetic seismograms produced with the Cagniard de Hoop and reflectivity methods constrains the shear velocity increase to be 235 ± 0.25 per cent, comparable to upper mantle discontinuities. Short-period observations indicate that the velocity increase may be a sharp first-order discontinuity, or may extend over a transition zone no more than 50 km thick. The shear velocity gradient below the discontinuity, within the D" layer, is not well-constrained by the SH data, but slightly positive or near zero velocity gradients are consistent with the long-period amplitude ratios of ScSH/SH .     

Localized velocity anomalies in the lower mantle

Summary. Two localized regions of velocity heterogeneity in the lower mantle with scale lengths of 1000–2000 km and 2 per cent velocity contrasts are detected and isolated through comparison of S, ScS, P and PcP travel times and amplitudes from deep earthquakes in Peru, Bolivia, Argentina and the Sea of Okhotsk. Comparison of the relative patterns of ScS-S differential travel times and S travel-time residuals across North American WWSSN and CSN stations for the different source regions provides baselines for interpreting which phases have anomalous times. A region of low S and P velocities is located beneath Northern Brazil and Venezuela at depths of 1700–2700 km. This region produces S -wave delays of up to 4 s for signals from deep Argentine events recorded at eastern North American stations. The localized nature of the anomaly is indicated by the narrow bounds in azimuth (15°) and take-off angle (13°) of the arrivals affected by it. The long period S -waves encountering this anomaly generally show 30–100 per cent amplitude enhancement, while the short-period amplitudes show no obvious effect. The second anomaly is a high-velocity region beneath the Caribbean originally detected by Jordan and Lynn, who used travel times from deep Peruvian events. The data from Argentine and Bolivian events presented here constrain the location of the anomaly quite well, and indicate a possible short- and long-period S -wave amplitude diminution associated with it. When the travel-time data are corrected for the estimated effects of these two anomalies, a systematic regional variation in ScS-S station residuals is apparent between stations east of and west of the Rocky Mountains. One possible explanation of this is a long wavelength lateral variation in the shear velocity structure of the lower mantle at depths greater than 2000 km beneath North America.     

Regional 3-D heterogeneities by waveform inversion – application to the Atlantic area

The waveform inversion method described in Woodhouse & Dziewonski (1984) was modified to retrieve regional scale 3-D heterogeneities by using the minor arc part of seismograms. The lateral heterogeneities are expanded horizontally into blocks (10°× 10°) and radially into Legendre polynomials up to order 3 (0–670 km), and thus the results show much fine details of lateral variation than previous global scale studies. We assumed that the heterogeneities produce the perturbation of eigenfrequencies which are the minor arc average of local eigenfrequency shift. We applied the method to the upper mantle beneath the Atlantic Ocean and its environments. Care was taken about the weighting of the data set. We found that the fit of each seismogram became better when the weighting of each seismogram is proportional to the inverse of initial data residuals. Resolution is good in the triangular region surrounded by South America, Europe, and North America. Resolution is not good in the South Atlantic because of the poor path coverage. Depth resolution is not clear, because of the use of Legendre polynomials, though the results suggest a broad half-width of the order of 200 km or more. We found some similarities between previous global studies and our results. For example, low velocities beneath the East Pacific Rise, Chile Rise and Azores triple junction and a high velocity Canadian shield are obtained. However, there are also differences; the high-velocity zone beneath the Brazilian shield at shallow depth is not a prominent feature in this study. Instead, we found a somewhat unexpected feature near the Romanche and Vema fracture zones where shallow positive anomalies exist. Smoothed results calculated by the spherical harmonic expansion are also shown for the purpose of comparison with global studies.     

Born scattering of longperiod body waves

The Born approximation is applied to the modelling of the propagation of deeply turning longperiod body waves through heterogeneities in the lowermost mantle. We use an exact Green's function for a spherically symmetric earth model that also satisfies the appropriate boundary conditions at internal boundaries and the surface of the earth. The scattered displacement field is obtained by a numerical quadrature of the product of the Green's function, the exciting wavefield and structural perturbations. We study three examples: scattering of longperiod P waves from a plume rising from the coremantle boundary (CMB), generation of longperiod precursors to PKIKP by strong, localized scatterers at the CMB, and propagation of corediffracted P waves through largescale heterogeneities in D". The main results are as follows: (1) the signals scattered from a realistic plume are small with relative amplitudes of less than 2 per cent at a period of 20 s, rendering plume detection a fairly difficult task; (2) strong heterogeneities at the CMB of appropriate size may produce observable longperiod precursors to PKIKP in spite of the presence of a diffraction from the PKP B caustic; (3) corediffracted P  waves ( P _diff) are sensitive to structure in D" far off the geometrical ray path and also far beyond the entry and exit points of the ray into and out of D"; sensitivity kernels exhibit ringshaped patterns of alternating sign reminiscent of Fresnel zones; (4) P _diff also shows a nonnegligible sensitivity to shear wave velocity in D"; (5) down to periods of 40 s, the Born approximation is sufficiently accurate to allow waveform modelling of P _diff through largescale heterogeneities in D" of up to 5 per cent.     

The effect of a second-order velocity discontinuity on elastic waves near their turning point

Summary. The rather abrupt changes in velocity gradient which have sometimes been proposed, notably in the upper mantle and near the base of the mantle, have an effect equivalent to that of one or more second-order discontinuities, where partial reflection occurs due to a change in curvature of the wavefront across these discontinuities. The effect is ignored in the classical WKBJ approximation to the wave functions, but it can be explicitly demonstrated by applying the extended WKBJ method (Langer's approximation) to a piecewise smooth layered model. For the purpose of this study it is convenient to represent the response of such a modelby a generalized reflection coefficient. For a model of one or a system of several second-order discontinuities (approximating a change in velocity gradient over a finite depth interval), the reflection coefficient can be perhaps surprisingly large for long-period waves near their turning point. It is shown that this effect can significantly alter the amplitude decay of SH waves diffracted around the core, in models where a change in velocity gradient near the core—mantle boundary constitutes a low-velocity zone at the base of the mantle; such models have recently been proposed. With the same velocity gradients, the effect on P diffraction is less important. The results for SH diffraction in these models support the conclusion that a small amplitude decay must be explained by a velocity decrease with depth, i.e. a low-velocity zone at the base of the mantle.     

Numerical models of mantle convection with secular cooling

A 2-D time-dependent finite-difference numerical model is used to investigate the thermal character and evolution of a convecting layer which is cooling as it convects. Two basic cooling modes are considered: in the first, both upper and lower boundaries are cooled at the same rate, while maintaining the same temperature difference across the layer; in the second, the lower boundary temperature decreases with time while the upper boundary temperature is fixed at 0°C. The first cooling mode simulates the effects of internal heating while the second simulates planetary cooling as mantle convection extracts heat from, and thereby cools, the Earth's core. The mathematical analogue between the effects of cooling and internal heating is verified for finite-amplitude convection. It is found that after an initial transient period the central core of a steady but vigorous convection cell cools at a constant rate which is governed by the rate of cooling of the boundaries and the viscosity structure of the layer. For upper-mantle models the transient stage lasts for about 30 per cent of the age of the Earth, while for the whole mantle it lasts for longer than the age of the Earth. Consequently, in our models the bulk cooling of the mantle lags behind the cooling of the core-mantle boundary. Models with temperature-dependent viscosity are found to cool in the same manner as models with depth-dependent viscosity; the rate of cooling is controlled primarily by the horizontally averaged variation of viscosity with depth. If the Earth's mantle cools in a similar fashion, secular cooling of the planet may be insensitive to lateral variations of viscosity.     

Anisotropy of heterogeneity scale lengths in the lower mantle from PKIKP precursors

The anisotropy of heterogeneity scale lengths in the lower mantle is investigated by modelling its effect on the high-frequency precursors of PKIKP scattered by the heterogeneities. Although models having either an isotropic or an anisotropic distribution of scale lengths can fit the observed coda shapes of short-period precursors, the frequency content of broad-band PKIKP precursors favours a dominantly isotropic distribution of scale lengths. Precursor coda shapes are consistent with 1 per cent fluctuations in P velocity in the wavenumber band 0.05–0.5  km⁻¹ extending to 1000  km above the core–mantle boundary, and with a D" region open to circulation throughout the lower mantle. The level of excitation of PKIKP precursors observed in the frequency band 0.02–2  Hz requires a power spectrum of heterogeneity that is nearly white or slowly increasing with wavenumber. Anisotropy of scale lengths may exist in a D" layer having larger horizontal than vertical scale lengths and produce little or no detectable effects on PKIKP precursors for P -velocity perturbations as high as 3 per cent when averaged over a vertical scale of several kilometres, and much higher when averaged over scales of hundreds of metres or less.     

Waveform inversion of mantle Love waves:the Born seismogram approach

Summary. Normal mode theory, extended to the slightly laterally heterogeneous earth by the first-order Born approximation, is applied to the waveform inversion of mantle Love wave (200–500 s) for the Earth's lateral heterogeneity at l = 2 and a spherically symmétric anelasticity ( Q _μ) structure. The data are from the Global Digital Seismograph Network (GDSN). The l =2 pattern is very similar to the results of other studies that used either different méthods, such as phase velocity measurements and multiplet location measurements, or a different data set, such as mantle Rayleigh waves from different instruments. The results are carefully analysed for variance reduction and are most naturally explained by heterogeneity in the upper 420 km. Because of the poor resolution of the data set for the deep interior, however, a fairly large heterogeneity in the transition zones, of the order of up to 3.5 per cent in shear wave velocity, is allowed. It is noteworthy that Love waves of this period range cannot constrain the structure below 420 km and thus any model presented by similar studies below this depth are likely to be constrained by Rayleigh waves (spheroidal modes) only.
The calculated modal Q values for the obtained Q _μ model fall within the error bars of the observations. The result demonstrates the discrepancy of Rayleigh wave Q and Love wave Q and indicates that care must be taken when both Rayleigh and Love wave data, including amplitude information, are inverted simultaneously.
Anomalous amplitude inversions of G2 and G3, for example, are observed for some source-receiver pairs. This is due to multipathing effects. One example near the epicentral region, which is modelled by the obtained l = 2 heterogeneity, is shown.     

Inverse eigenvalue problems for the mantle

Summary. It is shown that if Adams—Williamson's equation is used in the lower mantle and if the mass of the core and the density at the core—mantle boundary are given then the density, the rigidity and the incompressibility are uniquely determined throughout the mantle and in the crust by the velocities of the P - and S -waves and by one torsional spectrum. The velocity of the S -waves in the upper mantle and in the crust can be replaced by an additional torsional spectrum.     

A three-dimensional radially anisotropic model of shear velocity in the whole mantle

We present a 3-D radially anisotropic S velocity model of the whole mantle (SAW642AN), obtained using a large three component surface and body waveform data set and an iterative inversion for structure and source parameters based on Non-linear Asymptotic Coupling Theory (NACT). The model is parametrized in level 4 spherical splines, which have a spacing of ∼ 8°. The model shows a link between mantle flow and anisotropy in a variety of depth ranges. In the uppermost mantle, we confirm observations of regions with   V_SH > V_SV   starting at ∼80 km under oceanic regions and ∼200 km under stable continental lithosphere, suggesting horizontal flow beneath the lithosphere. We also observe a   V_SV > V_SH   signature at ∼150–300 km depth beneath major ridge systems with amplitude correlated with spreading rate for fast-spreading segments. In the transition zone (400–700 km depth), regions of subducted slab material are associated with   V_SV > V_SH   , while the ridge signal decreases. While the mid-mantle has lower amplitude anisotropy (<1 per cent), we also confirm the observation of radially symmetric   V_SH > V_SV   in the lowermost 300 km, which appears to be a robust conclusion, despite an error in our previous paper which has been corrected here. The 3-D deviations from this signature are associated with the large-scale low-velocity superplumes under the central Pacific and Africa, suggesting that   V_SH > V_SV   is generated in the predominant horizontal flow of a mechanical boundary layer, with a change in signature related to transition to upwelling at the superplumes.     

Crustal structure from an OBS survey of the Nootka fault zone off western Canada

Summary. The Nootka fault zone is the boundary between the small Explorer and Juan de Fuca plates which are situated between the America and Pacific plates off western Canada. To investigate the crustal structure in the region, three explosive/large airgun refraction lines were shot into three ocean bottom seismometers (OBSs) with three-component geophone assemblies. In this phase of the study, P -wave velocity—depth models are interpreted by comparison of the travel time and amplitude characteristics of the observed data with theoretical seismograms computed using a WKBJ algorithm. The interpretation gives relatively consistent results for the upper crust. However, the structure of the lower crust is significantly different among the various profiles. Upper mantle velocities range from 7.5 to 8.3 kms⁻¹ and the sub-bottom crustal thickness vanes from 6.4 to 11 km. Nevertheless, these seismic models are consistent in general terms with oceanic crustal models represented by ophiolite complexes. Some aspects of the differences among profiles can be explained by consideration of a recent tectonic model for the development of the fault zone. This requires, within a 1 Myr time interval, variations in the process of crustal formation at the ridge, crustal 'maturing', or both. The abnormally thick crust near a spreading centre may result in part from the complex interaction of the Juan de Fuca and Explorer plates with the larger and older America and Pacific plates. Upper mantle velocity variations are consistent with the concept of velocity anisotropy. The different record sections show that seismic energy is attenuated for ray paths traversing the Nootka fault zone.     

Resolution potential of surface wave phase velocity measurements at small arrays

The deployment of temporary arrays of broadband seismological stations over dedicated targets is common practice. Measurement of surface wave phase velocity across a small array and its depth-inversion gives us information about the structure below the array which is complementary to the information obtained from body-wave analysis. The question is however: what do we actually measure when the array is much smaller than the wave length, and how does the measured phase velocity relates to the real structure below the array? We quantify this relationship by performing a series of numerical simulations of surface wave propagation in 3-D structures and by measuring the apparent phase velocity across the array on the synthetics. A principal conclusion is that heterogeneities located outside the array can map in a complex way onto the phase velocities measured by the array. In order to minimize this effect, it is necessary to have a large number of events and to average measurements from events well-distributed in backazimuth. A second observation is that the period of the wave has a remarkably small influence on the lateral resolution of the measurement, which is dominantly controlled by the size of the array. We analyse if the artefacts created by heterogeneities can be mistaken for azimuthal variations caused by anisotropy. We also show that if the amplitude of the surface waves can be measured precisely enough, phase velocities can be corrected and the artefacts which occur due to reflections and diffractions in 3-D structures greatly reduced.     

Seismic imaging of the laterally varying D" region beneath the Cocos Plate

We use an axisymmetric, spherical Earth finite difference algorithm to model SH -wave propagation through cross-sections of laterally varying lower mantle models beneath the Cocos Plate derived from recent data analyses. Synthetic seismograms with dominant periods as short as 4 s are computed for several models: (1) a D" reflector 264 km above the core–mantle boundary with laterally varying S -wave velocity increases of 0.9–2.6 per cent, based on localized structures from a 1-D double-array stacking method; (2) an undulating D" reflector with large topography and uniform velocity increase obtained using a 3-D migration method and (3) cross-sections through the 3-D mantle S -wave velocity tomography model TXBW. We apply double-array stacking to assess model predictions of data. Of the models explored, the S -wave tomography model TXBW displays the best overall agreement with data. The undulating reflector produces a double Scd arrival that may be useful in future studies for distinguishing between D" volumetric heterogeneity and D" discontinuity topography. Synthetics for the laterally varying models show waveform variability not observed in 1-D model predictions. It is challenging to predict 3-D structure based on localized 1-D models when lateral structural variations are on the order of a few wavelengths of the energy used, particularly for the grazing geometry of our data. Iterative approaches of computing synthetic seismograms and adjusting model characteristics by considering path integral effects are necessary to accurately model fine-scale D" structure.     

The lithosphere–asthenosphere boundary beneath the western United States

S receiver functions from 67 broad-band seismic stations in the western United States clearly reveal the existence of a mantle discontinuity with velocity reduction downward, which we interpret as the lithosphere–asthenosphere boundary (LAB). The average depth of the LAB is ∼70 km. The boundary is relatively sharp with an overall sharpness of less than 20 km. The boundary is more prominent south of the Mendocino Triple Junction, where the Farallon Plate has completely subducted. This may indicate partial melts at the base of the lithosphere caused by the upwelling of the asthenospheric flow through the slab window. A double low velocity zone is observed at base of the lithosphere beneath southern Sierra Nevada, implying a second melting zone at a depth of ∼100 km, well correlated with previous studies of lithospheric delamination in the area.     

Small-scale heterogeneities below the Gräfenberg array, Germany from seismic wavefield fluctuations of Hindu Kush events

Small-scale elastic heterogeneities (<5  km) are found in the upper lithosphere underneath the Gräfenberg array, southeast Germany. The results are based on the analysis of broadband recordings of 17 intermediate-depth (201–272  km) events from the Hindu Kush region. The wavefront of the first P arrival and the following 40  s coda are separated into coherent and incoherent (scattered) parts in the frequency range from 0.05 to 5  Hz. The frequency-dependent intensities of the mean and fluctuation wavefields are used to describe the scattering characteristics of the lithosphere underneath the receivers. It is possible to discriminate a weak-fluctuation regime of the wavefield in the frequency range below approximately 1.5–2.5  Hz and a strong-fluctuation regime starting at 2.0–2.5  Hz and continuing to higher frequencies. In order to explain the observed wavefield fluctuations, an approach with seismic scattering at random media-type structures is proposed. The preferred model contains heterogeneities with 3–7 per cent perturbations in seismic velocity and correlation lengths of 0.6–4.8  km in the crust. This is compatible with models from active seismic experiments. Scattering in the lithospheric mantle is not required, but cannot be excluded at weak velocity contrasts (<3 per cent).