Scattering of plane P waves by a semi-cylindrical hill: analytical solution

An analytical solution for scattering of plane P waves by a semi-cylindrical hill was derived by using the wave function expansion method, and convergence of the solution and accuracy of truncation were verified. The effect of incident frequency and incident angle on the surface motion of the hill was discussed, and it was shown that a hill greatly amplifies incident plane P waves, and maximum horizontal displacement amplitudes appear mostly at the inclined incidence of waves, which are located at the half-space; and maximum vertical displacement amplitudes emerge mostly at the vertical incidence of waves, which are situated at the hill.

Diffraction of plane P waves around an alluvial valley in poroelastic half-space

Diffraction of plane P waves around an alluvial valley of arbitrary shape in poroelastic half-space is investigated by using an indirect boundary integral equation method. Based on the Green＇s fimctions of line source in poroelastic half-space, the scattered waves are constructed using the fictitious wave sources close to the interface of the valley and the density of ficti- tious wave sources are determined by boundary conditions. The precision of the method is verified by the satisfaction extent of boundary conditions, and the comparison between the degenerated solutions and available results in single-phase case. Finally, the nature of diffraction of plane P waves around an alluvial valley in poroelastic half-space is investigated in detail through nu- merical examples.

3-D Scattering of Obliquely Incident Plane P Waves by Alluvial Valley Embedded in Layered Half-Space

The indirect boundary element method(IBEM) was established to solve the problem of 3-D seismic responses of 2-D topographies,by calculating the free-field responses with the direct-stiffness method and simulating the scattering wave fields with the dynamic Green's functions of moving distributed loads.The proposed method yields accurate results,because the 3-D dynamic stiffness matrixes used are exact and the fictitious moving distributed loads can be acted directly on the interface between the alluvial valley and the layered half-space without singularity.The comparison with the published methods verifies the validity of the proposed method.And the numerical analyses are performed to give some beneficial conclusions.The study shows that 3-D scattering by an alluvial valley is essentially different from the 2-D case,and that the presence of soil layer affects not only the amplitude value of surface displacements but also the distribution of surface displacements.

Diffraction of plane P waves by a canyon of arbitrary shape in poroelastic half-space (Ⅰ): Formulation

This paper presents an indirect boundary integration equation method for diffraction of plane P waves by a two-dimensional canyon of arbitrary shape in poroelastic half-space. The Green＇s functions of compressional and shear wave sources in poroelastic half-space are derived based on Biot＇s theory. The scattered waves are constructed using the fictitious wave sources close to the boundary of the canyon, and magnitude of the fictitious wave sources are determined by the boundary conditions. The precision of the method is verified by the satisfaction extent of boundary conditions, the comparison between the degenerated solutions of single-phased half-space and the well-known solutions, and the numerical stability of the method.

Diffraction of plane P waves by a canyon of arbitrary shape in poroelastic half-space (Ⅱ): Numerical results and discussion

This paper investigates in detail the nature of diffraction of plane P waves around a canyon in poroelastic half-space, and studies the effects of incident frequency, drainage condition, porosity, etc, on the diffraction of waves. It is shown that the surface displacement amplitudes of the drained case are close to those of the undrained case, however, the surface displacement amplitudes of the dry case are very different from those of the saturated （either drained or undrained） cases. There are large phase shift between the dry case and the saturated cases, as well as slightly longer resultant wavelengths for the undrained case than those for the drained case and longer resultant wavelengths for the drained case than those for the dry case. For small porosity the surface displacement amplitudes for the saturated cases are almost identical to those for the dry case; while for large porosity, the effect of drainage condition becomes significant, and the surface displacement amplitudes for the undrained case are larger than those for the drained case. As the incident frequency increases, the effect of porosity becomes significant, and more significant for the undrained case than that for the drained case. As the porosity increases, the pore pressures increase significantly but their oscillations become smoother. As the incident frequency increases, the pore pressures become more complicated.

A series solution for surface motion amplification due to underground group cavities:Incident P waves

A series solution for surface motion amplification due to underground group cavities for incident plane P waves is derived by Fourier-Bessel series expansion method. It is shown that underground group cavities significantly am-plify the surface ground motion nearby. It is suggested that the effect of subways on ground motion should be con-sidered when the subways are planned and designed.

Scattering of plane P waves by canyons containing multiple circular-arc-shaped layers

By expressing the wave functions in the form of Fourier-Bessel series, the analytical solution for the two-dimension scattering problem of plane P waves by the cylindrical canyon topography that contains arbitrary number of circular-arc-shaped layers is presented firstly. And then, the convergence of the proposed series solution with the truncation number of terms is discussed, which demonstrates that the analytical solution can converge even for very high frequencies of the incident P wave. Finally, using this solution, the influences that are imposed on the stationary ground motion by the number and the sequence of alluvial layers, as well as the stiffness of soft interlayer contained in the canyon, are studied,

Variation of Q value before and after the 1999 Xiuyan, Liaoning Province, M=5.4 earthquake on the basis of analysis on attenuation dispersion of P waves

A method for determining medium quality factor is developed on the basis of analyzing the attenuation dispersion of the arrived first period P wave. In order to enhance signal to noise ratio, improve the resolution in measurement and reduce systematic error we applied the data resampling technique. The group velocity delay of P wave was derived by using an improved multi-filtering method. Based on a linear viscoelastic relaxation model we deduced the medium quality factor Qm, and associated error with 95% confidence level. Applying the method to the seismic record of the Xiuyan M=5.4 earthquake sequences we obtained the following result: 1 High Qm started to appear from Nov. 9, 1999. The events giving the deduced high Qm value clustered in a region with their epicenter dis- tances being between 32 and 46 km to the Yingkou station. This Qm versus distance observation obviously deviates from the normal trend of Qm linearly increasing with distance. 2 The average Qm before the 29 Dec. 1999 M=5.4 earthquake is 460, while the average Qm between the M=5.4 event and the 12 Jan. 2000 M=5.1 earthquake is 391, and the average Qm after the M=5.1 event is 204.

Scattering of Plane P Waves by Circular-arc Canyon Topography:High-frequency Solution

Through the Fourier-Bessel series expansion of wave functions,the analytical solution to the two-dimensional scattering problem of incidental plane P waves by circular-arc canyon topography with different depth-to-width ratio is deduced.Unlike other existing analytical solutions,in order to ensure that the analytical solution is valid for higher frequency incident waves,the asymptotic properties of cylindrical functions are in this paper introduced to directly determine the unknown coefficients of scattering waves,avoiding the solution of linear equation systems and corresponding numerical issues,which in turn expand the frequency band in which the analytical solution is valid.Comparison with other existing analytical solutions demonstrates that the proposed analytical solution is correct.Furthermore,the scattering effects of a circular-arc canyon on the incident plane P wave are analyzed in a comparatively broad frequency band.

Closed-form solution for dynamic responses of shaft-tunnel junction under uniform P waves

This paper discusses the special situation when a shaft-tunnel junction is subject to vertically propagating P waves.For a complicated system like the shaft-tunnel junction,it is necessary to investigate the most basic cases firstly,and the responses induced by uniform P waves are one of them.To this end,a closed-form solution is derived from the classical differential equation describing the forced vibration of a single degree-of-freedom system.The key issue is the characterization of the coupled dynamic interactions among the shaft,the tunnel,and the ground.The paradigm regards the three of them as a massive rigid body,a continuous Euler-Bernoulli beam,and a set of supporting elements,respectively.The final solution is to calculate the displacements of the shaft and the tunnel in the form of two compact equations,and the internal forces of the tunnel are therefore easily obtainable.By means of a finite element simulation,the validity as well as the accuracy of the closed-form solution is verified.The solution provides an explicit comprehension of the coupled dynamic interactions and thus enhances the understanding of the dynamic mechanics of the shaft-tunnel junction.

Effect of seawater on incident plane P and SV waves at ocean bottom and engineering characteristics of offshore ground motion records off the coast of southern California, USA

The effect of seawater on vertical ground motions is studied via a theoretical method and then actual offshore ground motion records are analyzed using a statistical method. A theoretical analysis of the effect of seawater on incident plane P and SV waves at ocean bottom indicate that on one hand, the affected frequency range of vertical ground motions is prominent due to P wave resonance in the water layer if the impedance ratio between the seawater and the underlying medium is large, but it is greatly suppressed if the impedance ratio is small; on the other hand, for the ocean bottom interface model selected herein, vertical ground motions consisting of mostly P waves are more easily affected by seawater than those dominated by SV waves. The statistical analysis of engineering parameters of offshore ground motion records indicate that:(1) Under the infl uence of softer surface soil at the seafl oor, both horizontal and vertical spectral accelerations of offshore motions are exaggerated at long period components, which leads to the peak spectral values moving to a longer period.(2) The spectral ratios(V/H) of offshore ground motions are much smaller than onshore ground motions near the P wave resonant frequencies in the water layer; and as the period becomes larger, the effect of seawater becomes smaller, which leads to a similar V/H at intermediate periods(near 2 s). These results are consistent with the conclusions of Boore and Smith(1999), but the V/H of offshore motion may be smaller than the onshore ground motions at longer periods(more than 5 s).

Nonlinear Seismic Response of Rock Tunnels Crossing Inactive Fault under Obliquely Incident Seismic P Waves

The failure mechanism of tunnels crossing faults is a critical issue for tunnels located in seismically active regions. This study aims to investigate the nonlinear response of rock tunnels crossing inactive faults under obliquely incident seismic P waves. Based on the equivalent nodal force method together with the viscous-spring boundary, an incident method for the site, which contains fault and is subjected to obliquely incident seismic P waves, is developed first. Then, based on the proposed incident method, the nonlinear response and the failure process of the tunnel crossing inactive fault are numerically studied. The numerical results show that the failure mechanism of the tunnel crossing inactive fault can be attributed to the combined action of the seismic waves and its associated fault slippage. Finally, parameter studies are conducted to investigate the effects of the wave impedance ratio of the fault to the surrounding rock and the incident angle of P waves. By the parameter analysis, it can be concluded that:(1) with decreasing the wave impedance ratio of the fault to the surrounding rock, the seismic response of the tunnel increases significantly;(2) the seismic response of the tunnel increases first and then decreases with the increasing of the incident angle of P waves. This study offers the insight for further research on the seismic stability of tunnels crossing inactive faults.

Seismic stability of jointed rock slopes under obliquely incident earthquake waves

Seismic stability of slopes has been traditionally analyzed with vertically propagated earthquake waves.However,for rock slopes,the earthquake waves might approach the outcrop still with a evidently oblique direction.To investigate the impact of obliquely incident earthquake excitations,the input method for SV and P waves with arbitrary incident angles is conducted,respectively,by adopting the equivalent nodal force method together with a viscous-spring boundary.Then,the input method is introduced within the framework of ABAQUS software and verified by a numerical example.Both SV and P waves input are considered herein for a 2 D jointed rock slope.For the jointed rock mass,the jointed material model in ABAQUS software is employed to simulate its behavior as a continuum.Results of the study show that the earthquake incident angles have significance on the seismic stability of jointed rock slopes.The larger the incident angle,the greater the risk of slope instability.Furthermore,the stability of the jointed rock slopes also is affected by wave types of earthquakes heavily.P waves induce weaker responses and SV waves are shown to be more critical.

Frequency-dependent attenuation of P and S waves in Yunnan region

We analyzed digital seismogram data of 5668 earthquakes that occurred in Yunnan region between July of 1999 and December of 2003. Among the 22 seismic stations, six ones, namely Baoshan, Yongsheng, Lijiang, Heqing, Yimen, and Luquan, were selected and their attenuations of P and S waves were measured by using the extended coda-normalization method. The six stations were classified into three regions according to their location, that is, Baoshan area, Yongsheng-Lijiang-Heqing (YLH) area and Luquan-Yimen (LY) area. The values of QS-1 and QP-1 are expressed as QS-1=0.00867 f-0.86, QP-1=0.01155 f-0.93, QS-1=0.01824 f-0.92, QP-1=0.02288 f-0.92, and QS-1=0.01647 f-0.91, QP-1=0.02826 f-0.97 in Baoshan, YLH, LY areas respectively. The attenuation of YLH, LY are closer to each other, however, Baoshan area is apparently lower. Comparing attenuation in the three areas with other areas of the world using the same method, it is suggested that the attenuations of P and S waves in YLH and LY areas are close to Kanto of Japan, but much higher than southeast of South Korea. The QS-1 and QP-1 in Baoshan area are slightly higher than southeastern South Korea. Furthermore, the results indicate that our QS-1 in Yunnan area is close to others by analyzing the coda attenuation.

Reduction of peak ground velocity by nonlinear soil response–Ⅱ:excitation by a P-wave pulse

We study the reduction of peak velocity on the ground surface of a soil valley caused by loss of wave energy by large nonlinear strains and strain localization inside the valley,for excitation by a half-sine P-wave pulse.This study is a follow up to our previous study of out of plane response for excitation by an SH-pulse.In this paper,we consider the in-plane response,and assume that the soil material does not support tension,but the normal stress at a point in the soil can be compression(negative)or zero.A point in the soil with zero stress behaves as a stress-free point,it does not transmit normal stress and appears as a crack point.Because of this,along with the nonlinear response associated with compression and shear,the in-plane response in this study is more complex than that of the out-of-plane SH response.We study the interplay of two opposing effects:(i)jump in impedance from a higher value(half-space)to a lower value(valley),which amplifies the linear motions at the free surface of the valley,and(ii)the occurrence of nonlinear zones in the valley,which reduce the motion at the valley surface.

P波时限、P波离散度对特发性心房颤动的预测价值初探(英文)

Objective:To assess the sensitivity and the specifity of predicting idiopathic AF with P wave duration and P wave dispersion. Methods:The maximum P wave duration and P wave dispersion in 36 patients with idiopathic AF were measured and compared with those of sex - and age - matched healthy subjects. Results:The maximum P wave duration and P wave dispersion were higher in patients with idiopathic Af than in control group. The maximum P wave duration ＞ 110ms or P wave dispersion ＞40ms was used to differentiate patients from healthy subjects, the sensitivity and the specifity value were 88% vs 82% and 75 % vs 86%, respectively. When the above two parameters were integrated, the sensitivity was 76 %, the specifity 88 %. Conclusion: The maximum P.wave duration and P wave dispersion are simple and practical ECG indexes for idiopathic AF patients.

Fracture detection by using full azimuth P wave attributes

A type of specific fractured hydrocarbon reservoir, a shale fractured reservoir, exists in the Shengli oilfield. Due to very small porosity of this type, low sensitivity to the variation of petrochemical property parameters, and strong anisotropy, it is very difficult to explore for them. So far, there is no set of mature methods for recognition of direction, distribution, and density of the fractures by an integrated analysis of geologic, geophysical, well log, drilling data, and etc. This paper presents a new method for acoustic impedance variation with azimuth （IPVA）, based on existing fracture detection methods. Seismic acquisition, processing, and recognition techniques were developed for detecting directional vertical fractures using multi-azimuth P wave data in combination with the seismic and geological features of shale fractures in the Luojia area. The IPVA research is carried out for recognizing the distribution, strike, and density of fractures based on the study of velocity variation with azimuth （VVA） and amplitude variation with azimuth （AVA） for full azimuth P wave data at different CMP positions. Through practical application in the Luojia area, primary results have been obtained which verifies that the IPVA method provides good potential for quantitative detection of parallel, high angle, shale fractures.

Analytical solutions for dynamic pressures of coupling fluid-solid-porous medium due to P wave incidence

Wave reflection and refraction in layered media is a topic closely related to seismology,acoustics,geophysics and earthquake engineering.Analytical solutions for wave reflection and refraction coefficients in multi-layered media subjected to P wave incidence from the elastic half-space are derived in terms of displacement potentials.The system is composed of ideal fluid,porous medium,and underlying elastic solid.By numerical examples,the effects of porous medium and the incident wave angle on the dynamic pressures of ideal fluid are analyzed.The results show that the existence of the porous medium,especially in the partially saturated case,may significantly affect the dynamic pressures of the overlying fluid.

Crustal structure and accurate hypocenter determination along the Longmenshan fault zone

A P and S wave velocity model is obtained for the crust in the region along the Longmenshan fault zone, Sichuan Province, China, by using data from a refraction profiling survey carried out in this region and those from local earthquakes. 202 local earthquakes along the fault zone are based on this velocity model, location errors being estimated to be about 1.5 km. The present relocations fairly improved the accuracy of hypocenter locations for earthquakes in this area, which is recognized from small scatter of data in the arrival time distance diagram compared with that for the original locations in the Earthquake Catalogue of Sichuan Seismic Network. The obtained hypocenter distribution shows that shallow earthquakes, confined to the upper crust in the depth range from 3 km to 22 km, are actively occurring along the main fault of the Longmenshan fault zone. The velocity model and the location method are presently used quite effective for precisely locating local earthquakes such as those in Sichuan Province. Installation of these with the real time processing system developed by Tohoku University in the Sichuan Telemetered Seismic Network would help to improve the location accuracy of events beneath the network.

Forward Modeling of the Relationship Between Reflection Coefficient and Incident Angle of the P Wave in a Coal Seam

Although the Zoeppritz equation is suitable for a single interface in a thick deposit, it has some limitations for composite reflection waves from both the floor and the roof of coal seams. Based on the ray model, the relationship of the overall reflection coefficient of composite reflection P waves, from coal seam versus incidence angle (AVO), is dis- cussed. The result shows that: 1) the overall reflection coefficient of composite reflection waves from coal seams is a negative value and is determined mainly by the lithology of roof and floor, which is different from the reflection coeffi- cient of a single interface; 2) if the incidence angle ranges from 0° to 6°, the reflection coefficient of composite waves of a coal seam does not change with the incidence angle and 3) if the incidence angle ranges from 6–60° , the reflection coefficient increases monotonically.