High-frequency seismic radiation from a buried circular fault

Summary. We propose a simplified method for the calculation of near field accelerograms. It is based upon the hypothesis that, in the course of dynamic faulting, the dominating part of the seismic radiation is emitted by the rupture front. As the rupture moves smoothly it radiates continuously, generating the low-frequency part of the field. High-frequency waves are produced by jumps in the rupture velocity and abrupt changes in the stress intensity factor. The wave-front discontinuities created in this fashion are evaluated by asymptotic methods and may be propagated away from the source by ray theoretical methods. We apply our technique to the evaluation of asymptotic near field accelerograms for a circular fault buried in a half-space. The agreement with numerical accelerograms calculated by full-wave theory is very satisfactory. Two problems are given particular emphasis: (1) the phase shifts introduced by focusing and (2) a simpler method, based on dislocation theory, is proposed for the calculation of the radiation coefficients from a discontinuously moving rupture front.     

Induction in a thin sheet of variable conductance at the surface of a stratified earth - I. Two-dimensional theory

Summary. An existing 2-D integral equation method for modelling electromagnetic induction in a thin sheet at the surface of a uniform half-space can be generalized to deal with a layered half-space by the inclusion of an extra term in the integral equation. The results obtained are shown to be in excellent agreement with finite difference solutions to the same modelling problem.     

Three-dimensional induction in a non-uniform thin sheet at the surface of a uniformly conducting earth

Summary. A new method for solving problems in three-dimensional electromagnetic induction in which the Earth is represented by a uniformly conducting half-space overlain by a surface layer of variable conductance is presented. Unlike previous treatments of this type of problem the method does not require the fields to be separated into their normal and anomalous parts, nor is it necessary to assume that the anomalous region is surrounded by a uniform structure; the model may approach either an E- or a B -polarization configuration at infinity. The solution is expressed as a vector integral equation in the horizontal electric field at the surface. The kernel of the integral is a Green's tensor which is expressed in terms of elementary functions that are independent of the conductance. The method is applied to an illustrative model representing an island near a bent coastline which extends to infinity in perpendicular directions.     

The Love wave scattering matrix for a continental margin (numerical)

Summary . This paper presents the numerical computation of the results previously obtained by the author through a scattering matrix formulation (together with plane wave and variational approximations) which describes the diffraction of plane, harmonic, monochromatic Love waves incident normally (from either side) upon the plane of discontinuity in a structure consisting of a half-space with a surface step — an idealized model of a continental margin. Magnitudes of reflection and transmission coefficients are computed numerically for different frequencies for a model which has been considered previously by Knopoff & Hudson and also by Alsop in their studies of the same problem. The results obtained under the plane wave approximation are compared with those obtained under the variational approximation in order to assess the effects of the body-wave contributions. Finally, the results of both approximations are compared with those obtained by previous authors.     

Gaussian beams for surface waves in laterally slowly-varying media

Summary. Asymptotic ray theory is applied to surface waves in a medium where the lateral variations of structure are very smooth. Using ray-centred coordinates, parabolic equations are obtained for lateral variations while vertical structural variations at a given point are specified by eigenfunctions of normal mode theory as for the laterally homogeneous case. Final results on wavefields close to a ray can be expressed by formulations similar to those for elastic body waves in 2-D laterally heterogeneous media, except that the vertical dependence is described by eigenfunctions of 'local' Love or Rayleigh waves. The transport equation is written in terms of geometrical-ray spreading, group velocity and an energy integral. For the horizontal components there are both principal and additional components to describe the curvature of rays along the surface, as in the case of elastic body waves. The vertical component is decoupled from the horizontal components. With complex parameters the solutions for the dynamic ray tracing system correspond to Gaussian beams: the amplitude distribution is bell-shaped along the direction perpendicular to the ray and the solution is regular everywhere, even at caustics. Most of the characteristics of Gaussian beams for 2-D elastic body waves are also applicable to the surface wave case. At each frequency the solution may be regarded as a set of eigenfunctions propagating over a 2-D surface according to the phase velocity mapping.     

基于多源遥感数据的中山站附近地区冰架和冰川变化监测

南极冰架和冰川的变化是全南极动态变化的主要过程之一。利用MODIS L1B级250 m分辨率数据和Landsat陆地卫星15 m分辨率数据,针对不同尺度试验区域,分别监测2000—2016年间中山站附近地区的埃默里冰架、极时代冰川、极记录冰川和达尔克冰川的动态变化过程,并对试验区的动态变化进行分析。结果表明,埃默里冰架在近16年间一直处于向外扩展状态,前缘年扩展速率和扩展面积量较为稳定;极时代和极记录冰川不断向海洋流动,极时代冰川于2007年发生大型崩解,而极记录冰川前端的冰山在2014年发生崩解,冰山面积逐年递减,于2016年完全漂离冰川前缘;达尔克冰川则在监测年份内呈现出了交替性扩展和崩解的变化规律。     

Diffraction of P, S and Rayleigh waves by three-dimensional topographies

The diffraction of P, S and Rayleigh waves by 3-D topographies in an elastic half-space is studied using a simplified indirect boundary element method (IBEM). This technique is based on the integral representation of the diffracted elastic fields in terms of single-layer boundary sources. It can be seen as a numerical realization of Huygens principle because diffracted waves are constructed at the boundaries from where they are radiated by means of boundary sources. A Fredholm integral equation of the second kind for such sources is obtained from the stress-free boundary conditions. A simplified discretization scheme for the numerical and analytical integration of the exact Green's functions, which employs circles of various sizes to cover most of the boundary surface, is used.
The incidence of elastic waves on 3-D topographical profiles is studied. We analyse the displacement amplitudes in the frequency, space and time domains. The results show that the vertical walls of a cylindrical cavity are strong diffractors producing emission of energy in all directions. In the case of a mountain and incident P, SV and SH waves the results show a great variability of the surface ground motion. These spatial variations are due to the interference between locally generated diffracted waves. A polarization analysis of the surface displacement at different locations shows that the diffracted waves are mostly surface and creeping waves.     

B-polarization induction in two generalized thin sheets at the surface of a conducting half-space

Summary. A new closed-form solution is obtained analytically for a B- polarization induction problem of geophysical interest, in which a local region of the Earth is represented by a generalized thin sheet at the surface of and in electrical contact with a uniformly conducting half-space. The generalized sheet, first introduced by Ranganayaki & Madden, is a mathematical idealization of a double layer which consists, in this problem, of two adjacent half-planes with distinct conductances representing a surface conductivity discontinuity such as an ocean—coast boundary, underlain by a uniform sheet of finite integrated resistivity representing the lower crust. The resistive sheet exerts a considerable mathematical influence on the solution causing, under certain conditions, an additional pole to appear in one of the forms of contour integral by which the solution can be expressed; it also weakens or eliminates field singularities that would otherwise occur at the conductance discontinuity. A numerical calculation is made for model parameters typifying an ocean—coast boundary underlain by a highly resistive crust. It is found that the residue of the pole associated with the resistive sheet dominates the solution for this example, the main consequence of which is a huge increase in the horizontal range over which the induced currents adjust themselves between the different 'skin-effect' distributions at infinity on either side of the model. Moreover the solution shows that this 'adjustment distance' has a more complicated dependence on the conductance and integrated resistivity of the sheet than that given simply by the square root of their product which was the length parameter proposed by Ranganayaki & Madden.     

A hybrid calculation technique of the Indirect Boundary Element Method and the analytical solutions for three-dimensional problems of topography

We present a new approach of the Indirect Boundary Element Method (IBEM) for 3-D topographic problems which can be used to deal with an infinitely spread free surface owing to the introduction of a reference solution, that is the analytical solution for the half-space with a flat free surface. This approach is an efficient countermeasure for the non-physical waves owing to the domain truncation which contaminates the computed results in the ordinary approach. Theoretical consideration shows that this newly proposed approach is a higher-grade approximation than some existing ones and achieves a higher efficacy and accuracy than those of existing ones. The discretization of the resulting boundary integral equation for this formulation is carried out with triangular elements. Their contributions to the solution are calculated by Gaussian numerical integration except in the case where the wavefield is evaluated on the source element itself. For this case, we present an analytical formula based on the reasonable assumption that the elements are much smaller than the wavelengths appearing in the calculation. Several numerical examples used for validation show acceptably precise results.     

Two-dimensional induction in a thin sheet of variable integrated conductivity at the surface of a uniformly conducting earth

Summary. The forward solution of the general two-dimensional problem of induction in a model earth comprising a uniformly conducting half-space covered by a thin sheet of variable integrated conductivity is obtained. Unlike some previous treatments of similar problems, the method presented here does not require the field to be separated into its normal and anomalous parts. Both the E - and B -polarization modes of induction are considered and in each case the solution is expressed in terms of the horizontal component of the electric field satisfying, on the surface of the conductor, a singular integral equation whose kernel is a well-known analytic function. A recently published solution of the coast effect is included as a special case. The numerical procedure for solving the integral equations is described and some illustrative calculations are presented.     

Transient electromagnetic fields about an infinitesimally long grounded horizontal electric dipole on the surface of a uniform half-space

Summary. Laplace and Bessel Transforms are used to solve for the transient behaviour of the electromagnetic fields after switching off a steady current in a grounded infinitesimal horizontal dipole on the surface of a uniformly conducting half-space. Simple analytic expressions, which are valid for times sufficiently long after the switch that displacement terms can be ignored, are obtained on the surface of the half-space for the electric field and the time derivative of the magnetic field. At the instant of switching an infinitesimally long image becomes established directly under the source dipole. It is the diffusion of this image which gives the vertical magnetic field and horizontal electric fields their transient behaviour. During the transient, there is also a decaying charge distribution on the surface.     

A surge of Perseibreen, Svalbard, examined using aerial photography and ASTER high resolution satellite imagery

The identification of surge activity is important in assessing the duration of the active and quiescent phases of the surge cycle of Svalbard glaciers. Satellite and aerial photographic images are used to identify and describe the form and flow of Perseibreen, a valley glacier of 59 km² on the east coast of Spitsbergen. Heavy surface crevassing and a steep ice front, indicative of surge activity, were first observed on Perseibreen in April 2002. Examination of high resolution (15 m) Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) satellite imagery confirmed this surge activity. Perseibreen retreated by almost 750 m between 1961 and 1990. Between 1990 and the summer of 2000, Perseibreen switched from retreat and its front began to advance. Rapid advance was underway during the period June 2000 to May 2001, with terminus advance at over 400 m yr⁻¹. Between May and August 2001 the rate increased to over 750 m yr⁻¹. The observed crevasse orientation indicates that ice was in longitudinal tension, suggesting the down-glacier transfer of mass. Ice surface velocities, derived from image correlation between ASTER images, were 2-2.5 m d⁻¹ between May and August 2001. The glacier was flowing at a relatively uniform speed with sharp velocity gradients located close to its lateral margins, a velocity structure typical of ice masses in the active phase of the surge cycle. The stress regime is extensional throughout and the surge appears to be initiated low on the glacier. This is similar to the active-phase dynamics of other Svalbard tidewater glaciers. Perseibreen has probably been inactive since at least 1870, a period of about 130 years to the present surge which defines a minimum length for the quiescent phase.     

High-frequency radiation from crack (stress drop) models of earthquake faulting

We present a theory for the radiation of high-frequency waves by earthquake faults. We model the fault as a planar region in which the stress drops to the kinematic friction during slip. This model is entirely equivalent to a shear crack. For two-dimensional fault models we show that the high frequencies originate from the stress and slip velocity concentrations in the vicinity of the fault's edges. These stress concentrations radiate when the crack expands with accelerated motion. The most efficient generation of high-frequency waves occurs when the rupture velocity changes abruptly. In this case, the displacement spectrum has an ω^-2 behaviour at high frequencies. The excitation is proportional to the intensity of the stress concentration near the crack tips and to the change in the focusing factor due to rupture velocity. We extend these two-dimensional results to more general three-dimensional fault models in the case when the rupture velocity changes simultaneously on the rupture front. Results are similar to those described for two-dimensional faults. We apply the theory to the case of a circular fault that grows at constant velocity and stops suddenly. The present theory is in excellent agreement with a numerical solution of the same problem.
Our results provide upper bounds to the high-frequency radiation from more realistic models in which rupture velocity does not change suddenly. The ω^-2 is the minimum possible decay at high frequencies for any crack model of the source.     

Frontal advance of turf-banked solifluction lobes, Kluane Range, Yukon Territory, Canada

Humus horizons associated with thirteen solifluction lobes on a single slope were radiocarbon dated at fixed distances behind the risers, as well as ahead of the lobes. The dated horizons, together with stratigraphic observations of planar discontinuities inside the lobes and shallow burial of vegetation ahead of the lobes, all suggest rapid advance of lobe fronts. We infer that lobe advance at this site results from slow accumulation of soliflucted material behind a relatively rigid riser, progressive steepening of the riser and build-up of stress, and finally rupture of the front and its collapse onto the slope. Rebuilding of the lobe usually then takes place. The time for a full cycle of development is estimated to be in the order of a few hundred years. Long-term frontal movement appears inversely related to lobe size, and is mainly controlled by soil moisture and sediment characteristics. These findings call into question the usefulness of solifluction lobe advance rates for paleoclimate reconstructions, at least at this site.     

Scattering of horizontally-polarized shear waves by surface irregularities

Summary. The problem of the scattering of harmonic SH waves by an arbitrary surface irregularity in an otherwise semi-infinite elastic, homogeneous, isotropic two-dimensional half-space is examined in this study in order to ascertain the effect of topography on this type of seismic ground motion and to develop a useful scheme which can realistically handle arbitrary two-dimensional topography. Three geometric models are considered: a semicircular hill which is of academic interest; a mountain with a Gaussian shape which utilizes realistic dimensions and the combination of a ridge and a depression that models a region in Sylmar, California.
A singular Fredholm integral equation of the second kind for the displacement at the free surface is developed and solved numerically. In the case of the semicircular hill, horizontal ground motion can be more than twice that occurring in the case of smooth topography. The mountain simulated by a Gaussian profile experiences at its crest amplifications for certain angles of incidence and de-amplifications for other angles of incidence, as well as displacements whose amplitudes vary slowly with frequency on the side of the mountain which is in the same direction as the incident waves. The ridge-depression combination which is approximated by a sixth-order polynomial actually experienced shattered earth at its ridge crest during the San Fernando, California earthquake of 1971. This amplification is also exhibited by the results of the analysis which, predicts amplifications of over 75 per cent at the top of the ridge for waves arriving on the same side as the ridge.     

The correspondence between gravitational attraction and surface displacement due to volume expansion

Summary. It is shown that the formulas for the calculation of surface displacement due to a volume source in a half-space may be derived from a potential of the same form as the gravitational potential. The similarity between these expressions allows the use of methods developed for gravity in the study of surface displacement. As an example of the applicability of the correspondence, an efficient algorithm is developed for the calculation of uplift due to volume expansion within a homogeneous half-space. The method may be generalized to three-dimensional volumes undergoing expansion in a half-space.     

Glaciomarine sedimentation in a modern fjord environment, Spitsbergen

By means of high resolution acoustic profiling and correlation of echo character and sediment lithology, fjords in western and northern Spitsbergen are shown to be blanketed by a 5-20 m layer of acoustically transparent sediments consisting mainly of soft homogeneous mud with ice rafted clasts. Acoustically semi-transparent material is found on slopes and sills reflecting their coarser composition. The areal average depositional rate in the outer fjord is in the range of from 0.1 to 1.0 mm/year, increasing towards the glaciers. In Kongsfjorden, 50-100 mm/year of muddy sediments is deposited at a distance of 10 km from the calving Kongsvegen glacier. Close to the ice front (<0.5 km) coarser grained, interbedded (sand/mud) sediments are deposited. The main sediment sources are from settlement out of the turbid surface sediment plume, combined with various types of gravity flow (sediment creep, minor slides, and slumping). Material deposited from turbidity current is probably of minor importance. On shallow sills the sediments are remobilized by icebergs. The sediment adjacent to the ice front is reworked and compacted during surges, a common form of glacial advance for Spitsbergen glaciers. During the surge considerable amounts of coarse-grained sediment are deposited by meltwater in front of the ice margin.     

Changes in the hypsometric curve through mountain building resulting from concurrent tectonics and denudation

The stages of geomorphic development of mountains have sometimes been explained based on Strahler's diagram of hypsometric curves. Although the Japanese mountains are young, they do not follow his diagram. Hypsometric curves, simulated using empirical laws deduced from the Japanese mountains, indicate that mountain building resulting from concurrent tectonics and denudation does not produce convex curves but concave and/or s-shaped curves. The hypsometric curve of a mountain changes from a concave curve to an s-shaped curve in accordance with the increase in mountain altitude. The succession of the hypsometric curve during concurrent tectonics and denudation is the reverse of Strahler's diagram. The hypsometric integral increases with the advance in stage which is evaluated based on the change in mountain altitude. It has a relatively good correlation with the stage. However, the sequence of change in the hypsometric integral is different according to the extent of the terrain examined, whether the terrain is restricted to the interior of a mountain or pertains to the whole mountain, and whether it includes newly emerged land. The stage should be evaluated based on the course of change in the integral characteristics for the extent of the mountain examined.     

Effects of the free surface on shear wavetrains

Summary. The behaviour of shear-waves is of great importance in identifying and investigating seismic anisotropy in the Earth. However, shear wavetrains recorded at the Earth's surface do not always reflect the motion at depth, introducing practical problems of interpretation. Shear wavetrains incident on the surface of an isotropic half-space at angles less than critical (about 35°) are broadly preserved, but at greater angles substantial distortions can occur. For stations situated close to the source, as in local earthquake studies, the local SP phase, a radially polarized precursor to S , may occur. The behaviour at the surface of an anisotropic half-space is further complicated by the divergence of phase and energy propagation vectors. All of these complications suggest that detailed seismogram modelling is essential to any study of shear wave propagation in the Earth, and in particular to investigations of anisotropy-induced shear-wave splitting.     

A perturbation theory for Love waves in anelastic media

Summary. We give a systematic formulation and a rigorous justification of a perturbation technique for the computation of the eigenvalues and eigenfunctions of Love waves (and toroidal oscillations by an appropriate change for variables) in an anelastic medium with a constitutive law modelling geophysical media of current interest such as the Kelvin—Voigt Solid, the Maxwell Solid, the Standard Linear Solid, and the Standard Linear Solid with a continuous spectrum of relaxation times. We develop expressions relating the eigenvalues of eigenfunctions for Love waves in a continuously varying vertically stratified anelastic half-space to the corresponding elastic eigenvalues and eigenfunctions. Analytically, our correspondence principle has the form of a regular perturbation expansion in terms of a parameter for both the eigenvalues and eigenfunctions. The identification of ɛ is motivated by the dissipativity principle of viscoelasticity theory. Moreover, we show that our correspondence principle applies respectively only in the high and low frequency range for the Maxwell and Kelvin—Voigt Solids. Outside of the applicable range of frequencies, our correspondence principle yields no useful information. For the family of Standard Linear Solids it is uniformly applicable for all non-zero frequencies.
We also derive an explicit formula to estimate the radius of convergence of our perturbation expansions. This estimate of the radius of convergence for each eigenvalue and eigenfunction is functionally defined by the constitutive model for the anelastic medium. The estimate is frequency dependent and depends on the separation distance between the eigenvalue and the remainder of the spectrum of the corresponding elastic problem.