Propagation of a P-pulse in a solid sphere

1965 ◽  
Vol 55 (5) ◽  
pp. 821-861
Author(s):  
Z. Alterman ◽  
F. Abramovici
Keyword(s):  
Rayleigh Waves ◽  
Group Velocity Dispersion ◽  
Surface Displacement ◽  
Elastic Solid ◽  
Solid Sphere ◽  
Reflected Waves ◽  
Arrival Times ◽  
Angular Component ◽  
Diffracted Waves ◽  
Deep Focus

abstract An exact solution is obtained for the displacement of the surface of a uniform elastic solid sphere of radius a due to an impulsive compressional pulse from a point-source situated at a distance b from the center. The duration of the source is δa/c where c denotes the shear-wave velocity, and its time-variation is such that the surface-displacement stays finite when the time tends to infinity. The solution is applied to a source at a distance of one-eighth of the radius below the surface, approximating a deep-focus earthquake. Theoretical seismograms, radial and angular component, are given at distances 0 < ϑ < π for a source of duration 0.03a/c. Rayleigh waves are clearly seen at ϑ ≧ 45 °. Groups of reflected waves, especially predominant in the angular component, have the velocity of the lowest Airy phase in the group-velocity dispersion-curves. Diffracted waves, discussed in a previous paper, are found here again and in certain cases have an amplitude seven times larger than the amplitude of the direct pulse and also larger than any of the reflected pulses at the same distance. The transformed phases PSn, P2Sn have in general larger amplitude than the reflected Pn. Arrival times, initial amplitudes, reflection and convergence coefficients of pulses are obtained by steepest descents analysis and compared with the complete results.

scholarly journals Rayleigh-Type Waves in a Rotating Fiber-Reinforced Half Space under the Action of Magnetic Field, Gravity and Surface Stress

2021 ◽  
pp. 1-7
Author(s):  
Narottam Maity ◽  
◽  
S P Barik Barik ◽  
P K Chaudhuri ◽  
◽  
...  
Keyword(s):  
Magnetic Field ◽  
Surface Stress ◽  
Rayleigh Waves ◽  
Elastic Solid ◽  
Frequency Equation ◽  
Complete Agreement ◽  
Fiber Reinforced ◽  
Electrically Conducting ◽  
Stress Rotation ◽  
Wave Velocity Equation

The aim of the present article is to analyze the propagation of Rayleigh waves in a rotating fiber-reinforced electrically conducting elastic solid medium under the influence of surface stress, magnetic field and gravity. The magnetic field is applied in such a direction that the problem can be considered as a two dimensional one. The wave velocity equation for Rayleigh waves has been obtained. In the absence of gravity field, surface stress, rotation and fiberreinforcement, the frequency equation is in complete agreement with the corresponding classical results. The effects on various subjects of interest are discussed and shown graphically. Comparisons are made with the corresponding results in absence of surface stress

Tuning S-Wave Velocity Structure of Deep Sedimentary Layers in the Shimousa Region of the Kanto Basin, Japan, Using Autocorrelation of Strong-Motion Records

2020 ◽  
Vol 110 (6) ◽  
pp. 2882-2891
Author(s):  
Kosuke Chimoto ◽  
Hiroaki Yamanaka
Keyword(s):  
Wave Velocity ◽  
Velocity Structure ◽  
Strong Motion ◽  
S Wave ◽  
Reflected Waves ◽  
Arrival Times ◽  
Strong Motion Records ◽  
Kanto Basin ◽  
Determination Of Parameters

ABSTRACT The autocorrelation of ambient noise is used to capture reflected waves for crustal and sedimentary structures. We applied autocorrelation to strong-motion records to capture the reflected waves from sedimentary layers and used them for tuning the S-wave velocity structure of these layers. Because a sedimentary-layered structure is complicated and generates many reflected waves, it is important to identify the boundary layer from which the waves reflected. We used spectral whitening during autocorrelation analysis to capture the reflected waves from the seismic bedrock with an appropriate smoothing band, which controls the wave arrival from the desired layer boundary. The effect of whitening was confirmed by the undulation frequency observed in the transfer function of the sedimentary layers. After careful determination of parameters for spectral whitening, we applied data processing to the strong-motion records observed at the stations in the Shimousa region of the Kanto Basin, Japan, to estimate the arrival times of the reflected waves. The arrival times of the reflected waves were found to be fast in the northern part of the Shimousa region and slow in the western and southern parts. These arrival times are consistent with those obtained using existing models. Because we observed a slight difference in the arrival times, the autocorrelation function at each station was used for tuning the S-wave velocity structure model of the sedimentary layers using the inversion technique. The tuned models perfectly match the autocorrelation functions in terms of the arrival time of the reflected waves from the seismic bedrock.

scholarly journals Separation of diffracted waves via SVD filter

2020 ◽  
Vol 17 (5) ◽  
pp. 1259-1271
Author(s):  
Hong-Yan Shen ◽  
Qin Li ◽  
Yue-Ying Yan ◽  
Xin-Xin Li ◽  
Jing Zhao
Keyword(s):  
Seismic Waves ◽  
Original Data ◽  
Identification Accuracy ◽  
Reflected Waves ◽  
Wave Separation ◽  
Imaging Results ◽  
Diffracted Waves ◽  
Fast Processing ◽  
The Difference ◽  
Value Decomposition

Abstract Diffracted seismic waves may be used to help identify and track geologically heterogeneous bodies or zones. However, the energy of diffracted waves is weaker than that of reflections. Therefore, the extraction of diffracted waves is the basis for the effective utilization of diffracted waves. Based on the difference in travel times between diffracted and reflected waves, we developed a method for separating the diffracted waves via singular value decomposition filters and presented an effective processing flowchart for diffracted wave separation and imaging. The research results show that the horizontally coherent difference between the reflected and diffracted waves can be further improved using normal move-out (NMO) correction. Then, a band-rank or high-rank approximation is used to suppress the reflected waves with better transverse coherence. Following, separation of reflected and diffracted waves is achieved after the filtered data are transformed into the original data domain by inverse NMO. Synthetic and field examples show that our proposed method has the advantages of fewer constraints, fast processing speed and complete extraction of diffracted waves. And the diffracted wave imaging results can effectively improve the identification accuracy of geological heterogeneous bodies or zones.

scholarly journals Improvement of Accuracy in Damage Localization Using Frequency Slice Wavelet Transform

2012 ◽  
Vol 19 (4) ◽  
pp. 585-596 ◽  
Author(s):  
Xinglong Liu ◽  
Zhongwei Jiang ◽  
Zhonghong Yan
Keyword(s):  
Wavelet Transform ◽  
Damage Identification ◽  
Lamb Waves ◽  
Group Velocity Dispersion ◽  
Propagation Distance ◽  
Primary Objective ◽  
Frequency Resolution ◽  
Damage Localization ◽  
Arrival Times ◽  
Time Frequency

Damage localization is a primary objective of damage identification. This paper presents damage localization in beam structure using impact-induced Lamb wave and Frequency Slice Wavelet Transform (FSWT). FSWT is a new time-frequency analysis method and has the adaptive resolution feature. The time-frequency resolution is a vital factor affecting the accuracy of damage localization. In FSWT there is a unique parameter controlling the time-frequency resolution. To improve the accuracy of damage localization, a generalized criterion is proposed to determine the parameter value for achieving a suitable time-frequency resolution. For damage localization, the group velocity dispersion curve (GVDC) of A0Lamb waves in beam is first accurately estimated using FSWT, and then the arrival times of reflection wave from the crack for some individual frequency components are determined. An average operation on the calculated propagation distance is then performed to further improve the accuracy of damage localization.

scholarly journals Unexpected Shallow Earthquake of August 1st, 2020 in the North of Indramayu, West Java, Indonesia

2021 ◽  
Vol 873 (1) ◽  
pp. 012043
Author(s):  
Jaya Murjaya ◽  
Pepen Supendi ◽  
Dwikorita Karnawati ◽  
Subagyo Pramumijoyo
Keyword(s):  
Seismic Station ◽  
Moment Tensor ◽  
Focal Mechanism Solution ◽  
West Java ◽  
Waveform Data ◽  
Arrival Times ◽  
S Waves ◽  
The North ◽  
Focus Depth ◽  
Deep Focus

Abstract During the last one hundred years, there are no shallow seismicity in the north of Java. This area is dominated by intermediate and deep focus earthquakes due to the subducted Indo-Australian slab. An earthquake with magnitude ML 4.5 struck Indramayu, north of West Java on August 1, 2020. According to the Agency for Meteorology, Climatology, and Geophysics (BMKG), the earthquake was felt III MMI scale in Indramayu and its vicinity. We used waveform data from BMKG seismic station in West Java, then we picked P-and S-waves arrival times from each station and hypocenter location was determined by Geiger method. We have detected Pn before Pg phase on four BMKG seismic stations, indicating a shallow crustal earthquake. Our inversion show that the earthquake occurred in 6.1805° S, 108.2612° E with 5 km focus depth at 16:24:38 GMT+7. Our focal mechanism solution was determined by using moment tensor inversion shows a strike-slip faulting, which corresponds to the active fault in the north of Indramayu.

scholarly journals The axisymmetric Rayleigh waves in a semi-infinite elastic solid

2020 ◽  
Vol 10 (2) ◽  
pp. 120-124
Author(s):  
Ji Wang ◽  
Shaoyun Wang ◽  
Longtao Xie ◽  
Yangyang Zhang ◽  
Lili Yuan ◽  
...  
Keyword(s):  
Rayleigh Waves ◽  
Elastic Solid

Transmission of Rayleigh waves at a corner

1966 ◽  
Vol 56 (2) ◽  
pp. 455-466 ◽  
Author(s):  
A. K. Mal ◽  
L. Knopoff
Keyword(s):  
Integral Equations ◽  
Rayleigh Waves ◽  
Wedge Angle ◽  
Body Waves ◽  
Algebraic Equations ◽  
Reflected Waves ◽  
Transmission And Reflection Coefficients ◽  
Transmitted Waves ◽  
New Feature ◽  
Transmission And Reflection

abstract Using a Green's function method of approximation, transmission and reflection coefficients are computed for the problem of Rayleigh waves normally incident upon the corner of a homogeneous elastic wedge formed by two stress-free planes. The Rayleigh waves are incident from infinity and travel along one surface of the wedge. The transmitted waves on the second surface and the reflected waves on the first surface are calculated by the application of Huygens' principle. A pair of coupled integral equations for the displacements are obtained by means of a representation theorem. Neglecting the diffracted body waves near the corner, the coupled integral equations are reduced to a pair of algebraic equations. A new feature of the calculation involves consideration of diffracted surface waves travelling toward the vertex. Numberical values of the phase shifts and attenuation factors in the transmitted and reflected waves are computed as functions of the wedge angle. Comparison with experimental results show considerably better agreement than has been obtained previously.

Pre-stack diffraction separation by parameterizing the reflection local slope

Geophysics ◽  
2021 ◽  
pp. 1-49
Author(s):  
Chuangjian Li ◽  
Suping Peng ◽  
Xiaoqin Cui ◽  
Qiannan Liu ◽  
Peng Lin
Keyword(s):  
Plane Wave ◽  
Separation Method ◽  
Small Scale ◽  
Reflected Waves ◽  
Local Slope ◽  
Illumination Direction ◽  
Novel Approach ◽  
Diffracted Waves ◽  
Slope Estimation ◽  
Ray Parameter

Diffracted waves provide the opportunity to detect small-scale subsurface structures because they give wide illumination direction of geological discontinuities such as faults, pinch-outs, and collapsed columns. However, separating diffracted waves is challenging because diffracted waves have greater geometrical amplitude losses and are generally weaker than reflections. To retain more diffracted waves, a pre-stack diffraction separation method is proposed based on the local slope pattern and plane-wave destruction method. Generally, it is difficult to distinguish between the hyperbolic reflections and hyperbolic diffractions using the data-driven local slope estimation in the shot domain. Therefore, we transfer the slope estimation in the shot domain to the velocity analysis in the common midpoint domain and the ray parameter calculation in the stack domain. The connection between the local slope and the normal move-out velocity and the surface-ray parameter is known, which provides a novel approach for estimating the local slope of the hyperbolic reflected waves in the shot domain. The estimated slope can provide an exact slope-based operator for the plane-wave destruction (PWD) method, thus allowing the PWD to separate diffracted waves from reflected waves in the shot domain. Synthetic and field data tests demonstrate the feasibility and effectiveness of the proposed pre-stack diffraction separation method.

Real-Time Tsunami Prediction System Based on Seafloor Observatory Data Applied to the Inland Sea, Japan

2018 ◽  
Vol 52 (3) ◽  
pp. 120-127 ◽  
Author(s):  
Narumi Takahashi ◽  
Kentaro Imai ◽  
Kentaro Sueki ◽  
Ryoko Obayashi ◽  
Masanobu Ishibashi ◽  
...  
Keyword(s):  
Real Time ◽  
Local Governments ◽  
Nankai Trough ◽  
Plate Boundary ◽  
Maximum Height ◽  
Prediction System ◽  
Worst Case ◽  
Reflected Waves ◽  
Arrival Times ◽  
Tsunami Waveforms

AbstractThe damage and loss of life caused by tsunamis can be reduced by timely warnings, which predict the arrival time and maximum height of tsunamis, to support evacuations and other mitigating actions. We have developed a real-time tsunami prediction system based on data from the Dense Oceanfloor Network system for Earthquakes and Tsunamis (DONET) that has been implemented in some local governments along the Pacific coast of Japan. The system generates estimates of tsunami arrival times and the height, inundation areas, and worst case using selected fault rupture models. The main objective of this paper is to show the possibility of applying the above system for a complicated topography area, and we report a successful application of the system in Sakaide, a city on the Shikoku coast of the Inland Sea, using a simulated great plate-boundary earthquake in the Nankai Trough. The simulated tsunami propagates to Sakaide by complicated routes between several islands. According to calculated tsunami waveforms of 1,506 cases, waveforms of tsunamis propagating to the Inland Sea have a relatively uniform frequency, regardless of the magnitude of the causative event, after running through the narrow straits in the Inland Sea. At the same time, waves are amplified as they pass between the islands of Shodoshima and Shikoku by an interaction with reflected waves. These effects are compatible with this prediction system, and we confirmed that our predicted tsunami is consistent with the final result from a model of a magnitude 9 Nankai Trough earthquake.

Rayleigh waves in southern New Guinea

1969 ◽  
Vol 59 (2) ◽  
pp. 945-958 ◽  
Author(s):  
J. A. Brooks
Keyword(s):  
Rayleigh Waves ◽  
Velocity Structure ◽  
Group Velocity Dispersion ◽  
Focal Depth ◽  
New Guinea ◽  
Shear Velocity ◽  
Stationary Wave ◽  
Period Range ◽  
Mode Group ◽  
Path Lengths

abstract A shear velocity structure having features similar to the Gutenberg model for the upper 200 km of the mantle is consistent with features of higher mode Rayleighwave group-velocity dispersion curves in the period range 4 to 30 seconds, for paths across southern New Guinea. Pronounced discontinuities appear to be absent within the crust where shear velocities are expected to gradually increase with depth. Clearly dispersive second mode (M21) Rayleigh waves, well separated in time from the fundamental mode, are shown for path lengths less than 2000 km. Frequencies excited show some dependence on focal depth. Stationary wave groups of period 10-20 seconds, very like the Sa phase, and generated by earthquakes of focal depth between 100 and 160 km coincide with expected normal mode group arrivals.

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