Attenuation of shear-waves in the lithosphere for frequencies from 0.05 to 25 Hz

Q for shear-waves in the crust and upper mantle was determined as a function of frequency in the range 1–25 Hz, using band-pass filtered records of about 900 earthquakes occurring in the central Japan area with focal depths from 0 to 150 km. The data were supplied from two stations in the Kanto region, operated by the Earthquake Research Institute, University of Tokyo. The method is taken from Aki and Chouet (1975) and Rautian and Khalturin (1978), and is based on elimination of the source effect from observed spectra of shear-waves, by taking the ratio of their amplitudes to those of coda-waves (measured at a fixed lapse time). The effect of radiation patterns is removed by averaging the ratio over many events. The experimental procedure uses basically a single-station method, and its validity was confirmed by the agreement between results obtained from station Tsukuba and those from Dodaira. We found that Q shows a strong dependence on frequency: Q increases with frequency f proportionally to fⁿ, where n was found to be 0.8 in the northeastern part of Kanto (area A), and 0.6 in the rest of the region (areas B + C). Previously, a value for n of 0.5 had been determined for the Garm area in central Asia by Rautian and Khalturin. In general, our results agree with those of Fedotov and Boldyrev (1969), who obtained values of n around 0.6 for the Kuril-Islands, using a single-station method based on assumptions more restrictive than those adopted here. Q values for the lithosphere have been estimated by various workers using surface-waves with periods greater than 15 s. If we combine the results from surface-waves with those obtained from the S- to coda-amplitude ratio, we find that the frequency-dependence of Q^?1 is similar to that obtained from a simple relaxation model, with the peak somewhere around 0.5 Hz.     

Scattering and attenuation of high-frequency body waves (1–25 Hz) in the lithosphere

A strong frequency dependence of apparent Q_β^?1 of shear waves was found for the frequency range from 1 to 25 Hz using band-pass filtered records of about 900 earthquakes occurring in the central Japan area with focal depths from 0 to 150 km. The method used for estimating Q_β is a single-station method based on elimination of the source effect from S waves by the use of coda spectra. The validity of the method is confirmed by agreement between the results obtained independently using data from two stations in the same area.     

Intrinsic noise of seismometers at frequencies from 0.01 to 0.1 Hz

The paper presents a comparative analysis of the intrinsic noises of seismometers operating at Kamchatka seismic stations: CMG-3TB (GURALP), CMG-5TD (GURALP), CMG-6TD (GURALP), GMS-AC-73i HHV (GeoSIG), SM3os (GEOTECH+), S5Sos (KF GS), and SM3kv. It is shown that the dynamic range of the seismometers is narrower at low frequencies in the area of weak signals.     

Rock-mass characterization using intrinsic and scattering attenuation estimates at frequencies from 400 to 1600 Hz

Intrinsic and scatteringS-wave quality factors (Q ) were estimated using the Multiple Lapse Time Window Analysis (MLTWA) for microseismic events (M<–1) with source-sensor distances of 45 to 120 m, associated with an excavation at 630 m depth in Strathcona Mine, Sudbury, Canada. Additional information on the rock mass was provided by underground structural mapping data. IntrinsicQ values, at 800 Hz, were on the order of 140, similar to quality factor values obtained in previous studies using Spectral Decay and Coda-Q methods (120 to 170). The scattering quality factor at this frequency was about 520. An observed frequency dependence of the scattering attenuation suggested that a decrease in the density of scatterers, with scale lengths on the order of 2 m, exists at the site. Characteristic fracture scale lengths were considered to range from 4 to 6 m as identified in the mapping data. These observations were supported by the increase in scattering found for seismic waves with frequencies less than 1000 Hz. By assuming that the identified scatters are characteristic faults, these scatterers can then be considered to increase nonsimilar behavior in source scaling. Overall, our results suggest that MLTWA provides a practical method for remotely characterizing the quality of a rock mass when visual observations are not attainable.     

The scattering of shear-waves in the crust

The two major sources of scattering for shear-waves in the crust, interactions with the topography at the surface and the effective anisotropy of aligned cracks throughout the rockmass, introduce first-order changes to the shear-wave particle-motion. At the surface, shear-waves are scattered by the topography within a wavelength or two of the recording site so that, unless the effective incidence angle is less than the critical angle sin^–1 V _S/V _P, the recorded waveforms may bear little relationship to the waveforms of the incident wave. Within the rockmass, shear-waves are scattered by extensive-dilatancy anisotropy (EDA), the distribution of stress-aligned fluid-filled cracks, microcracks, and preferentially oriented pore-space pervading most rocks in the crust. Analysis of this shear-wave splitting yields new information about the internal structure of thein situ rockmass which is not otherwise available.     

A Summary of Attenuation Measurements from Borehole Recordings of Earthquakes: The 10 Hz Transition Problem

—Earthquake seismograms recorded by instruments in deep boreholes have low levels of background noise and wide signal bandwidth. They have been used to extend our knowledge of crustal attenuation both in the near-surface and at seismogenic depths. Site effects are of major importance to seismic hazard estimation, and the comparison of surface, shallow and deep recordings allows direct determination of the attenuation in the near-surface. All studies to date have found that Q is very low in the near-surface (～ 10 in the upper 100 m), and increases rapidly with depth. Unlike site amplification, attenuation at shallow depths exhibits little dependence on rock-type. These observations are consistent with the opening of fractures under decreasing lithostatic pressure being the principal cause of the severe near-surface attenuation. Seismograms recorded in deep boreholes are relatively unaffected by near-surface effects, and thus can be used to measure crustal attenuation to higher frequencies (≥ 100 Hz) than surface recordings. Studies using both direct and coda waves recorded at over 2 km depth find Q to be high (～ 1000) at seismogenic depths in California, increasing only weakly with frequency between 10 and 100 Hz. Intrinsic attenuation appears to be the dominant mechanism. These observations contrast with those of the rapidly increasing Q with frequency determined from surface studies in the frequency range 1 to 10 Hz. Further work is necessary to constrain the factors responsible for this apparent change in the frequency dependence of Q, but it is clearly unwise to extrapolate Q estimates made below about 10 Hz to higher frequencies.     

Shear-wave splitting in the crust: Regional compressive stress from polarizations of fast shear-waves

When propagating through anisotropic rocks in the crust, shear-waves split into faster and slower components with almost orthogonal polarizations. For nearly vertical propagation the polarization of fast shearwave (PFS) is parallel to both the strike of the cracks and the direction of maximum horizontal stress, therefore it is possible to use PFS to study stress in the crust. This study discusses several examples in which PFS is applied to deduce the compressive stress in North China, Longmenshan fault zone of east edge of Tibetan plateau and Yunnan zone of southeast edge of Tibetan plateau, also discusses temporal variations of PFS orientations of 1999 Xiuyan earthquake sequences of northeastern China. The results are consistent to those of other independent traditional stress measurements. There is a bridge between crustal PFS and the crustal principal compressive stress although there are many unclear disturbance sources. This study suggests the PFS results could be used to deduce regional and in situ principal compressive stress in the crust only if there are enough seismic stations and enough data. At least, PFS is a useful choice in the zone where there are a large number of dense seismic stations.     

Approximate solutions for the formation of the lithosphere

The lithosphere is interpreted as a thermal boundary layer. Approximate solutions of the boundary layer cooling problem are developed which include mantle radioactivity, partial melt in the asthenosphere, a temperature gradient in the asthenosphere, and a non-zero lithospheric thickness at the ridge crests. The cooling history of oceanic lithosphere is found to be remarkably insensitive to assumptions about the amount of radioactivity in the upper mantle and the extent of melting in the asthenosphere. Determinations of the thickness of oceanic lithosphere and the depths of oceans as a function of age are in excellent agreement with boundary layer predictions which include a heat flux from the asthenosphere. However, the determinations do not resolve how much of the total asthenospheric heat flux might be caused by a temperature gradient in the asthenosphere. Simple thermal arguments indicate that the initial lithospheric thickness, L₀, at ridge crests should depend on the local half-spreading rate, V, as L₀ = 3 km/V(cm/year).     

An improved method of evaluating liquefaction potential with the velocity of shear-waves

According to the results of cyclic triaxial tests, a linear correlation is presented between liquefaction resistance and elastic shear modulus, which shows the relation of G _max (kPa) with (σ_d/2)^1/2(kPa)^1/2. When applied to soils from different sites, the correlation can be normalized in reference to its minimum void ratio (e _min). Accordingly, an improved method is established to evaluate the liquefaction potential with shear-wave velocity. The critical shear-wave velocity of liquefaction is in linear relation with 1/4 power of depth and the maximum acceleration during earthquakes, which can be used to explain the phenomenon that the possibility of liquefaction decreases with the increment of the depth. Compared with previous methods this method turns out simple and effective, which is also verified by the results of cyclic triaxial tests. Foundation item: State Natural Science Foundation (59678020) and Natural Science Foundation of Zhejiang Province (RC9609).     

Stress in the lithosphere: Inferences from steady state flow of rocks

Mechanical data and flow processes from steady state deformation experiments may be used to infer the state of stress in the lithosphere and asthenosphere. Extrapolations of flow equations to a representative geologic strain rate of 10^–14/sec. for halite, marble, quartzite, dolomite, dunite and enstatolite are now warranted because the steady state flow processes in the experiments are identical to those in rocks and because the geotherms are reasonably well established. More direct estimates are obtained from free dislocation densities, subgrain sizes and recrystallized grain sizes all of which are functions only of stress. Using the last of these techniques, we have estimated stress profiles as a function of depth from xenoliths in basalts and kimberlites, whose depths of equilibration were determined by pyroxene techniques, from four different areas of subcontinental and suboceanic upper mantle. The results are similar and indicate stress differences of about 200 to 300 bars at 40 to 50 km, decaying to a few tens of bars at depths betow 100 km. These stresses are reasonable and are in accord with extrapolations of the mechanical data provided that allowance is made for a general increase in strain rate and decrease in viscosity with depth.     

Stresses and displacements in the lithosphere due to terrain topography

Summary The complete two-dimensional theory of stresses and displacements in the loaded elastic floating lithosphere is presented. Analytical expressions are derived describing these quantittes as functions of the physical and geometrical parameters of the model. It is shown that horizontal stresses _xx may considerably exceed the surface load and that values of _xx200 MPa can be generated under certain conditions. Numerical calculations are carried out for geophysically acceptable input parameters.

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Regional fabric of the deep lithosphere in central Europe from seismic anisotropy

Summary The large scale anisotropic structures with plunging symmetry axes in the subcrustal lithosphere of central Europe were derived from independent observations of teleseismic P-residual spheres and polarizations of the split SKS waves. The dipping structures are interpreted as remnants of palaeo-subduction systems which retain olivine orientations from ancient oceanic lithosphere. Values of k_P and k_S estimated from observed teleseismic P and SKS data are within the range of anisotropies found for the upper mantle rocks. The Variscides of central Europe may thus be characterized by two palaeo-subduction systems, with symmetry axes divergent relative to the suture between the Moldanubicum and Saxothuringicum.     

Seismic anisotropy of the crust in Yunnan, China： Polarizations of fast shear-waves

Introduction Anisotropy of the crust is a common phenomenon(Crampin,1984).Shear-wave splitting can be used to study the earthquake anisotropic characteristic in crust,to analyze crustal stress field condition,and to describe the static and the dynamic state of the related anisotropic parameters(GAO et al,1999).Shear-wave splitting is quite sensitive to anisotropy.The domestic scholars applied shear-wave splitting to studying the crustal anisotropy(YAO et al,1992;GAO and FENG,1990).The st…     

State of stress in the lithosphere: Inferences from the flow laws of olivine

The experimental flow data for rocks and minerals are reviewed and found to fit a law of the form $$\dot \varepsilon = A'\left[ {sinh (\alpha \sigma )} \right]^n \exp \left[ {{{ - (E * + PV * )} \mathord{\left/ {\vphantom {{ - (E * + PV * )} {RT}}} \right. \kern-\nulldelimiterspace} {RT}}} \right]$$ where \(\dot \varepsilon \) This law reduces to the familiar power-law stress dependency at low stress and to an exponential stress dependency at high stress. Using the material flow law parameters for olivine, stress profiles with depth and strain rate are computed for a representative range of temperature distributions in the lithosphere. The results show that the upper 15 to 25 km of the oceanic lithosphere must behave elastically or fail by fracture and that the remainder deforms by exponential law flow at intermediate depths and by power-law flow in the rest. A model computation of the gravitational sliding of a lithospheric plate using olivine rheology exhibits a very sharp decoupling zone which is a consequence of the combined effects of increasing stress and temperature on the flow law, which is a very sensitive function of both.     

The fate of eclogites in the lithosphere

<正>1. Eclogites and the concept of viscous drainage Eclogites are a distinctive rock type, mainly composed of garnet and omphacite and formed through ultra-high-pressure metamorphism, wherein oceanic or continental crustal rocks undergo burial processes such as subduction and collision, experiencing pressures exceeding 1–1.5 GPa.     

Inhomogeneous structure of the Voronezh shield lithosphere from explosion seismology data

This paper presents the results of a seismological investigation of the Voronezh shield. The use of industrial quarry blasts, as the most economic seismic energy source, and telemetric arrays of the Taiga type for deep seismic sounding observations has enabled the Geophysical Research Group of the Voronezh State University to obtain complete and valid information concerning the deep structure of the shield.Seismic records of refracted and reflected P and S phases from the intracrustal and subcrustal discontinuities allow the determination of independent and compatible velocity models V_P(Z) and V_S(Z).Analysis of the travel-time and amplitude curves derived from the deep seismic sounding data reveals a complex and inhomogeneous structure of the Voronezh shield lithosphere. The major discontinuities are found in the middle part of the consolidated crust. Several rather thick layers can be resolved, which are separated by first-order seismic boundaries.In the consolidated crust beneath the southeastern part of the shield at depths from 6–7 to 11–13 km, a low-velocity layer is clearly established from the compressional wave data. Within the low-velocity channel, V_P appears to decrease by 5–6%. The low-velocity channel in the uppermost consolidated crust is assumed to be due to metamorphogeneous granitization. This is revealed by the Precambrian basement structure.Poisson's ratio calculated from the compatible velocity models V_P(Z) and V_S(Z) shows a systematic increase down to the crustal basement and becomes discontinuous only in the low-velocity channel. At the top of the mantle, Poisson's ratio decreases on all the deep seismic sounding profiles. The systematic variation of Poisson's ratio is related to changes in the composition and mineralogy of the Voronezh shield lithosphere.     

Application of the Lorenz equations for studying thermal convection in the lithosphere

Stationary solutions including wave solutions with constant amplitudes are found for nonlinear equations of thermal convection in a layer with nonlinear rheology. The solution is based on the Fourier expansion of unknown velocities and temperatures with only the first and first two terms retained in the velocity and temperature series, respectively. This method, which can be regarded as the Lorenz method, yields the Lorenz equations that fairly well describe the thermal convection in a layer with Newtonian rheology if the Rayleigh number is not very large. The obtained generalization of the Lorenz equations to the case of an integral (having a memory) nonlinear rheology implies that only the first term is retained in the Fourier series for the stress components, i.e., the nonlinear rheological equation is harmonically linearized. However, in the Fourier series of temperature, it is essential to keep the second term: this term, which is independent of the horizontal coordinate, models the thermal boundary layer that characterizes the developed convection. We constructed the bifurcation curves that describe the stationary convection in the nonlinear integral medium simulating the rheology of the mantle, and analyzed the stability of stationary convective flows. The Lorenz method is applied to study small-scale thermal convection in the lithosphere of the Earth.     

The global stress field in the lithosphere obtained from the satellite gravitational harmonics

In this paper, the lithosphere is considered to be a homogeneous elastic spherical shell for the sake of simplicity and the stress equations for the base of the lithosphere are taken as boundary conditions. Then the stress equations are obtained for use in the computation of the stress field in the lithosphere with the satellite gravitational harmonic coefficients. The 5 × 5° global stress field in the lithosphere is computed from harmonics of 2–30°. The directions of principal stresses of this stress field agree favourably with the directions of principal stresses indicated by mid-plate earthquake mechanisms, in situ stress measurements and sensitive geological features. This result indicates that the drag forces exerted on the base of the lithosphere, due to gravitational mantle convection, may be among the driving forces of plate motion and a major source for the stress field in the lithosphere.     

The fractal nature of the inhomogeneities in the lithosphere evidenced from seismic wave scattering

In this paper we show evidences of the fractal nature of the 3-D inhomogeneities in the lithosphere from the study of seismic wave scattering and discuss the relation between the fractal dimension of the 3-D inhomogeneities and that of the fault surfaces. Two methods are introduced to measure the inhomogeneity spectrum of a random medium: 1. the coda excitation spectrum method, and 2. the method of measuring the frequency dependence of scattering attenuation. The fractal dimension can be obtained from the inhomogeneity spectrum of the medium. The coda excitation method is applied to the Hindu-Kush data. Based on the observed coda excitation spectra (for frequencies 1–25 Hz) and the past observations on the frequency dependence of scattering attenuation, we infer that the lithospheric inhomogeneities are multiple scaled and can be modeled as a bandlimited fractal random medium (BLFRM) with an outer scale of about 1 km. The fractal dimension of the 3-D inhomogeneities isD ₃=31/2–32/3, which corresponds to a scaling exponent (Hurst number)H=1/2–1/3. The corresponding 1-D inhomogeneity spectra obey the power law with a powerp=2H+1=2–5/3. The intersection between the earth surface and the isostrength surface of the 3-D inhomogeneities will have fractal dimensionD ₁=1.5–1.67. If we consider the earthquake fault surface as developed from the isosurface of the 3-D inhomogeneities and smoothed by the rupture dynamics, the fractal dimension of the fault trace on the surface must be smaller thanD ₁, in agreement with recent measurements of fractal dimension along the San Andreas fault.     

Normal state of stress in the lithosphere

Summary It is argued that normally the stresses in the lithosphere are hydrostatic or pseudohydrostatic. Several mechanisms are discussed that account for this feature, the more important one being plastic deformation leading to a situation in which the crustal material can be considered as pre-stressed inthe horizontal plane. The proposed stress distribution has consequences for crustal model studies, especially when ductile flow is involved.