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.     

Ivrea seismic array: a study of continental crust and upper mantle

A seismic-array study of the continental crust and upper mantle in the Ivrea-Yerbano and Strona-Ceneri zones (northwestern Italy) is presented. A short-period network is used to define crustal P - and S -wave velocity models from earthquakes. The analysis of the seismic-refraction profile LOND of the CROP-ECORS project provided independent information and control on the array-data interpretation.
Apparent-velocity measurements from both local and regional earthquakes, and time-term analysis are used to estimate the velocity in the lower crust and in the upper mantle. The geometry of the upper-lower crust and Moho boundaries is determined from the station delay times.
We have obtained a three-layer crustal seismic model. The P -wave velocity in the upper crust, lower crust and upper mantle is 6.1±0.2 km s⁻¹, 6.5±0.3 km s⁻¹ and 7.8±0.3 km s⁻¹ respectively. Pronounced low-velocity zones in the upper and lower crust are not observed. A clear change in the velocity structure between the upper and lower crust is documented, constraining the petrological interpretation of the Ivrea-type reflective lower continental crust derived from small-scale petrophysical data. Moreover, we found a V _P/ V _S ratio of 1.69±0.04 for the upper crust and 1.82±0.08 for the lower crust and upper mantle. This is consistent with the structural and petrophysical differences between a compositionally uniform and seismically transparent upper crust and a layered and reflective lower crust. The thickness of the lower crust ranges from about 8 km in front of the Ivrea body (ARVO, Arvonio station) in the northern part of the array to a maximum of about 15 km in the southern part of the array. The lower crust reaches a minimum depth of 5 km below the PROV (Provola) station.     

Structural effects of the crust on the geoid modelled using deep seismic sounding interpretations

According to the theory of isostasy, the Earth has a tendency to deform its surface in order to reach an equilibrium state. The land-uplift phenomenon in the area of the Fennoscandian Shield is thought to be a process of this kind. The geoid, as an equipotential surface of the Earth's gravity field, contains information on how much the Earth's surface departs from the equilibrium state. In order to study the isostatic process through geoidal undulations, the structural effects of the crust on the geoid have to be investigated.
  The structure of the crust of the Fennoscandian Shield has been extensively explored by means of deep seismic sounding (DSS). The data obtained from DSS are used to construct a 3-D seismic-velocity structure model of the area's crust. The velocity model is converted to a 3-D density model using the empirical relationship that holds between seismic velocities and crustal mass densities. Structural effects are then estimated from the 3-D density model.
  The structural effects computed from the crustal model show that the mass deficiency of the crust in Fennoscandia has caused a geoidal depression twice as deep as that observed from the gravimetric geoid. It proves again that the crust has been isostatically compensated by the upper mantle. In other words, an anomalously high-density upper mantle must exist beneath Fennoscandia.     

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.     

龙陵地区强震活动的深部背景

对研究区（23.9°N～25.1°N,97.8°E～99.0°E）内地壳和上地幔S波速度结构与强震的关系和强震活动的深部背景进行了探讨。活动断裂的运动是孕育和发生强震的重要诱因,而有利于高应变积聚的深部地质构造则是产生强震的关键条件。研究区内,以瑞丽—龙陵断裂为界,西北侧地壳和上地幔存在大范围低速区,不利于高应变的积聚,不容易孕育和发生强震;东南侧上地幔无明显低速层,地壳内有较小范围低速层,介质偏于刚性,易于积累高应变,孕育和发生强震的可能性较大。     

Numerical models of a subsidence mechanism in intracratonic basins: application to North American basins

McKenzie's model of sedimentary basin evolution and its modification, widely used in geophysics, sometimes fails to explain discrepancies between predicted and observed values of extension, thinning and subsidence of the Earth's crust, as for the North Sea. We develop a numerical model of sedimentary basin evolution based on the mechanism suggested by Lobkovsky. In the course of rifting, accompanied by thinning of lower parts of the lithosphere, the roof of the underlying asthenosphere moves upward. the material of the mantle lifts and partially melts owing to the reduction of pressure. the density difference between the melt and the crystalline skeleton results in the filtration of the lighter melt and its accumulation in the form of a magmatic lens. Due to changed P-T conditions, the material of the lens undergoes the gabbro-eclogite phase transformation. the resultant anomalously heavy eclogite lens sinks in the surrounding material. This induces a viscous flow, changing the surface topography and forming a sedimentary basin. We construct a 2-D numerical model describing a viscous flow induced by subsidence of a heavy body and compute changes of surface topography. to compute the flow we employ the Galerkin-spline approach, with modifications allowing for density discontinuities and time dependence of the phase transformation. We apply the model to the cases of the Illinois, Michigan and Williston basins. the computed and tectonic subsidence curves agree well for these cases. the proposed model is compatible with the seismic structure of the crust and upper mantle below these basins. the model is also consistent with gravity data. the approach is applicable to other intracratonic basins.     

Upper mantle shear structure of North America

Summary. The waveforms and travel times of S and SS phases in the range 10°–60° have been used to derive upper mantle shear velocity structures for two distinct tectonic provinces in North America. Data from earthquakes on the East Pacific Rise recorded at stations in western North America were used to derive a tectonic upper mantle model. Events on the north-west coast of North America and earthquakes off the coast of Greenland provided the data to investigate the upper mantle under the Canadian shield. All branches from the triplications due to velocity jumps near 400 and 660 km were observed in both areas. Using synthetic seismograms to model these observations placed tight constraints on heterogeneity in the upper mantle and on the details of its structure. SS–S travel-time differences of 30 s along with consistent differences in waveforms between the two data sets require substantial heterogeneity to at least 350 km depth. Velocities in the upper 170 km of the shield are about 10 per cent higher than in the tectonic area. At 250 km depth the shield velocities are still greater by about 4.5 per cent and they gradually merge near 400 km. Below 400 km no evidence for heterogeneity was found. The two models both have first-order discontinuities of 4.5 per cent at 405 km and 7.5 per cent at 695 km. Both models also have lids with lower velocities beneath. In the western model the lid is very thin and of relatively low velocity. In the shield the lid is 170 km thick with very high elocity (4.78 km s^-1); below it the velocity decreases to about 4.65 km s^-1. Aside from these features the models are relatively smooth, the major difference between them being a larger gradient in the tectonic region from 200 to 400 km.     

Internal waves in the earth's core

This paper investigates possible long-period oscillations of the earth's fluid outer core. Equations describing free oscillations in a stratified, self-gravitating, rotating fluid sphere are developed using a regular perturbation on the equations of hydrodynamics. The resulting system is reduced to a finite set of ordinary differential equations by ignoring the local horizontal component of the earth's angular velocity vector, Ω, and retaining only the vertical component. The angular dependence of the eigensolutions is described by Hough functions, which are solutions to Laplace's tidal equation.
The model considered here consists of a uniform solid elastic mantle and inner core surrounding a stratified, rotating, inviscid fluid outer core. The quantity which describes the core's stratification is the Brunt—Väisälä frequency N , and for particular distributions of this parameter, analytical solutions are presented. The interaction of buoyancy, and rotation results in two types of wave motion, the amplitudes of which are confined predominantly to the outer core: (1) internal gravity waves which exist when N ² > 0, and (2) inertial oscillations which exist when N ²<4Ω². For a model with a stable density stratification similar to that proposed by Higgins & Kennedy (1971), the resulting internal gravity wave eigenperiods are all at least 8 hr, and the fundamental modes have periods of at least 13 hr. A model with an unstable density stratification admits no internal gravity waves but does admit inertial oscillations whose eigenperiods have a lower bound of 12hr.     

A Teleseismic Delay Time Study Across the Central African Shear Zone In the Adamawa Region of Cameroon, West Africa

Summary. P -wave relative teleseismic residuals were measured for a network of seismological stations along a 300 km profile across the Adamawa Plateau and the Central African Shear Zone of central Cameroon, to determine the variation in crust and upper mantle velocity associated with these structures. A plot of the mean relative residuals for the stations shows a long wavelength (> 300 km) variation of amplitude 0.45 s. the slowest arrivals are located over and just to the north, of the faulted northern margin of the Adamawa Plateau. the residuals do not correlate with topography, surface geology or the previously determined crustal structure, in any simple way.
The Aki inversion technique has been used to invert the relative residuals into a 3-D model of velocity perturbations from a mean earth model. the results show the region is divided roughly into three blocks by two subvertical boundaries, striking ENE and traversing both the crust and upper mantle down to depths greater than 190km. the central block, which is 2 per cent slower than the adjacent blocks, roughly corresponds to the Central African Shear Zone. the Adamawa Plateau, as an individual uplifted area, is explained by the interaction of a regional anomalous upper mantle associated with the West African Rift System, and the Central African Shear Zone, which provided a conduit for heat flow to the surface.     

Determination of the three-dimensional seismic structure of the crust and upper mantle in the Central Midlands of England

Summary. Teleseismic P -wave residuals relative to CWF, a permanent shortperiod seismic station on Charnwood Forest in the Central Midlands of England, have been determined for two small aperture arrays deployed over the Precambrian block of Charnwood and its surrounding Phanerozoic sediments. The data have been inverted to produce a block model of the P -wave velocity variations in the crust and upper mantle beneath the study region. The results are consistent with significant variations penetrating to a depth of at least 50 km. Low velocities are associated with two upper crustal intrusive bodies, the Caledonian Mountsorrel granodiorite and the South Leicestershire diorites. A longer-wavelength variation at lower crustal/upper mantle depths could arise from the Moho dipping to the south-west beneath the study region, and whose strike sub-parallels the dominant Charnian trend of the major basement structures in this part of Central England.     

Surface wave array tomography in SE Tibet from ambient seismic noise and two-station analysis – II. Crustal and upper-mantle structure

We determine the 3-D shear wave speed variations in the crust and upper mantle in the southeastern borderland of the Tibetan Plateau, SW China, with data from 25 temporary broad-band stations and one permanent station. Interstation Rayleigh wave (phase velocity) dispersion curves were obtained at periods from 10 to 50 s from empirical Green's function (EGF) derived from (ambient noise) interferometry and from 20 to 150 s from traditional two-station (TS) analysis. Here, we use these measurements to construct phase velocity maps (from 10 to 150 s, using the average interstation dispersion from the EGF and TS methods between 20 and 50 s) and estimate from them (with the Neighbourhood Algorithm) the 3-D wave speed variations and their uncertainty. The crust structure, parametrized in three layers, can be well resolved with a horizontal resolution about of 100 km or less. Because of the possible effect of mechanically weak layers on regional deformation, of particular interest is the existence and geometry of low (shear) velocity layers (LVLs). In some regions prominent LVLs occur in the middle crust, in others they may appear in the lower crust. In some cases the lateral transition of shear wave speed coincides with major fault zones. The spatial variation in strength and depth of crustal LVLs suggests that the 3-D geometry of weak layers is complex and that unhindered crustal flow over large regions may not occur. Consideration of such complexity may be the key to a better understanding of relative block motion and patterns of seismicity.     

Pre-drilling reflection survey of the Black Forest, SW Germany

Summary. The unified seismic exploration program, consisting of 345 km of deep reflection profiling, a 200 km refraction profile, an expanding spread profile and near-surface high resolution reflection meaasurements, revealed a strongly differentiated crust beneath the Black Forest. The highly reflective lower crust contains numerous horizontal and dipping reflectors at depths of 13-14 km down to the crust-mantle boundary (Moho). The Moho appears as a flat horizontal first order discontinuity at a relatively shallow level of 25–27 km above a transparent upper mantle. From modelling of synthetic near-vertical and wide-angle seismograms using the reflectivity method the lower crust is supposed to be composed of laminae with an average thickness of about 100 m and velocity differences of greater than 10% increasing from top to bottom. The upper crust is characterised by mostly dipping reflectors, associated with bivergent underthrusting and accretion tectonics of Variscan age and with extensional faults of Mesozoic age. A bright spot at 9.5 km depth is characterised by low velocity material suggesting a fluid trap. It appears on all of the three profiles in the centre of the intersection region. The upper crust seems to be decoupled from the lowest crust by a relatively transparent zone which is' also identified as a low-velocity zone. This low velocity channel is situated directly above the laminated lower crust. The laminae in the Rhinegraben area are displaced vertically to greater depths indicating an origin before Tertiary rift formation and a subsidence of the whole graben wedge.     

The influence of a stratified rheology on the flexural response of the lithosphere to (un)loading by extensional faulting

We present a two-layered finite difference model for the flexural response of the lithosphere to extensional faulting. The model allows for three modes of flexure: (1) fully coupled, with the upper crust and mantle welded together by the lower crust; (2) fully decoupled, with the upper crust and mantle behaving as independent layers; and (3) partly decoupled, signifying that the response of the upper crust to small-wavelength loads is superimposed on the response of the entire lithosphere to long-wavelength loads. Which of these modes of flexure is to be expected depends on the rheology and especially the thermal state of the lithosphere. Coupled behaviour is related to a cold and strong lithosphere. The Baikal Rift Zone provides a typical example for this mode of flexure. A fully decoupled lithosphere is an exceptional case, related to anomalous high temperatures in the lower crust, and is observed in the Basin and Range province. The most common case is a partly decoupled lithosphere, with the degree of decoupling depending on the thickness and viscosity of the lower crust. This is inferred, for example, for the Bay of Biscay margin.     

Oceanic crustal structure—Mid-Atlantic Ridge at 45° N

Summary. We present a velocity—depth model for the crust beneath the Mid-Atlantic Ridge at 45° N which is derived from a comparison of waveforms corresponding to observed and synthetic seismograms. The model which best fits the observations includes a high-velocity layer at the base of the crust (layer 3B) and a velocity gradient in the upper mantle. These results are in agreement with other recent seismic studies on the Mid-Atlantic Ridge and indicate that the velocity structure is more complex than that obtained from travel-time analysis. There is no evidence for a low-velocity zone at the base of the crust.     

Numerical models of ductile rebound of crustal roots beneath mountain belts

Crustal roots formed beneath mountain belts are gravitationally unstable structures, which rebound when the lateral forces that created them cease or decrease significantly relative to gravity. Crustal roots do not rebound as a rigid body, but undergo intensive internal deformation during their rebound and cause intensive deformation within the ductile lower crust. 2-D numerical models are used to investigate the style and intensity of this deformation and the role that the viscosities of the upper crust and mantle lithosphere play in the process of root rebound. Numerical models of root rebound show three main features which may be of general application: first, with a low-viscosity lower crust, the rheology of the mantle lithosphere governs the rate of root rebound; second, the amount of dynamic uplift caused by root rebound depends strongly on the rheologies of both the upper crust and mantle lithosphere; and third, redistribution of the rebounding root mass causes pure and simple shear within the lower crust and produces subhorizontal planar fabrics which may give the lower crust its reflective character on many seismic images.     

Heterogeneous structure around the Jemez volcanic field, New Mexico, USA, as inferred from the envelope inversion of active-experiment seismic data

We analyse active-experiment seismic data obtained by the 1993 Jemez Tomography Experiment (JTEX) programme to elucidate the heterogeneous structure of the Jemez volcanic field, which is located at the boundary between the Colorado Plateau and the Rio Grande Rift. Using a single isotropic scattering assumption, we first calculate the envelope Green's functions for the upper and lower crust and the uppermost mantle. By fitting the theoretical envelopes with the observed three-component data, we estimate depth-dependent features of the scattering coefficients around Valles Caldera. We estimate the ratios of scattering coefficients, rather than scattering coefficients themselves, because of the uncertainty of the seismic efficiency of the explosive sources and knowledge of absolute site-amplification factors. The strongest scattering coefficients are observed at a shallow depth beneath the Valles Caldera. This is considered to be related to the complex structure caused by two episodes of caldera formation and the ensuing resurgent uplift in the caldera, etc. The depth-dependent characters of the scattering coefficients for the Colorado Plateau and the Rio Grande Rift are similar to each other: a transparent upper crust and a heterogeneous lower crust (small and large scattering coefficients, respectively). However, the scattering coefficients beneath the Rio Grande Rift are several times larger than those beneath the Colorado Plateau. Depths of the lower crust and the Moho boundary beneath the Rio Grande Rift are shallower than those of the Colorado Plateau. From their geological settings and other geophysical results around the region, we infer that the larger scattering coefficients of the rift are associated with rift formation and volcanic activity, such as magma ascent from the upper mantle to the crust.     

EARTH MODELS WITH CONTINUOUS DENSITY DISTRIBUTION

Summary. Eight different Earth models have been set up, all with the property that the density p varies continuously from just below the crust to the centre. The distributions of the pressure p , gravity g , incompressibility k and rigidity are also given; and values of a parameter equal to (k/p)dp/dp , indicate the deviations from (chemical) homogeneity in the lower mantle and outer core. The models are designed to provide a numerical background towards testing the view that there is no density jump between the Earth's mantle and core.
A discussion shows that this view is difficult to reconcile with a homogeneous core unless an implausibly low value is assumed for the density just below the crust.     

Ray-mode duality for SH waves in earth models with crust and mantle discontinuities—II. The case of N discontinuities

Summary. In examining the effect of discontinuities in the Earth's interior on free oscillations, McNabb, Anderssen & Lapwood derived an equation for the asymptotic behaviour of torsional overtone eigenfrequencies of a discontinuous earth model, the constants in their equation being explicitly determined only for the case of one internal discontinuity. Since Brune's phase correlation method for the evaluation of eigenfrequencies from body-wave data implies a ray-mode duality only for continuous earth models, it is desirable to justify the McNabb et al. formulation from the point of view of ray theory.
By a novel method of ray analysis, Wang, Cleary & Anderssen showed that, for earth models with a single discontinuity between the Earth's surface and the core—mantle boundary, the McNabb et al. formulation can be derived from an adaptation of Brune's method to multiply reflected SH body waves recorded at small epicentral distances. In this paper, the technique of Wang et al. is extended to derive the McNabb et al. formulation (with constants explicitly determined) for the general case of earth models with N discontinuities. This establishes a basis for a ray-mode duality for discontinuous earth models.     

Crustal structure beneath exposed accreted terranes of Southern Alaska

Summary. The crustal structure beneath the exposed terranes of southern Alaska has been explored using coincident seismic refraction and reflection profiling. A wide-angle reflector at 8–9 km depth, at the base of an inferred low-velocity zone, underlies the Peninsular and Chugach terranes, appears to truncate their boundary, and may represent a horizontal decollement beneath the terranes. The crust beneath the Chugach terrane is characterized by a series of north-dipping paired layers having low and high velocities that may represent subducted slices of oceanic crust and mantle. This layered series may continue northward under the Peninsular terrane. Earthquake locations in the Wrangell Benioff zone indicate that at least the upper two low-high velocity layer pairs are tectonically inactive and that they appear to have been accreted to the base of the continental crust. The refraction data suggest that the Contact fault between two similar terranes, the Chugach and Prince William terranes, is a deeply penetrating feature that separates lower crust (deeper than 10 km) with paired dipping reflectors, from crust without such reflectors.     

Wide-angle deep crustal reflections in the northern Appalachians

Summary. Seismic refraction data collected in the northern Appalachians provide an unusual opportunity to use wide-angle reflections to examine the lower crust and upper mantle. The PmP phase, clearly identified on several hundred records, has been used to construct an isopach map of the crust which shows a stepwise regional thickening of the crust beneath the axis of the Appalachians. The data have been examined to times of up to 40 s two-way travel time to investigate the possibility of coherent upper-mantle reflections such as those recently observed by BIRPS on near-vertical data northwest of Britain. Although substantial coherent energy appears after the PmP phase, synthetic seismogram modelling shows that all of these arrivals are explicable by S-phases, converted phases and multiples from within the crust. We conclude that in this region of the northern Appalachians we have not detected any significant regionally extensive reflecting horizons within the upper mantle.