Deglacial land emergence and lateral upper-mantle heterogeneity in the Svalbard Archipelago—II. Extended results for high-resolution load models

In Paper I (Breuer & Wolf 1995), a preliminary interpretation of the postglacial land emergence observed at a restricted set of six locations in the Svalbard Archipelago was given. The study was based on a simple model of the Barents Sea ice sheet and suggested increases in lithosphere thickness and asthenosphere viscosity with increasing distance from the continental margin.
In the present paper, the newly developed high-resolution load model. BARENTS-2, and land-uplift observations from an extended set of 25 locations are used to study further the possibility of resolving lateral heterogeneity in the upper mantle below the northern Barents Sea. A comparison of the calculated and observed uplift values shows that the lithosphere thickness is not well resolved by the observations, although values above 110 km are most common for this parameter. In contrast to this, there are indications of a lateral variation of asthenosphere viscosity. Whereas values in the range 10¹⁸-10²⁰Pas are inferred for locations close to the continental margin, 10²⁰-10²¹ Pa s are suggested further away from the margin.
A study of the sensitivity of the values found for lithosphere thickness and asthenosphere viscosity to modifications of load model BARENTS-2 shows that such modifications can be largely accommodated by appropriate changes in lithosphere thickness, whereas the suggested lateral variation of asthenosphere viscosity is essentially unaffected. An estimate of the influence of the Fennoscandian. ice sheet leads to the conclusion that its neglect results in an underestimation of the thickness of the Barents Sea ice sheet by about 10 per cent.     

One-way representations of seismic data

A general one-way representation of seismic data can be obtained by substituting a Green's one-way wavefield matrix into a reciprocity theorem of the convolution type for one-way wavefields. From this general one-way representation, several special cases can be derived.
By introducing a Green's one-way wavefield matrix for primaries , a generalized Bremmer series representation is obtained. Terminating this series after the first-order term yields a primary representation of seismic reflection data. According to this representation, primary seismic reflection data are proportional to a reflection operator, 'modified' by primary propagators for downgoing and upgoing waves. For seismic imaging, these propagators need to be inverted. Stable inverse primary propagators can easily be obtained from a one-way reciprocity theorem of the correlation type.
By introducing a Green's one-way wavefield matrix for generalized primaries , an alternative representation is obtained in which multiple scattering is organized quite differently (in comparison with the generalized Bremmer series representation). According to the generalized primary representation, full seismic reflection data are proportional to a reflection operator, 'modified' by generalized primary propagators for downgoing and upgoing waves. Internal multiple scattering is fully included in the generalized primary propagators {either via a series expansion or in a parametrized way). Stable inverse generalized primary propagators can be obtained from the one-way reciprocity theorem of the correlation type. These inverse propagators are the nucleus for seismic imaging techniques that take the angle-dependent dispersion effects due to fine-layering into account.     

The transition from subduction to continental collision: crustal structure in the North Canterbury region, New Zealand

The North Canterbury region marks the transition from Pacific plate subduction to continental collision in the South Island of New Zealand. Details of the seismicity, structure and tectonics of this region have been revealed by an 11-week microearthquake survey using 24 portable digital seismographs. Arrival time data from a well-recorded subset of microearthquakes have been combined with those from three explosions at the corners of the microearthquake network in a simultaneous inversion for both hypocentres and velocity structure. The velocity structure is consistent with the crust in North Canterbury being an extension of the converging Chatham Rise. The crust is about 27 km thick, and consists of an 11 km thick seismic upper crust and 7 km thick seismic lower crust, with the middle part of the crust being relatively aseismic. Seismic velocities are consistent with the upper and middle crust being composed of greywacke and schist respectively, while several lines of evidence suggest that the lower crust is the lower part of the old oceanic crust on which the overlying rocks were originally deposited.
The distribution of relocated earthquakes deeper than 15 km indicates that the seismic lower crust changes dip markedly near 43S. To the south-west it is subhorizontal, while to the north-east it dips north-west at about 10. Fault-plane solutions for these earthquakes also change near 43S. For events to the south, P -axes trend approximately normal to the plate boundary (reflecting continental collision), while for events to the north, T -axes are aligned down the dip of the subducted plate (reflecting slab pull). While lithospheric subduction is continuous across the transition, it is not clear whether the lower crust near 43S is flexed or torn.     

Spectral analysis using orthonormal functions with a case study on the sea surface topography

b
Spherical harmonics are orthonormalized using the Gram-Schmidt process in a function space. The problem of linear dependence of spherical harmonics over the oceans is studied using the Gram matrices and consequently three sets of orthonormal (ON) functions have been constructed. For the process an efficient formula for computing inner products of spherical harmonics has been developed. Important spectral properties of the ON functions are addressed. The ON functions may be used for representing the sea surface topography (SST) in the analysis of satellite altimeter data. The geoid error can be transformed to a representation by the ON functions and hence the comparison of powers of the geoid error and the SST signal only over the oceans is possible, leading to a better way of determining the cut-off frequency of the SST in the simultaneous solution using satellite altimeter data. As a case study, the modified Levitus SST is expanded into the ON functions. The results show that 99.90 per cent of that signal's energy is contained within degree 24 of the orthonormal functions. Such expansions also render better spectral behaviour of oceanic signals as compared to that from spherical harmonic expansions. The study shows that these generalized Fourier functions are suitable for spectral analyses of oceanic signals and they can be applied to future altimetric mission where the geoid and the SST are to be recovered.     

Asymptotic eigenfrequencies of the Earth's normal modes

We derive asymptotic formulae for the toroidal and spheroidal eigenfrequencies of a SNREI earth model with two discontinuities, by considering the constructive interference of propagating SH and P-SV body waves. For a model with a smooth solid inner core, fluid outer core and mantle, there are four SH and 10 P-SV ray parameters regimes, each of which must be examined separately. The asymptotic eigenfrequency equations in each of these regimes depend only on the intercept times of the propagating wave types and the reflection and transmission coefficients of the waves at the free surface and the two discontinuities. If the classical geometrical plane-wave reflection and transmission coefficients are used, the final eigenfrequency equations are all real. In general, the asymptotic eigenfrequencies agree extremely well with the exact numerical eigenfrequencies; to illustrate this, we present comparisons for a crustless version of earth model 1066A.     

On the frequency contents of local events: source or path effect?

Local events which occurred in the Timanfaya volcanic field are analysed and their spectral contents are interpreted as being due to the effect of a finely layered medium with large impedance contrast, the presence of which is well known from well-logging data. By considering the layered medium as a filter, its spectral response (amplitude and phase) is computed from different randomly generated values of its parameters (total thickness, mean thickness of the individual layers and impedance contrast), showing that this stratigraphic filter acts as a low-pass filter. This effect can be correctly modelled by means of an exponential correlation function. However, in some cases resonant peaks appear in the spectrum superimposed on the low-pass filter effect, which can only be attributed to resonant scattering. An analysis of the phase and group delay associated with the amplitudes is made and strongly suggests that it is necessary to incorporate the theory of resonant scattering for the retrieval of medium properties. From the point of view of the amplitudes, the superposition of both effects, low-pass filter and resonant peaks, allows us to reproduce the gross features that are usually attributed to source effects. The need for a careful analysis of the local site response previous to any interpretation of the spectral features in terms of source characteristics is thus emphasized.     

Non-linear optimization for seismic traveltime tomography

This paper presents a non-linear algorithmic approach for seismic traveltime. It is based on large-scale optimization using non-linear least-squares and trust-region methods. These methods provide a natural way to stabilize algorithms based on Newton's iteration for non-linear minimization. They also correspond to an alternative (and often more efficient) view of the Levenberg-Marquardt method. Numerical experience on synthetic data and on real borehole-to-borehole problems are presented. In particular, results produced by the new algorithm are compared with those of Ivansson (1985) for the Kråkemåla experiment.     

反演地壳磁化强度等效源法的模型验证及实际资料试算

等效源法曾被广泛应用于卫星磁异常解释,而本文是将等效源法引用到航空△T磁场的解释中,用其研究区域地质构造。根据等效源法的理论,推导出球坐标系下球棱柱体的△T磁场公式,采用线性反演的方法进行模型验证,同时将该方法用于秦巴地区航空△T磁异常的试算,得到了一些有意义的结论。利用该方法可由所求得的磁场强度来得到居里深度分布。