Crustal and upper mantle structures of the brazilian coast

The Rayleigh wave phase and group velocities in the period range of 24–39 sec, obtained from two earthquakes which occurred in northeastern brazil and which were recorded by the Brazilian seismological station RDJ (Rio de Janeiro), have been used to study crustal and upper mantle structures of the Brazilian coastal region. Three crustal and upper mantle models have been tried out to explain crustal and upper mantle structures of the region. The upper crust has not been resolved, due basically to the narrow period range of the phase and group velocities data. The phase velocity inversions have exhibited good resolutions for both lower crust and upper mantle, with shear wave velocities characteristic of these regions. The group velocity data inversions for these models have showed good results only for the lower crust. The shear wave velocities of the lower crust (3.86 and 3.89 km/sec), obtained with phase velocity inversions, are similar to that (=3.89 km/sec) found byHwang (1985) to the eastern South American region, while group velocity inversions have presented shear velocity (=3.75 km/sec) similar to that (=3.78 km/sec) found byLazcano (1972) to the Brazilian shield. It was not possible to define sharply the crust-mantle transition, but an analysis of the phase and group velocity inversions results has indicated that the total thickness of the crust should be between 30 and 39 km. The crustal and upper mantle model, obtained with phase velocity inversion, can be used as a preliminary model for the Brazilian coast.     

裸眼井中弹性波传播的非对称模式的数值研究

本文从数值上研究了裸眼井中弹性波传播的非对称模式,给出了合成微地震图和导波（弯曲波）的频散曲线,发现在“硬”地层和“软”地层的井中,导波都是高度频散的,其最大相速度等于地层的横波速度,其截止频率低于对称模式的伪瑞利波的截止频率;在低频（2—3kHz）和长源距（3—4m）的条件下,由非对称的声源（如声偶极子）所产生的微地震图中,初至信号是以横波速度传播的,而以纵波速度传播的信号被抑制。本文的结果对研制横波速度测井仪是有意义的。     

Rayleigh wave dispersion equation for a layered spherical earth with exponential function solutions in each shell

We consider the second-order differential equations ofP-SV motion in an isotropic elastic medium with spherical coordinates. We assume that in the medium Lamé's parameters , r ^p and compressional and shear-wave velocities , r, wherer is radial distance. With this regular heterogeneity both the radial functions appearing in displacement components satisfy a fourth-order differential equation which provides solutions in terms of exponential functions. We then consider a layered spherical earth in which each layer has heterogeneity as specified above. The dispersion equation of the Rayleigh wave is obtained using the Thomson-Haskel method. Due to exponential function solutions in each layer, the dispersion equation has similar simplicity, as in a flat-layered earth. The dispersion equation is further simplified, whenp=–2. We obtain numerical results which agree with results obtained by other methods.     

Internal gravity wave selection in the upper troposphere and lower stratosphere observed by the MU radar: Preliminary results

Marked wavelike variations of the lower stratospheric wind observed on 7–10 May, 1985 by an MST radar in Japan (by the MU radar) are analyzed assuming that they are induced by monochromatic internal inertio-gravity waves. These variations are mainly composed of two modes (periods: 22 and 24 hours), both of which have zonal phase velocities (C _X ) slower than the mean westerly wind (). A statistical analysis of the zonal phase velocity shows thatC _X above andC _X below the tropopause jet stream, which is considered to be a vivid proof of wave selection due to the tropospheric mean flow and upward wave emission from the tropopause jet. A comparison between the MU radar results and routine meteorological observations leads to the conclusion that the marked waves appear when the jet stream takes a maximum wind speed.     

Crust and upper mantle structure of the Bohemian Massif from the dispersion of seismic surface waves

Summary The phase velocity dispersion of Rayleigh waves for the Moxa-Vienna (MOX-VIE) and Moxa-Kaperské Hory (MOX-KHC) profiles, and of both Rayleigh and Love waves for the Kaperské Hory-Ksi (KHC-KSP) profile have been measured and inverted into models of shearwave velocity vs. depth. The three paths cross, respectively, the central part of the Bohemian Massif, its western margin, and the Bohemian Pluton and Cretaceous. For the MOX-VIE profile mean and lower crustal shear wave velocities of 3.7 and 3.9 km/s, respectively, a mean Moho depth of 34 km, and no existence of a low-velocity layer in the lower crust were found. The model obtained for the MOX-KHC profile is characterized by a slightly lower velocity in the lower crust (3.8 km/s), by a slightly lower Moho depth (32 km), and by the appearance of a weak low-velocity channel between 55 and 140 km. The crustal section of the final model for the KHC-KSP profile agrees well with the KHKS82 model derived by Novotný from results of DSS along international profile VII. Our final Rayleigh-wave model has significantly lower shear-wave velocities down to 215 km in the mantle. A systematic difference of 0.18 km/s between the average velocities of Rayleigh and Love waves has been revealed for the depth range from 30 to 215 km. Since almost no contamination of the fundamental Love mode with higher modes has been observed, and since the investigated structure hardly contains an unresolved system of thin, alternately low- and high-velocity layers, the cause of the difference is evidently polarization anisotropy of the upper mantle beneath the Bohemian Massif. It is recommended that the discussed investigations should be supplemented with data from the fan of KSP-GRF (Gräfenberg Array, Germany) paths and from the KHC-BRG (Berggiesshübel, Germany) profile.     

On reflection and diffraction of pressure waves from floating ice

Summary The diffraction of a pressure wave arising from the edge of the floating ice due to an incident wave of the formH[t–(xcos/)+ (ysin/)], whereH(t) is the Heaviside step function, has been studied. The ice sheet has been taken to be moving with a velocity much less than the velocity of sound in the liquid. The problem has been solved using an approximate method of solving Wiener Hopf problems. Finally, the pressure field at a large distance from the edge has been derived in a closed form evaluating the integrals by the saddle point method.     

Hm-wave filtration in a horizontally stratified Earth's magnetosphere

Summary Drawing on papers [4, 5] a semi-quantitative model of filtration and resonance of a linearly polarized HM-wave has been constructed in a horizontally stratified Earth atmosphere. The wave is filtered in a system of 3 homogeneous layers, limited by two halfspaces. Attenuation of the wave is only assumed in the lower layer, i.e. in the ionosphere. A relation has been derived for the amplitude coupling factor H_T/H_F expressing the absolute ratio of the amplitude of the wave after transmission through the system of layers and the amplitude of the wave, incident at the system of layers. The mechanism of geomagnetic pulsations is illustrated on the principle of the resonance of a HM-wave in the Earth's magnetosphere. The magnetosphere has been replaced by the said system of layers, and the dependence of H_T/H_F=f() on the parameters of the system of layers has been studied using a computer.     

Source characteristics of the 1992 Nicaragua tsunami earthquake inferred from teleseismic body waves

We analyzed the broadband body waves of the 1992 Nicaragua earthquake to determine the nature of rupture. The rupture propagation was represented by the distribution of point sources with moment-rate functions at 9 grid points with uniform spacing of 20 km along the fault strike. The moment-rate functions were then parameterized, and the parameters were determined with the least squares method with some constraints. The centroid times of the individual moment-rate functions indicate slow and smooth rupture propagation at a velocity of 1.5 km/s toward NW and 1.0 km/s toward SE. Including a small initial break which precedes the main rupture by about 10 s, we obtained a total source duration of 110 s. The total seismic moment isM _o =3.4×10²⁰ Nm, which is consistent with the value determined from long-period surface waves,M _o =3.7×10²⁰ Nm. The average rise time of dislocation is determined to be 10 s. The major moment release occurred along a fault length of 160 km. With the assumption of a fault widthW=50 km, we obtained the dislocationD=1.3 m. From andD the dislocation velocity isD=D/0.1 m/s, significantly smaller than the typical value for ordinary earthquakes. The stress drop =1.1 MPa is also less than the typical value for subduction zone earthquakes by a factor of 2–3. On the other hand, the apparent stress defined by 2E _s /M _o , where andE _s are respectively the rigidity and the seismic wave energy, is 0.037 MPa, more than an order of magnitude smaller than . The Nicaragua tsunami earthquake is characterized by the following three properties: 1) slow rupture propagation; 2) smooth rupture; 3) slow dislocation motion.     

The effects of sliding velocity on the frictional and physical properties of heated fault gouge

The frictional properties of a crushed granite gouge and of gouges rich in montmorillonite, illite, and serpentine minerals have been investigated at temperatures as high as 600°C, confining pressures as high as 2.5 kbar, a pore pressure of 30 bar, and sliding velocities of 4.8 and 4.8×10^–2 m/sec. The gouges showed nearly identical strength behaviors at the two sliding velocities; all four gouges, however, showed a greater tendency to stick-slip movement and somewhat higher stress drops in the experiments at 4.8×10^–2 m/sec. Varying the sliding velocity also had an effect on the mineral assemblages and deformation textures developed in the heated gouges. The principal mineralogical difference was that at 400°C and 1 kbar confining pressure a serpentine breakdown reaction occurred in the experiments at 4.8×10^–2 m/sec but not in those at 4.8 m/sec. The textures developed in the gouge layers were in part functions of the gouge type and the temperature, but changes in the sliding velocity affected, among other features, the degree of mineral deformation and the orientation of some fractures.     

Upper mantle structure of the Apulian plate from Rayleigh waves

Phase velocities of Rayleigh waves for the Adriatic Sea area are obtained in the period range 25–190 sec along the path (l'Aquila-Trieste) AQU-TRI and 20–167 sec along the path (Trieste-Bari) TRI-BAI.The phase velocities are systematically higher than the known values for the surrounding regions. The data inversion indicates the presence of a lithosphere typical of stable continental areas with clear high-velocity lid (V _s 4.6 km/sec) overlying a well developed low velocity zone (V _s 4.2 km/sec).P. F. Geodinamica C.N.R., Roma Pubbl. N. 189.     

Recurrence of major flank landslides during the last 2-Ma-history of Reunion Island

New detailed swath bathymetry and backscatter data corroborate the existence of four large bulges on the submarine flanks of Reunion Island. These fan-shaped promontories are 20–25 km wide at the coastline and 70–150 km across the seafloor 40–50 km offshore. Their surfaces are characterized by a speckle sonar pattern, indicating the presence of large blocks up to several hundred meters across. Each bulge results from the superposition of multiple landslide deposits whose older ones are dissected and delimited by erosive channels as much as 200 m deep and 20 km long. The submarine flanks of Reunion Island are thus mostly built by accumulation of debris avalanche fans. Morphologic and geologic evidence define large subaerial source areas for these mass-wasting events. In particular, inferred headwalls of most landslides having affected the Piton des Neiges massif generally coincide with the boundaries of its cirques (Mafate, Salazie, and Cilaos), whereas recurrent landslides have resulted in the formation of large concentric amphitheatre structures through the Piton de la Fournaise massif. Thus, about 15 slide events accompanied growth of the Reunion Island shield since 2 Ma.Editorial responsibility: J. Stix     

Gravity current down a steeply inclined slope in a rotating fluid

The sinking of dense water down a steep continental slope is studied using laboratory experiments, theoretical analysis and numerical simulation. The experiments were made in a rotating tank containing a solid cone mounted on the tank floor and originally filled with water of constant density. A bottom gravity current was produced by injecting more dense coloured water at the top of the cone. The dense water plume propagated from the source down the inclined cone wall and formed a bottom front separating the dense and light fluids. The location of the bottom front was measured as a function of time for various experimental parameters. In the majority of runs a stable axisymmetric flow was observed. In certain experiments, the bottom layer became unstable and was broken into a system of frontal waves which propagated down the slope. The fluid dynamics theory was developed for a strongly non-linear gravity current forming a near-bottom density front. The theory takes into account both bottom and interfacial friction as well as deviation of pressure from the hydrostatic formula in the case of noticeable vertical velocities. Analytical and numerical solutions were found for the initial (t < 1/f), intermediate (t 1/f), and main (t 1/f) stages, where f is the Coriolis parameter. The model results show that during the initial stage non-linear inertial oscillations are developed. During the main stage, the gravity current is concentrated in the bottom layer which has a thickness of the order of the Ekman scale. The numerical solutions are close to the same analytical one. Stability analysis shows that the instability threshold depends mainly on the Froude number and does not depend on the Ekman number. The results of laboratory experiments confirm the similarity properties of the bottom front propagation and agree well with the theoretical predictions.     

Structure of the crust in the Black Sea and adjoining regions from surface wave data

Group velocities of Rayleigh and Love waves along the paths across the Black Sea and partly Asia Minor and the Balkan Peninsula are used to estimate lateral variations of the crustal structure in the region. As a first step, lateral variations of group velocities for periods in the range 10–20 s are determined using a 2D tomography method. Since the paths are oriented predominantly in NE–SW or N–S direction, the resolution is estimated as a function of azimuth. The local dispersion curves are actually averaged over the extended areas stretched in the predominant direction of the paths. The size of the averaging area in the direction of the best resolution is approximately 200 km. As a second step, the local averaged dispersion curves are inverted to vertical sections of S-wave velocities. Since the dispersion curves in the 10–20 s period range are mostly affected by the upper crustal structure, the velocities are estimated to a depth of approximately 25 km. Velocity sections along 43° N latitude are determined separately from Rayleigh and Love wave data. It is shown that the crust under the sea contains a low-velocity sedimentary layer of 2–3 km thickness, localized in the eastern and western deeps, as found earlier from DSS data. Beneath the sedimentary layer, two layers are present with velocity values lying between those of granite and consolidated sediments. Velocities in these layers are slightly lower in the deeps, and the boundaries of the layers are lowered. S-wave velocities obtained from Love wave data are found to be larger than those from Rayleigh wave data, the difference being most pronounced in the basaltic layer. If this difference is attributed to anisotropy, the anisotropy coefficient = (SH - SV)/Smean is reasonable (2–3%) in the upper layers, and exceeds 9% in the basaltic layer.     

On the propagation of wave from a cylindrical cavity

Summary This paper discusses the disturbance produced in an infinite layer of non-homogeneous elastic material characterised by =0 ⁿ and =0ⁿ(n>0) where and are the density and shear modulus respectively of the material, due to periodic torsional force applied on the wall of a cylindrical hole in the layer. The variation of the displacement component with the radius vector is shown graphically and compared with the corresponding homogeneous case.     

裸眼井中弹性波传播的非对称模式的数值研究

本文从数值上研究了裸眼井中弹性波传播的非对称模式,给出了合成微地震图和导波（弯曲波）的频散曲线,发现在“硬”地层和“软”地层的井中,导波都是高度频散的,其最大相速度等于地层的横波速度,其截止频率低于对称模式的伪瑞利波的截止频率;在低频（2-3kHz）和长源距（3-4m）的条件下,由非对称的声源（如声偶极子）所产生的微地震图中,初至信号是以横波速度传播的,而以纵波速度传播的信号被抑制。本文的结果对研制横波速度测井仪是有意义的。     

On the propagation of certain types of surface waves in a non-homogeneous elastic layer

Summary The propagation of a certain type of surface waves in a non-homogeneous elastic layer of finite thickness lying in welded contact with a semi-infinite homogeneous elastic medium has been investigated in this paper. The surface wave is characterised by the fact that the dilatation and the vertical displacement component are both zero. It has been proved that such disturbance can propagate only when the phase velocity of the wave is greater than the shear wave velocity and the group velocity is inversely proportional to the phase velocity.     

Characteristics of very large aspect angle E-region coherent echoes at 933 MHz

The EISCAT UHF radar system was used to study the characteristics of E-region coherent backscatter at very large magnetic aspect angles (5–11°). Data taken using 60 s pulses during elevation scans through horizontally uniform backscatter permitted the use of inversion techniques to determine height profiles of the scattering layer. The layer was always singly peaked, with a mean height of 104 km, and mean thickness (full width at half maximum) of 10 km, both independent of aspect angle. Aspect sensitivities were also estimated, with the Sodankylä-Tromsø link observing 5 dB/degree at aspect angles near 5°, decreasing to 3 dB/degree at 10° aspect angle. Observed coherent phase velocities from all three stations were found to be roughly consistent with LOS measurements of a common E-region phase velocity vector. The E-region phase velocity had the same orientation as the F-region ion drift velocity, but was approximately 50% smaller in magnitude. Spectra were narrow with skewness of about –1 (for negative velocities), increasing slightly with aspect angle.     

Coulomb constitutive laws for friction: Contrasts in frictional behavior for distributed and localized shear

We describe slip-rate dependent friction laws based on the Coulomb failure criteria. Frictional rate dependence is attributed to a rate dependence of cohesionc and friction angle . We show that differences in the stress states developed during sliding result in different Coulomb friction laws for distributed shear within a thick gouge layer versus localized shear within a narrow shear band or between bare rock surfaces. For shear within gouge, shear strength is given by =c cos + _n sin, whereas for shear between bare rock surfaces the shear strength is =c cos + _n tan, where and _n are shear and normal stress, respectively. In the context of rate-dependent Coulomb friction laws, these differences mean that for a given material and rate dependence of the Coulomb parameters, pervasive shear may exhibit velocity strengthening frictional behavior while localized shear exhibits velocity weakening behavior. We derive from experimental data the slip-rate dependence and evolution ofc and for distributed and localized shear. The data show a positive rate dependence for distributed shear and a negative rate dependence for localized shear, indicating that the rate dependence ofc and are not the same for distributed and localized shear, even after accounting for differences in stress state. Our analysis is consistent with the well-known association of instability with shear localization in simulated fault gouge and the observation that bare rock surfaces exhibit predominantly velocity weakening frictional behavior whereas simulated fault gouge exhibits velocity strengthening followed by a transition to velocity weakening with increasing displacement. Natural faults also exhibit displacement dependent frictional behavior and thus the results may prove useful in understanding the seismic evolution of faulting.     

横向各向同性地层井孔伪瑞利波、弯曲波、螺旋波的低频极限速度

在多极源声测井中, 低频弯曲波或螺旋波被广泛应用于测量地层的横波速度. 前人的研究已证明在各向同性地层中井孔伪瑞利波、弯曲波及螺旋波的低频极限速度都等于地层横波速度. 大量的数值计算结果似乎表明此结论在横向各向同性（TI）地层情况下也能成立, 但缺乏理论证明. 本文在井孔平行于TI弹性地层对称轴的模型下, 考察了井内声源激发的波在流-固边界上的反射和透射情况, 阐述了非泄漏模式导波产生的必要条件并讨论了其速度上限值. 我们发现在各向异性参数满足一定条件的TI地层中,导波速度的低频极限值小于沿井孔方向上的横波速度. 通过对井孔导波的频散分析以及对时域全波列的数值模拟, 论证了在这类地层中进行多极源声测井时,不可能根据弯曲波或螺旋波的到达时间准确获取地层的横波速度值.     

A note on the general concept of wave breaking for Rossby and gravity waves

A recently proposed general definition of wave breaking is further discussed, in order to deal with some points on which misunderstanding appears to have arisen. As with surface and internal gravity waves, the classification of Rossby waves into breaking and not breaking is a generic classification based on dynamical considerations, and not a statement about any unique signature or automatically recognizable shape. Nor is it a statement about passive tracers uncorrelated with potential vorticity on isentropic surfaces. A strong motivation for the definition is that proofs of the nonacceleration theorem of wave, mean-flow interaction theory rely, explicitly or implicitly, on a hypothesis that the waves do not break in the sense envisaged.The general definition refers to the qualitative behaviour of a certain set of material contours, namely those, and only those, which would undulate reversibly, with small slopes, under the influence of the waves' restoring mechanism, in those circumstances for which linearized, nondissipative wave theory is a self-consistent approximation to nonlinear reality. The waves' restoring mechanism depends upon the basic-state vertical potential density gradient in the case of gravity waves, and upon the basic-state isentropic gradient of potential vorticity in the case of Rossby waves. In the usual linearized theory of planetary scale Rossby waves on a zonal shear flow, the relevant material contours lie along latitude circles when undisturbed.