Torsional vibrations of elastic foundation on saturated media

A comprehensive analytical solution is developed to examine the torsional vibration of an elastic foundation on a semi-infinite saturated elastic medium for the first time. First, the governing equations of saturated media are solved by use of Hankel transform techniques. Then, based on the assumption that the contact between the foundation and the half-space is perfectly bonded, this dynamic mixed boundary-value problem can lead to dual integral equations, which are further reduced to the standard Fredholm integral equations of the second kind and solved by numerical procedures. Numerical examples are given at the end of the paper. The numerical results indicate that the response of the elastic foundation strongly depends on the material and geometrical properties of both the saturated soil-foundation system and the load acting on the foundation. In most of the cases, the dynamic behavior of an elastic foundation on saturated media significantly differs from that of a rigid plate bearing on the elastic half-space.     

Moment-tensor statistics of the 1997 Long Valley microearthquake swarm

Abstract. A simple, fast, moment-tensor inversion method using bandpass-filtered P-amplitudes was used to study the moment-tensor statistics of Long Valley caldera microearthquakes. The events were recorded in the summer of 1997, during a swarm in the caldera. The swarm was associated with geodetic extension, uplift, and subsequent moderate earthquake activity. The moment tensor solutions for 1,993 events were calculated using the new method. The majority of the resulting focal mechanisms appear to be explained in terms of double couple mechanisms. Since some events did exhibit considerable deviation from double-couples, the moment data were studied for their statistical significance. The moments of the actual data were compared to the moments of synthetic data with varying degrees of random noise in their spectra. The results of this study suggested that unless data from more than 20 stations are used and the earthquake epicenter is located inside or very close to the network area, moment-tensor inversion does not correctly resolve the non-double-couple components of microearthquakes. Analysis of the inversion residuals shows that the average noise in the P-wave spectra was close to 20%. The fluctuations of the volumetric components of the moment-tensor are in good agreement with those of the synthetic pure double-couples with 20% of added noise. Thus the moment-tensor statistics suggests that little if any volume change is required to explain the observed seismic energy release in the swarm. However, the statistics do show that a significant compensated-linear-vector-dipole component maybe present in the bulk of the seismicity. Given the network used in this study, such a component could not be precisely resolved for individual earthquakes. This possibility deserves further investigation because of its bearing on the nature of fluid-fault-earthquake processes in swarms.     

Surface vibration due to a sequence of high speed moving harmonic rectangular loads

The transmission of vibrations over the surface of the ground, due to high-speed moving, vertical harmonic rectangular loads, is investigated theoretically. The problem is three-dimensional and the interior of the ground is modelled as an elastic half-space or a multilayered ground. The transformed solutions are obtained using the Fourier transform on the space variable. A new damping model in the spatial wavenumber domain, presented in Lefeuve-Mesgouez et al. [J. Sound. Vibr. 231 (2000) 1289] is used. Numerical results for the displacements on the surface are presented for loads moving with speeds up to and beyond the Rayleigh wave speed of the half-space.     

Relation of the Wave-Propagation Metric Tensor to the Curvatures of the Slowness and Ray-Velocity Surfaces

The contravariant components of the wave-propagation metric tensor equal half the second-order partial derivatives of the selected eigenvalue of the Christoffel matrix with respect to the slowness-vector components. The relations of the wave-propagation metric tensor to the curvature matrix and Gaussian curvature of the slowness surface and to the curvature matrix and Gaussian curvature of the ray-velocity surface are demonstrated with the help of ray-centred coordinates.     

对波达波夫和Pride震电波方程组的对比分析

用Biot介质参数说明了波达波夫震电波方程组中弹性动力学 参数的含义，解释了第一类和第二类震电效应的意义，在忽略第一类震电效应条件下将该方 程组与Pride方程组进行比较，说明了二者在描述第二类震电效应方面的异同点. 同时指出 ：波达波夫方程组忽略了流体与固体的耦合质量；方程中的黏性耗散项丢掉了一个孔隙度因 子，依据该方程组计算出的弹性波和转换电场的幅度将偏大；边界条件之一存在错误，会影 响对波在界面上的反射透射规律的描述.     

弹性波有限元逆时偏移技术研究

改善弹性波有限元逆时偏移剖面的质量是目前该方法面临的难题，为此，首先在有限元方程中，合理地加入边界力项，并找到准确的成像条件，以及对炮集资料用惠更斯（Huygens）原理消除直达波和面波干扰等措施，提高了复杂含油气结构的偏移剖面质量．本文重点研究单分量资料弹性波偏移的可靠性，利用单分量、抽炮集资料，模拟实际资料处理典型含油气构造，得到了高质量的自激自收和炮集资料的偏移剖面．     

Ambiguous Moment Tensors and Radiation Patterns in Anisotropic Media with Applications to the Modeling of Earthquake Mechanisms in W-Bohemia

Anisotropic material properties are usually neglected during inversions for source parameters of earthquakes. In general anisotropic media, however, moment tensors for pure-shear sources can exhibit significant non-double-couple components. Such effects may be erroneously interpreted as an indication for volumetric changes at the source. Here we investigate effects of anisotropy on seismic moment tensors and radiation patterns for pure-shear and tensile-type sources. Anisotropy can significantly influence the interpretation of the source mechanisms. For example, the orientation of the slip within the fault plane may affect the total seismic moment. Also, moment tensors due to pure-shear and tensile faulting can have similar characteristics depending on the orientation of the elastic tensor. Furthermore, the tensile nature of an earthquake can be obscured by near-source anisotropic properties. As an application, we consider effects of inhomogeneous anisotropic properties on the seismic moment tensor and the radiation patterns of a selected type of micro-earthquakes observed in W-Bohemia. The combined effects of near-source and along-path anisotropy cause characteristic amplitude distortions of the P, S1 and S2 waves. However, the modeling suggests that neither homogeneous nor inhomogeneous anisotropic properties alone can explain the observed large non-double-couple components.The results also indicate that a correct analysis of the source mechanism, in principle, is achievable by application of anisotropic moment tensor inversion.     

Regional moment tensor uncertainty due to mismodeling of the crust

The retrieval of earthquake moment tensor (MT) requires the response of the medium, in which seismic waves travel from the hypocenter to the stations, to be known. In inverting long-period (LP) seismic data (teleseismic and LP regional records), a gross earth model is sufficient; with decreasing periods, a more detailed model is needed. This is the case when waveforms of weak earthquakes at regional distances are to be inverted. Regional moment tensors (RMTs) of mostly Mediterranean earthquakes are determined on a routine basis by the Swiss Seismological Survey (SED) by using averaged models of the earth's crust. By inverting broad-band records of the M_w=4.8 earthquake near Udine, N Italy, on Feb. 14, 2002, we tested the sensitivity of the MT solution with respect to possible errors in the earth model used and in the location of the hypocenter depth. We perturbed the P and S velocities and the thickness in the 1-D earth model in the range from 3% to 30% of the parameter values and constructed estimates of confidence regions of the MT and error bars of the source time function (STF) and scalar moment in three frequency bands. Similarly, these error characteristics were determined assuming a mislocation in the hypocenter depth. We found that, in the band of periods from 25 to 50 s, the mechanism is resolved well (at the confidence level 95% at least) up to an earth model uncertainty of 30%, in the passband 10–25 s up to about 10%, but it is undetermined completely at periods of 5–10 s. An error in hypocenter depth of as much as double the value reported by the location procedure does not destroy the resolution of the mechanism at periods above 10 s. In the RMT catalog of the SED, earthquakes of M_w greater than about 3.5 are processed at periods above 30 s; thus, the solutions for these events are robust with respect to a possible uncertainty in the earth model used. Mechanisms of weaker earthquakes, retrieved from short periods, should be interpreted with caution.     

Determination of the elastic modulus set of foliated rocks from ultrasonic velocity measurements

Ultrasonic measurements of compressional and shear wave velocities under hydrostatic pressure up to 70 MPa were carried out on cylindrical specimens cored across and along the foliation planes. Our measurements revealed that the foliation of the metamorphic rocks induces a clear velocity anisotropy between two orthogonal directions; faster along the foliation plane and slower across the plane in most rock types. All velocity components monotonically increase with the confining pressure, probably due to the closure of microcracks distributed in rock specimens. We determined the complete set of dynamic moduli of foliated metamorphic rocks with two assumptions; transverse isotropy due to the foliation and ellipsoidal seismic energy propagation from a point source. The calculated elastic moduli referring to different directions could be valuable for the design of various engineering structures in planar textured rock mass.     

Reduction of ground vibration by means of barriers or soil improvement along a railway track

Trains running in built-up areas are a source to ground-borne noise. A careful design of the track may be one way of minimizing the vibrations in the surroundings. For example, open or infilled trenches may be constructed along the track, or the soil underneath the track may be improved. In this work, the influence of the track design and properties on the level of ground vibration due to a vehicle moving with subsonic speed is examined. A coupled finite element-boundary element model of the track and subsoil is employed, adopting a formulation in the moving frame of reference following the vehicle. The computations are carried out in the frequency domain for various combinations of the vehicle speed and the excitation frequency. The analyses indicate that open trenches are more efficient than infilled trenches or soil stiffening–even at low frequencies. However, the direction of the load is of paramount importance. For example, the response outside a shallow open trench may change dramatically when horizontal load is applied instead of vertical load.