Slipping interfaces: A possible source of S radiation from explosive sources

We consider the problem of reflection and refraction of purely compressional waves incident on an interface separating identical solid half-spaces in which the condition of continuity of shear displacement at the boundary is generalized to one that allows slippage. The problem is solved using the Cagniard-de Hoop technique. It is found that the generation of reflected P and S waves, as well as transmitted S waves, is most effective in the case of perfectly unbounded half-spaces. We discuss the implications of this model for the generation of S waves by block movement in the vicinity of an underground explosion

Multi-mode analysis of Rayleigh-type Lg. Part 1. Theory and applicability of the method

Rayleigh-type Lg propagating in a laterally homogeneous continental crust can be synthesized by adding only a few overtones at periods greater than 2 sec. Under minimal assumptions, we show that wavenumber analysis of Lg recorded on a several hundred kilometers long linear array of 10 stations allow us to isolate the different overtones, providing a tool to study crustal structures and excitation of the overtones at the source. In this first paper, we use synthetic Lg seismograms to investigate the applicability of a time-frequency-wavenumber analysis technique (UC diagram algorithm) to realistic arrays of stations. The behavior of the algorithm in the presence of lateral heterogeneities is studied numerically by introducing either random or coherent phase perturbations. We find that (1) the method is tractable if random phase fluctuations from station to station are spread over less than half a cycle, and (2) coherent velocity changes between two halves of a profile are spatially averaged if they are too small to be resolved by the array

The frequency dependence of Q in the Earth and implications for mantle rheology and Chandler wobble

For most solids the ‘high temperature background’ attenuation dominates at low frequencies and temperatures greater than about one-half the melting temperature. It is likely to be important in the mantle at seismic frequencies. The same mechanism also contributes to transient creep at low stresses and low total strains. A relaxation spectrum is found which satisfies the frequency dependence of laboratory Q and the time dependence of transient creep data. This makes it possible to provide a physical interpretation of the parameters in Jeffrey's modified Lomnitz creep function. Q is predicted to increase as ω^α in the lower Q regions of the mantle. At high and low frequencies Q should increase as ω and ω^(−1), respectively. The location of the ω^α band depends on temperature and therefore shifts with depth. At high temperatures, seismic waves are on the low-frequency side of the absorption band and Q decreases with frequency. Far from the melting point and at sufficiently high frequencies Q should increase linearly with frequency. We use Chandler wobble, tidal and free oscillation data to estimate that α is ∼ 1/5 to 1/3, consistent with laboratory measurements of transient creep and internal friction at high temperature. A preliminary attempt is made to estimate the transient creep response of the mantle from Q measurements. The inferred viscosity agrees well with direct measurements. The effect of anelasticity is to lengthen the calculated period of the Chandler wobble by 5-20 days, depending on the Chandler wobble Q. A Q of 300 for the wobble, which is within the experimental uncertainty of recent determinations, gives the observed period after correcting for the effect of the oceans

Dislocations and nonelastic processes in the mantle

Dislocations in solids contribute to anelastic attenuation, relaxation of the shear modulus, transient creep, and steady state flow. These properties of the mantle may therefore be related. The glide and climb of dislocations appear to have the appropriate time constants to explain seismic wave attenuation and mantle viscosity, respectively. The dislocation density of the mantle depends on the ambient stress. The characteristic time scales of dislocation relaxation depend on dislocation length and temperature. These time scales for the mantle can be inferred from seismic wave attenuation and postglacial rebound, thereby potentially yielding information about dislocation density, stress, and temperature. The thickness of the ‘rheological’ lithosphere depends on stress and duration of load as well as age. Kilobar level stresses can be supported in the lithosphere for times greater than 106 years. The relaxation time decreases rapidly with temperature. The asthenosphere can therefore only support small stresses on time scales of geological interest

Elastodynamics of Failure in a Continuum

A general treatment of the elastodynamics of failure in a prestressed elastic continuum is given, with particular emphasis on the geophysical aspects of the problem. The principal purpose of the study is to provide a physical model of the earthquake phenomenon, which yields an explicit description of the radiation field in terms of source parameters. The Green's tensor solution to the equations of motion in a medium with moving boundaries is developed. Using this representation theorem, and its specialization to the scalar case by means of potentials, it is shown that material failure in a continuum can be treated equivalently as a boundary value problem or as an initial value problem. The initial value representation is shown to be preferable for geophysical purposes, and the general solution for a growing and propagating rupture zone is given. The energy balance of the phenomenon is discussed with particular emphasis on the physical source of the radiated energy. It is also argued that the flow of energy is the controlling factor for the propagation and growth of a failure zone. Failure should then be viewed as a generalized phase change of the medium. The theory is applied to the simple case of a growing and propagating spherical failure zone. The model is investigated in detail both analytically and numerically. The analysis is performed in the frequency domain and the radiation fields are given in the form of multipolar expansions. The necessary theorems for the manipulation of such expansions for seismological purposes are proved, and their use discussed on the basis of simple examples. The more realistic ellipsoidal failure zone is investigated. The static problem of an arbitrary ellipsoidal inclusion under homogeneous stress of arbitrary orientation is solved. It is then shown how the analytical solution can be combined with numerical techniques to yield more realistic models. The conclusion is that this general approach yields a very flexible model which can be adapted to a wide variety of physical circumstances. In spite of the simplicity of the model, the predicted radiation field is rather complex; it is discussed as a function of source parameters, and scaling laws are derived which ease the interpretation of observed spectra. Preliminary results in the time domain are also shown. It is concluded that the model can be compared favorably both with the observations, and with results obtained from purely numerical models

A numerical boundary integral equation method for elastodynamics. I

The boundary initial value problems of elastodynamics are formulated as boundary integral equations. It is shown that these integral equations may be solved by time-stepping numerical methods for the unknown boundary values. A specific numerical scheme is presented for antiplane strain problems and a numerical example is given

P_n velocity anisotropy in Southern California

We analyze P_n propagation as a function of azimuth across a 28-station, 150-km aperture subarray of the SCARLET network centered near the central Transverse Ranges, California. We selected signals from 81 earthquakes and explosions with epicentral distances ranging from 150 to 400 km, covering all azimuths except a 40° gap from the southwest and a lesser gap from the northeast direction. For each source the apparent velocity of P_n was determined using a one-norm measure of misfit. The apparent P_n velocity does not show any systematic variation with epicentral distance but exhibits a strong azimuthal dependence. Our preferred interpretation calls for a slightly dipping (2° to N40W) planar moho, with 3 to 4 per cent anisotropy of subcrustal material. Transverse isotropy with a nearly horizontal symmetry axis is sufficient to explain the data; the direction of sagittal symmetry is N50W. The isotropic velocity of P_n is 7.8 km/sec. In contrast, a higher (8.1 km/sec) P_n velocity is found in the Mojave block, with no indication of anisotropy. These observations are consistent with a subcrustal model of the Pacific-North America plate boundary where ductile flow is characterized by simple shear in a vertical plane with strike parallel to the direction of relative plate motion

Multi-mode analysis of Rayleigh-type Lg. Part 2. Application to southern California and the northwestern Sierra Nevada

The UC diagram technique described in the companion paper (Part 1), is applied to nine sets of Lg phases recorded through the CEDAR system in southern California, and two sets of Lg phases recorded along the northwestern margin of the Sierra Nevada. A clear image of the signal is obtained in time-frequency-wavenumber space, and we discuss in particular observations at 2.5-sec period, for events 200 to 300 km outside the profiles. From the gross features of UC diagrams we conclude that a representation of Lg as a single coherent multi-mode wave train is oversimplified in the case of southern California but is more appropriate for the Sierra block. In southern California, peaks observed at group velocities smaller than 3.2 km/sec are not predicted by realistic crustal models of the area, and are probably due to lateral heterogeneities effects such as mode conversion and multipathing. On the other hand, for group velocities between 3.2 and 3.6 km/sec, peaks observed in either area can generally be interpreted in terms of overtones excited at the source and propagating through spatially averaged structures, although care must be taken to monitor the stability of the algorithm on actual short-period records

The Algorithm Theoretical Basis Document for Tidal Corrections

This Algorithm Theoretical Basis Document deals with the tidal corrections that need to be applied to range measurements made by the Geoscience Laser Altimeter System (GLAS). These corrections result from the action of ocean tides and Earth tides which lead to deviations from an equilibrium surface. Since the effect of tides is dependent of the time of measurement, it is necessary to remove the instantaneous tide components when processing altimeter data, so that all measurements are made to the equilibrium surface. The three main tide components to consider are the ocean tide, the solid-earth tide and the ocean loading tide. There are also long period ocean tides and the pole tide. The approximate magnitudes of these components are illustrated in Table 1, together with estimates of their uncertainties (i.e. the residual error after correction). All of these components are important for GLAS measurements over the ice sheets since centimeter-level accuracy for surface elevation change detection is required. The effect of each tidal component is to be removed by approximating their magnitude using tidal prediction models. Conversely, assimilation of GLAS measurements into tidal models will help to improve them, especially at high latitudes

Report of the panel on plate motion and deformation, section 2

Given here is a panel report on the goals and objectives, requirements and recommendations for the investigation of plate motion and deformation. The goals are to refine our knowledge of plate motions, study regional and local deformation, and contribute to the solution of important societal problems. The requirements include basic space-positioning measurements, the use of global and regional data sets obtained with space-based techniques, topographic and geoid data to help characterize the internal processes that shape the planet, gravity data to study the density structure at depth and help determine the driving mechanisms for plate tectonics, and satellite images to map lithology, structure and morphology. The most important recommendation of the panel is for the implementation of a world-wide space-geodetic fiducial network to provide a systematic and uniform measure of global strain