Search

We perform numerical calculations for onshore seismic amplifications, taking into consideration the effect of bathymetric features on the propagation of seismic movements. To this end, the boundary element method is applied. Boundary elements are employed to irradiate waves and, consequently, force densities can be obtained for each boundary element. From this assumption, Huygens' principle is applied, and since the diffracted waves are built at the boundary from which they are radiated, this idea is equivalent to Somigliana's representation theorem. The application of boundary conditions leads to a linear system being obtained (Fredholm integral equations). Several numerical models are analyzed, with the first one being used to verify the proposed formulation, and the others being used to estimate onshore seismic amplifications due to the presence of bathymetric features. The results obtained show that compressional waves (P-waves) generate onshore seismic amplifications that can vary from 1.2 to 5.2 times the amplitude of the incident wave. On the other hand, the shear waves (S-waves) can cause seismic amplifications of up to 4.0 times the incident wave. Furthermore, an important result is that in most cases the highest seismic amplifications from an offshore earthquake are located on the shoreline and not offshore, despite the seafloor configuration. Moreover, the influence of the incident angle of seismic waves on the seismic amplifications is highlighted.

The adaptive optimized window generalized S transform (AOGST) variant with frequency and time is a method for the time–frequency mapping of a signal. According to the AOGST method, an optimized regulation factor is calculated based on the energy concentration of the S transform. The value of this factor is 1 for standard S transform where in the AOGST method its value is limited by the interval of [0, 1]. However, AOGST may not produce an acceptable resolution for all parts of the time–frequency representation. We applied aggregation of confined interval-adaptive optimized generalized S transforms (ACI-AOGST) instead of the AOGST method. The proposed method applies the modified AOGST method to specific frequency and time intervals. By calculating regulation factors for limited frequency and time intervals of signal, arranging them in a suitable order and applying the ACI-AOGST one can provide a transformation with lowest distortion and highest resolution in comparison to other transformations. The proposed method has been used to analyse the time–frequency distribution of a synthetic signal as well as a real 2D seismic section of a producing gas reservoir located south of Iran. The results confirmed the robustness of the ACI-AOGST method.

Teleseismic SH waves are essential for imaging the rupture processes of large earthquakes. However, for great earthquakes (M8+) such as the 2004 Sumatra earthquake, the 2008 Wenchuan earthquake and the recent Tohoku-Oki earthquake, the source duration is very long (>100 s). Thus the direct SH waves are overlapped with ScS waves for epicentral distances larger than 60°, leaving contaminated S waves for source processes modelling. Therefore artefacts in finite fault models of large earthquake could be produced with such contaminated body waves. We propose an iterative algorithm based on the slowness information of S and ScS waves and stacking technique, to separate S and ScS waves with records from a regional seismic network. Tests on various synthetic data sets show that the algorithm is effective in retrieving teleseismic SH waveforms from complicated wave trains containing both S and ScS. Separation of waveforms for the 2008 Wenchuan earthquake with our algorithm clearly demonstrates the influence of ScS energy, suggesting necessity of recovering S waves.

Summary Seismic waves caused by earthquakes radiate infrasound into the atmosphere as they proceed over the Earth's surface. Several instances of such sound waves radiated locally by seismic waves passing through the Washington, D.C., area have been observed at the infrasonic station there. A notable instance was the great Montana earthquake of 1959 August 18. Measurements of the radiated infrasound gave data on the seismic waves, including their travel times, local speeds, directions of travel, amplitudes, and waveforms.

Microphones and seismographs were co-located in arrays on Skidaway Island, Georgia, for the launchings of Apollo 13 and 14, 374 km to the south. Simultaneous acoustic and seismic waves were recorded for both events at times appropriate to the arrival of the acoustic waves from the source. The acoustic signal is relatively broadband compared to the nearly monochromatic seismic signal; the seismic signal is much more continuous than the more pulse-like acoustic signal; ground loading from the pressure variations of the acoustic waves is shown to be too small to account for the seismic waves; and the measured phase velocities of both acoustic and seismic waves across the local instrument arrays differ by less than 6 per cent and possibly 3 per cent if experimental error is included. It is concluded that the seismic waves are generated by resonant coupling to the acoustic waves along some 10 km of path on Skidaway Island.

Douglas, Hudson & Blamey (1972) suggest that the relative amplitudes of P and Rayleigh waves generated by underground explosions depend on the properties of the source medium. Calculations based on an assumption of a flat spectrum for P waves radiated at source, indicate that the relation between the body wave magnitude, mb (computed at 1 Hz) and the surface wave magnitude, M , (computed at 0.05 Hz) should be

SUMMARY The technique of passive image interferometry applies interferometric methods to correlation functions of seismic noise to monitor small temporal variations of the Earth interior. We computed the autocorrelation function of seismic noise recorded at a single seismometer located in the vicinity of the source region of the Mw = 6.6 Mid-Niigata earthquake. Analysing the temporal evolution of the autocorrelation function, which is interpreted as the source‐ receiver collocated elastic wave Green’s function, we detect a sudden decrease of relative seismic velocity in the Earth crust of −0.6 per cent that coincides with the occurrence of the earthquake. This drop of seismic velocity is likely to be caused by the change of stress in the source region of the earthquake.

SUMMARY The coupling between the solid earth and its atmosphere is responsible for vertically propagating infrasonic waves generated by seismic surface waves. These pressure waves are amplified as they propagate upward, and produce perturbations of ionospheric electron density. The electron density perturbations above California, due to the seismic surface waves generated by the Denali earthquake on 2002 November 3, have been imaged from GPS data by a tomographic method. The integrated electron content along GPS ray paths presents a noise level that is lower in the acoustic wave frequency band than in the gravity wave frequency band. Therefore, the filtered GPS data from Californian networks are inverted for a tomographic reconstruction of electron density perturbations in the acoustic frequency band. The inversion is properly resolved only in a small number of areas due to the geometry of GPS ray paths. In these areas, a wave propagating upward at 1.2 ± 0.3 km s−1 and horizontally at 4 ± 1 km s−1 is observed, with a timing consistent with an infrasonic wave generated by the path of seismic surface waves. The discrepancies between the observed electron density perturbation structure and the expected infrasonic wave can be explained by the poor resolution of the inverse problem or by a simple model of interactions between the neutral wave and the plasma. Future development of dense GPS networks and the advent of the Galileo system will overcome the resolution problems, and allow us to relate ionospheric perturbations to the seismic signal. Such a relation can be used to constrain the source and propagation of seismic waves as well as upper atmosphere characteristics.

SUMMARY We locate the concealed Carlsberg Fault zone along a 12-km-long trace in the Copenhagen city centre by seismic refraction, reflection and fan profiling. The Carlsberg Fault is located in a NNW-SSE striking fault system in the border zone between the Danish Basin and the Baltic Shield. Recent earthquakes indicate that this area is tectonically active. A seismic refraction study across the Carlsberg Fault shows that the fault zone is a low-velocity zone and marks a change in seismic velocity structure. A normal incidence reflection seismic section shows a coincident flower-like structure. We have recorded seismic signals in a fan geometry from shots detonated both inside the low-velocity fault zone and up to ∼500 m away from the fault zone. The seismic energy was recorded on three receiver arrays (1.5- to 2.4-km-long arcs) across the expected location of the ∼400- to 700-m-wide fault zone at distances of up to ∼7 km from the shots. Shots detonated inside the fault zone result in (1) weak and delayed first arrivals on the receivers located inside the fault zone compared to earlier and stronger first arrivals outside the fault zone; (2) strong guided P and S waves as well as surface waves inside the fault zone. The fault zone is a shadow zone to shots detonated outside the fault zone. Finite-difference wavefield modelling supports the interpretations of the fan recordings. Our fan recording approach facilitates cost-efficient mapping of fault zones in densely urbanized areas where seismic normal incidence and refraction profiling are not feasible.

SUMMARY We analyse quantitatively a waveform data set of 238 earthquakes recorded by a dense seismic array across and along the rupture zone of the 1992 Landers earthquake. A grid-search method with station delay corrections is used to locate events that do not have catalogue locations. The quality of fault zone trapped waves generated by each event is determined from the ratios of seismic energy in time windows corresponding to trapped waves and direct S waves at stations close to and off the fault zone. Approximately 70 per cent of the events with S‐P times of less than 2 s, including many clearly off the fault, produce considerable trapped wave energy. This distribution is in marked contrast with previous claims that trapped waves are generated only by sources close to or inside the Landers rupture zone. The time difference between the S arrival and trapped waves group does not grow systematically with increasing hypocentral distance and depth. The dispersion measured from the trapped waves is weak. These results imply that the seismic trapping structure at the Landers rupture zone is shallow and does not extend continuously along-strike by more than a few kilometres. Synthetic waveform modelling indicates that the fault zone waveguide has depth of approximately 2‐4 km, a width of approximately 200 m, an S-wave velocity reduction relative to the host rock of approximately 30‐40 per cent and an S-wave attenuation coefficient of approximately 20‐30. The fault zone waveguide north of the array appears to be shallower and weaker than that south of the array. The waveform modelling also indicates that the seismic trapping structure below the array is centred approximately 100 m east of the surface break.

SUMMARY The seismic structure of the stratovolcano Merapi (Java, Indonesia) was studied using an active seismic experiment. Three 3 km long seismic profiles each consisting of up to 30 three-component seismometers with an interstation distance of 100 m were built up in an altitude range between 1000 and 2000 m above sea level. The detailed study of the seismic properties of the propagation media in active volcanic regions is important to understand the natural seismic signals used for eruption forecasting. The seismic experiment at Merapi therefore concentrates on the heterogeneous structure within a radius of 5 km from the active dome, where the sources of most of the natural volcanic seismic events are located. The cone of Merapi volcano consists of different materials changing on a small scale due to the layering of eruptive material. Additionally, the topography of the erosion valleys leads to an irregular deposition, which cannot be described by a simple 1-D layering. These inhomogeneities have a strong influence on seismic signals. The direct P and S waves are attenuated quickly and show only small amplitudes on seismograms. The energy lost from the direct waves, however, is not changed into heat but scattered and can be observed as seismic coda following the direct waves. The observed seismograms show a spindle-like amplitude increase after the direct P phase. This shape of the envelope can be explained by the diffusion model. According to this model there are so many strong inhomogeneities that the direct wave can be neglected and all energy is concentrated in multiple scattered waves. Besides the envelope, the coherence and polarization properties of the wavefield also indicate strong scattering. Only the first onset shows coherence over a station spacing of 100 m, whereas the late phases carrying the major part of the energy are mainly incoherent. The horizontal components of the seismograms have larger amplitudes than the vertical component, but within the horizontal plane the polarization is almost arbitrary, corresponding to waves arriving from scatterers located arbitrarily in space. As a result of the inversion using the diffusion model we obtain values of the S-wave scattering attenuation coefficient, gs, and the S-wave intrinsic absorption coefficient, gi. In the frequency range of 4‐20 Hz used in this study the scattering attenuation is at least one order of magnitude larger than the intrinsic absorption (gs&gi). The mean free path of S waves is as low as 100 m (gs1 #100 m). The scattering coefficient is independent of frequency (gsyf 0.0 ), whereas the coefficient of intrinsic attenuation increases with increasing frequency (giyf 1.6 ). The natural seismic signals at Merapi volcano show similar characteristics to the artificial shots. The first onsets have only small amplitudes and the energy maximum arrives delayed compared to the direct waves. Therefore, these signals appear to be strongly affected by multiple scattering also.

Volcano seismology often deals with rather shallow seismic sources and seismic stations deployed in their near field. The complex stratigraphy on volcanoes and near-field source effects have a strong impact on the seismic wavefield, complicating the interpretation techniques that are usually employed in earthquake seismology. In addition, as most volcanoes have a pronounced topography, the interference of the seismic wavefield with the stress-free surface results in severe waveform perturbations that affect seismic interpretation methods. In this study we deal predominantly with the surface effects, but take into account the impact of a typical volcano stratigraphy as well as near-field source effects. We derive a correction term for plane seismic waves and a plane-free surface such that for smooth topographies the effect of the free surface can be totally removed. Seismo-volcanic sources radiate energy in a broad frequency range with a correspondingly wide range of different Fresnel zones. A 2-D boundary element method is employed to study how the size of the Fresnel zone is dependent on source depth, dominant wavelength and topography in order to estimate the limits of the plane wave approximation. This approximation remains valid if the dominant wavelength does not exceed twice the source depth. Further aspects of this study concern particle motion analysis to locate point sources and the influence of the stratigraphy on particle motions. Furthermore, the deployment strategy of seismic instruments on volcanoes, as well as the direct interpretation of the broad-band waveforms in terms of pressure fluctuations in the volcanic plumbing system, are discussed.

Summary One answer to the question posed in the title is that we will have more accurate data for arrival times of SH waves, because the rotational component around the vertical axis is sensitive to SH waves although not to P-SV waves. Importantly, there is another answer related to seismic sources, which will be discussed in this paper. Generally, not only dislocations commonly used in earthquake models but also other kind of defects could contribute to producing seismic waves. In particular, rotational strains at earthquake sources directly generate rotational components in seismic waves. Employing the geometrical theory of defects, we obtain a general expression for the rotational motion of seismic waves as a function of the parameters of source defects. Using this expression, together with one for translational motion, we can estimate the rotational strain tensor and the spatial variation of slip velocity in the source area of earthquakes. These quantities will be large at the edges of a fault plane due to spatially rapid changes of slip on the fault and/or a formation of tensile fractures.

Acoustic measurements of deepwater fish from a deep-towed transducer deployed at depths from 500 to 650 m over a seamount (rising from 1000 to 600 m depth) are compared with those from a vessel-mounted transducer. Algorithms were developed to correct for noise and to analyse signals near the bottom. The analysis showed that the vessel-mounted transducer can significantly underestimate the volume reverberation of deepwater fish by an average factor of 1.86, equating to 2.7 dB. This bias was largely attributed to beam thresholding and calibration, acoustic attenuation from nearsurface bubbles, ship motion, and uncertainties in the sound absorption constant. On the steepest slope of the seamount the near-bottom shadow zone was reduced by 50% and the extrapolated biomass in this zone reduced by 47% using the deep-towed transducer. These results confirm that a deep-towed transducer will improve absolute abundance measurements of deepwater resources. ? 1996 International Council for the Exploration of the Sea

SUMMARY Because of the zone of damage that is created around an explosion it is unlikely that simple elastic reflection of seismic waves takes place at the free surface, at least for small angles of incidence. Some attempts have been made to simulate the effect on P-wave radiation of the zone of damage but so far the only models used have been acoustic. Here we construct a fully elastic model. The damaged zone is represented in a highly simplified way by a horizontal screen centred on the source, which attenuates signals reflected back from the free surface. P-waveforms are computed for various angles of emergence using the Kirchhoff approximation. Two types of screen are considered: for one—the opaque screen—the downward radiation is reduced to zero over a circular area of radius a, and for the other the radiation at the level of the source is reduced by a factor [1 – exp(–r2/a2)], where r is the distance of a point on the screen from the focus and a is a constant, the scale size of the screen. This model is referred to as the semi-opaque screen. For steep take-off angles the arrivals generated by diffraction by the screen of pP and pS to P, are of significant amplitude relative to P and have negative polarity. For the opaque screen the principal contributions to these arrivals arise from diffraction at the near and far edges of the screen, of rays travelling in the vertical plane containing the focus. As the angle of incidence from source to receiver increases, the contributions from the far edge of the screen become insignificant. In the lit zone the diffraction of pP at the near edge produces arrivals with significant amplitudes and positive polarity for angles near the shadow edge. The change from negative to positive polarity in moving from the shadow zone into the lit is predicted by generalized ray theory. The results for the semi-opaque models are smoothed versions of those obtained for the opaque model. In addition to the impulsive arrivals the computed responses show a positive low-frequency step with an onset around the time of the first diffracted arrival generated by pP. Examples of seismograms computed for the opaque screen model using explosion source functions show some features of observed seismograms.

SUMMARY If a sharp edge occurs in a reflector, the wavefield predicted by geometric ray theory shows shadow boundaries between illuminated zones and shadow zones. One may correct for these discontinuities in the wavefield by adding edge waves as introduced by Klem-Musatov. In this paper the edge wave is analysed as a solution of a parabolic differential equation that describes transverse diffusion between the illuminated zone and the shadow zone across the shadow boundary. Here, the edge wave is described constructively in terms of dynamic ray tracing, thereby indicating how it can be implemented in a ray tracing program when the latter is equipped with the facility of dynamic ray tracing.

Summary. The slowness of the diffracted SH-wave around the core boundary is re-examined. The criticism that measurements from the Iranian earthquake of 1968 August 31 are affected by the focal mechanism is shown to be unjustified theoretically and by comparison with analogous recordings from the Imperial Valley earthquake of 1979 October 15. Evidence is presented that an SH ray parameter estimated from first impetus SH diffracted onsets does not represent a shear velocity averaged over a hundred kilometres depth but rather the velocity within a few tens of kilometres of the core–mantle boundary. In addition to a re-examination of the seismograms previously used for the 1968 August 3 1 Iran earthquake, long-period seismograms for 80° < ▵ < 150° have been studied for two Tonga earthquakes, 1967 October 9 and 1977 August 11. Exclusion of readings with ▵ < 105° from the Iranian earthquake increases the gradient from 8.68 ± 0.13 to 9.48 ± 0.26s deg−1. The exceptionally large ray parameter is not fully explained, but a plausible hypothesis is anisotropy in shear velocity near the core–mantle boundary. When observations are restricted to clear arrivals at distances exceeding a few degrees from the shadow boundary, reliable new estimates are obtained for the SH slowness, namely 8.41 ± 0.07s deg−1 for Tonga 1967 and 8.39 ± 0.06 for Tonga 1977. The statistical uncertainty of the estimates indicates no significant average change in SH velocity at the base of the mantle along two easterly profiles 3000 km apart under the east Pacific and North America. For a core radius of 3485 km and a slowness of 8.4s dec−1, the average velocity near the core–mantle boundary is 7.24km s−1. This value is in agreement with estimates in D″ by Mula & Muller. The observed attenuation of the diffracted SH ground motion amplitudes at periods of 15–20s is similar for the three profiles considered, with a reduction of an order of magnitude within a distance of 25° in the shadow zone. This corresponds to an equivalent decay parameter γ= 0.10 at the core boundary.

*Summary. Refraction seismic profiles in the Alpine area occasionally show seismic ‘shadows’ which cannot be explained by a horizontal low-velocity channel. An example is demonstrated where the low P-velocity zone (Flysch) dips below a wedge of high P-velocity (the Calcareous Alps) which is a typical Alpine structure. This feature has been studied by means of a seismic model experiment. The corner of the wedge works as a source of diffracted P-, Sand Rayleigh-waves, when met by seismic waves. The diffracted waves can be distinguished from conventional waves by their amplitude--distance relation when the extinction coefficient is well known by an independent experiment.

SUMMARY Physical seismic model experiments have been undertaken to study the detectability and lateral resolution of buried linear reflecting targets (slits in an aluminium plate) which might simulate a range of interesting geological structures, e.g. fracture zones, fault blocks, reefs, facies changes, cavities. The reflector length was varied from one-thirtieth to over 20 wavelengths. The depth of burial was 17 wavelengths. Even the smallest target yielded discernible diffractions on receivers located in the shadow zone of the reflector. The lateral extent of the reflector can be accurately determined in the subwavelength range by utilizing together the amplitude, frequency, moveout and polarity information contained in the composite diffractionlreflection signals. As the reflector length increases, the amplitude and travel time increase, but the predominant frequency decreases. The dominant polarity of the interference waveform changes as the reflector length exceeds one wavelength. For targets extended horizontally more than one wavelength, the time difference between the two edge-diffracted waves is a good measure of reflector extent. In the case of an inclined reflector, the moveout pattern of the two diffractions was asymmetrical, forming a convergence zone (and higher amplitude) on the downdip side of the shotpoint. The offset at which the diffraction wavelets merge serves to define the reflector dip. The reflector length can be estimated from the time separation between the two weaker diffractions observed on receivers located updip of the shot, after appropriate correction for target inclination.

Summary. This note reports on the remarkable focusing of seismic body waves at or near the antipode (Δ= 180°) of an earthquake's epicentre. The particular seismic velocity structure and sphericity of the Earth cause body-wave phases such as P(diff), PKP, PP, PPP, PcPPKP, SKSSKS, SS, etc. to converge individually at antipodal distances after being diffracted, reflected or refracted at discontinuities. This focusing strongly amplifies each signal up to almost one order of magnitude with respect to the normal phase recorded two or more degrees away. Since the signal/noise ratio is enhanced in the same proportion, seismograms at antipodal distances provide clear and strong arrivals of otherwise weak phases. Antipodal monitoring of seismic waves is suggested as a powerful means of exploring the Earth's interior. The study of these ‘seismic images’ generated at focal points of seismic rays will yield information on the departures from lateral homogeneity and sphericity of the core, as well as stronger constraints on earth models. To interpret the observations correctly, the data must be compared with theoretically generated seismograms. Since the appropriate ray theory equations (see, e.g. Scholte; Gilbert & Helmberger; Richards) are singular at Δ=180°, a corrective measure is taken which provides a formal expression for the wave amplitude that remains finite at the antipode, and reproduces the usual expressions at other distances.

Summary. Numerical modelling is one of the most efficient methods for an investigation of the relationship between structural features and peculiarities of observed wavefields. It is practically the only method for 2-D and 3-D inhomogeneous media. An algorithm based on ray theory has been developed for calculations of travel times and amplitudes of seismic waves in 3-D inhomogeneous media with curved interfaces. It was applied for numerical modelling of kinematic and dynamic characteristics of seismic waves propagating in laterally inhomogeneous media. Travel-time and amplitude patterns were studied in the 2-D and 3-D models of a geosyncline, in which velocity distribution was given by an analytical function of the coordinates. For a more complicated model representing a subducting high-velocity lithospheric plate in a transition zone between oceanic and continental upper mantle, the velocity distribution was given by discrete values on a 2-D non-rectangular grid. It was shown that when a source was placed above the lithospheric plate, a shadow zone appeared along a strike of the structure, i.e. in the direction which is perpendicular to a strong lateral velocity gradient. Travel-time residuals were calculated along the seismological profile for a 3-D velocity distribution in the upper mantle beneath Central Asia, obtained as a result of inversion of travel times by the Backus-Gilbert method. They were found to be in a good agreement with the observed data.

Summary This paper describes a simple, robust technique of 3-D seismic raytracing through anomalous receiver structure. The technique uses a shooting approach and a vectorial description of both the ray and the anomalous structure through which it passes. By representing the receiver structure as a network of blocks, each with a constant velocity anomaly, the technique may be applied to the newly developed least squares inversion method (Aki, Christoffersson & Husebye) to define the required travel times of each ray through each block. The technique enables subvertical and non-parallel block boundaries to be handled and positioned to mimic known tectonic contacts, such as the boundaries of descending plates or craton margins. An inversion using such a network will better define the velocity contrasts than one using a regular grid of arbitrarily positioned block boundaries. Alternatively, delay times, slowness and azimuth anomalies may be modelled by raytracing through assumed anomalous receiver structures. As the anomalies will deflect a ray away from its ‘mean-earth’ path an iterative procedure is necessary to achieve the required end point. A novel, efficient procedure is presented, which involves making a search for the point through which the ray passes at the base of the receiver structure. The slowness/azimuth anomaly of each trial ray is determined as a mislocation vector. Trial rays with significantly different mislocation vectors can initially be regarded as possible different phases. Convergence of more than one phase to the required end point indicates the presence of multipathing. Lack of convergence of all these phases indicates the presence of a shadow zone.

Summary New formulae for the determination of travel-times of seismic waves in the interior of the Earth. Applications of said formulae to the calculation of travel-times of SKP-waves recorded at Tolmezzo.

Summary The propagation of an impulsive torsional disturbance excited by a localized stress on the surface of a sphere consisting of a homogeneous mantle surrounding a liquid core is expressed as the sum of normal mode solutions. The formulas presented can be used for the calculation of the disturbance on the surface of a sphere having any arbitrary radial distribution of material. Since the medium is a finite bounded body, the normal modes offer a complete description of the propagating disturbance. The azimuthal component of displacement at various points on the surface is calculated numerically as a function of time by summing the spectral contributions from 360 normal modes equally distributed among the first six radial modes. The surface waves, which are similar to those observed from earthquakes, are caused primarily by the fundamental radial mode, while the body waves are primarily related to the higher radial modes. The liquid core causes a shadow zone for the S wave; travel times for diffracted S correspond to the simple geometrical theory of travel to and from the curved core boundary along the tangent paths. The core-mantle boundary also causes the ScS phases which may be multiply reflected from the free surface.

Suininary In this paper we have considered the diffraction of SH-waves from a point source by a rigid or fluid spherical core. The medium outside the core is assumed to be spherically isotropic about the centre of the core. It is found that the propagation of SH-waves in such a medium is characterized by two elastic parameters associated with the phase velocities C1 and C, along and perpendicular to a radius, respectively. Depending on the ratio l/a of these two velocities and the distance of the source from the centre, the region of space outside the core can be separated into three different regions: (i) an illuminated zone which is reached either by the rays going left or right from the source and their reflections from the sphere; (ii) a shadow zone, which may be bounded; and (iii) if the shadow is bounded, then there is a third zone which may be reached by both rays going left and right and their reflections. This classification is true provided c1 is greater than one, which is true in most geophysical applications. Furthermore, if c1 is 2 2, then there is no shadow when the distance b of the source from the centre is large enough. We have discussed the solutions for 1 < c1 < 2 and have given simple geometrical interpretations to these solutions.

Summary Well documented short period seismic observations from the nuclear explosion Longshot provide an unusual opportunity to study seismic wave propagation in the mantle beneath an island arc. Ray calculations for a model containing a descending lithospheric slab predict an extensive P-wave shadow zone covering much of Canada and Europe and this is in close agreement with the pattern of reported magnitudes. Other features of the short period waveform which occur on some seismograms also seem amenable to explanation in terms of the complications that a slab introduces into seismic wave propagation in the vicinity of an island arc. Many examples are cited, including instances where a slab beneath the observing station also modifies the waveform.

Summary Expressions are derived for the body wave and surface wave displacement at epicentral distances of between 30" and 100" from an extended or moving source. The source is assumed to lie entirely within a finite region on a plane. Otherwise it can be quite general. The effects of layering at the source and receiver are taken into account. Attenuation due to linear anelasticity is allowed for by an empirical factor. Propagation through the mantle is assumed to follow ray theory and the sphericity of the Earth is taken into account by the use of geometrical spreading factors. Expressions for the surface waves generated by a point source in a layered halfspace have been given by both Haskell (1964) and Harkrider (1964) using essentially the same method (i.e. the Thomson-Haskell matrix theory) but with different notations. Later on, Fuchs (1966) derived similar formulae in Harkrider's notation for the body waves radiating into the lower half-space. These correspond to the waves from a seismic source which travel through the mantle before being refracted back to the surface by the velocity gradient. A scheme by which the body wave pulse from a seismic source may be calculated, allowing for the effects of transmission through the mantle and crust, was given by Carpenter (1966). The analysis applies to the waves recorded at epicentral distances between 30" and 100"; i.e. waves travelling along a ray path which lies partly in the mantle and is unaffected by the core. Kogeus (1968) applied Fuchs's results to Carpenter's theory to allow for the effects of the layered crust. He derived teleseismic waveforms due to an explosive source near the surface. A method for extending these results to sources of finite extent was indicated by Harkrider (1964) who derived expressions for the surface waves radiated from a source consisting of a horizontal point force moving with finite speed along a line. More realistic models of explosive and earthquake sources and their integration into the Thomson-Haskell theory are given by Hudson (1969) (Part I of the present Methods are, therefore, available for constructing waveforms of body waves and surface waves at distances in the range 30"-100" from a wide range of source models. We shall begin by deriving expressions for the Fourier time transforms (with transform variable o) of the body waves and surface waves from a point source of

Summary A theoretical investigation is made of the changes of the polarization of transverse seismic waves during their propagation through the Earth. The polarizations have been computed theoretically and numerically for reflexion at the core boundary and at the Earth's surface, for refraction and reflexion at the base of the crust and for passages through continuously varying media. It is demonstrated that great changes of the vibration properties (vibration angle and particle orbit) may occur in all cases except for continuously varying media, through which transverse waves propagate with practically unchanged vibration properties. The consequences of these results for earthquake mechanism studies, based on transverse waves, are discussed.

Summary Body wave observations from large nuclear explosions at the Nevada Test Site have been used to model the P-velocity and Q structure along the top of the mantle. The amplitudes of short period waves in the range 1–4 degrees and 12–35 degrees indicate substantial absorption in the low velocity zone with Qα. of the order of 50. With the source treated as a known quantity we used the amplitude ratio of short to long period motion as a criterion in modelling structure. The Cagniard-de Hoop technique is used to compute synthetic seismograms for proposed models. The model obtained has a high velocity lid above a thin pronounced low velocity layer with a small positive gradient existing to depths of 220 km. The shadow zone boundary occurs near 12 degrees.