Analysis of seismic wave dynamics by means of integral representations and the method of discontinuities

Geophysics ◽  
2001 ◽  
Vol 66 (2) ◽  
pp. 413-418 ◽  
Author(s):  
Anton A. Duchkov ◽  
Sergey V. Goldin
Keyword(s):  
Seismic Wave ◽  
Seismic Waves ◽  
Seismic Signal ◽  
Integral Representations ◽  
Synthetic Signal ◽  
Point Of Interest ◽  
Series Approximation ◽  
The Time Domain ◽  
Phase Distortions ◽  
Ray Series

We analyze the dynamics (amplitudes and phase distortions) of seismic waves as they propagate along the ray. Our analysis is performed via a ray series approximation in the time domain. That is, we concentrate on characterizing the sharp changes (discontinuities) of the signal that are localized near the wavefront. After convolution of the terms of such a series with a proper temporally short (high‐frequency) wavelet, one obtains a synthetic seismic signal at a given point of interest. We present an outline of the proposed technique that yields integrals describing the wavefield. These integrals are similar to oscillatory integrals in the frequency domain. This description is uniformly valid near caustics, allowing the calculation of higher order terms of the ray series approximation. Practical use of the technique is illustrated by several examples which show two possible uses of the technique: general understanding of what is happening during wave propagation and practical calculations. First, we show how the structure of the ray decomposition changes near the simple caustic, and then we calculate a synthetic signal near the cusp caustic. The advantage of the technique is that the problem of seismic wave calculation is technically reduced to a problem of double integration of a Dirac δ-function; thus, it is computationally effective.

scholarly journals Rapid estimation of tsunami earthquake magnitudes at local distance

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
Akio Katsumata ◽  
Masayuki Tanaka ◽  
Takahito Nishimiya
Keyword(s):  
Magnitude Estimation ◽  
Seismic Wave ◽  
Seismic Waves ◽  
Wave Amplitude ◽  
Amplitude Distribution ◽  
Distribution Method ◽  
Finite Fault ◽  
Tsunami Earthquakes ◽  
Tsunami Earthquake ◽  
The Moment

AbstractA tsunami earthquake is an earthquake event that generates abnormally high tsunami waves considering the amplitude of the seismic waves. These abnormally high waves relative to the seismic wave amplitude are related to the longer rupture duration of such earthquakes compared with typical events. Rapid magnitude estimation is essential for the timely issuance of effective tsunami warnings for tsunami earthquakes. For local events, event magnitude estimated from the observed displacement amplitudes of the seismic waves, which can be obtained before estimation of the seismic moment, is often used for the first tsunami warning. However, because the observed displacement amplitude is approximately proportional to the moment rate, conventional magnitudes of tsunami earthquakes estimated based on the seismic wave amplitude tend to underestimate the event size. To overcome this problem, we investigated several methods of magnitude estimation, including magnitudes based on long-period displacement, integrated displacement, and multiband amplitude distribution. We tested the methods using synthetic waveforms calculated from finite fault models of tsunami earthquakes. We found that methods based on observed amplitudes could not estimate magnitude properly, but the method based on the multiband amplitude distribution gave values close to the moment magnitude for many tsunami earthquakes. In this method, peak amplitudes of bandpass filtered waveforms are compared with those of synthetic records for an assumed source duration and fault mechanism. We applied the multiband amplitude distribution method to the records of events that occurred around the Japanese Islands and to those of tsunami earthquakes, and confirmed that this method could be used to estimate event magnitudes close to the moment magnitudes.

scholarly journals Viscoelastic Boundary Conditions for Multiple Excitation Sources in the Time Domain

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Chen Xia ◽  
Chengzhi Qi ◽  
Xiaozhao Li
Keyword(s):  
Finite Element ◽  
Seismic Response ◽  
Time Domain ◽  
Seismic Waves ◽  
Three Dimensional ◽  
Seismic Loads ◽  
Element Analysis ◽  
Artificial Boundaries ◽  
The Time Domain ◽  
Transmitting Boundaries

Transmitting boundaries are important for modeling the wave propagation in the finite element analysis of dynamic foundation problems. In this study, viscoelastic boundaries for multiple seismic waves or excitations sources were derived for two-dimensional and three-dimensional conditions in the time domain, which were proved to be solid by finite element models. Then, the method for equivalent forces’ input of seismic waves was also described when the proposed artificial boundaries were applied. Comparisons between numerical calculations and analytical results validate this seismic excitation input method. The seismic response of subway station under different seismic loads input methods indicates that asymmetric input seismic loads would cause different deformations from the symmetric input seismic loads, and whether it would increase or decrease the seismic response depends on the parameters of the specific structure and surrounding soil.

Nonsplit complex-frequency shifted perfectly matched layer combined with symplectic methods for solving second-order seismic wave equations — Part 1: Method

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. T301-T311 ◽  
Author(s):  
Xiao Ma ◽  
Dinghui Yang ◽  
Xueyuan Huang ◽  
Yanjie Zhou
Keyword(s):  
Boundary Condition ◽  
Seismic Wave ◽  
Wave Equations ◽  
Perfectly Matched Layer ◽  
Absorbing Boundary Conditions ◽  
Second Order ◽  
Complex Frequency ◽  
Absorbing Boundary ◽  
Time Layer ◽  
The Time Domain

The absorbing boundary condition plays an important role in seismic wave modeling. The perfectly matched layer (PML) boundary condition has been established as one of the most effective and prevalent absorbing boundary conditions. Among the existing PML-type conditions, the complex frequency shift (CFS) PML attracts considerable attention because it can handle the evanescent and grazing waves better. For solving the resultant CFS-PML equation in the time domain, one effective technique is to apply convolution operations, which forms the so-called convolutional PML (CPML). We have developed the corresponding CPML conditions with nonconstant grid compression parameter, and used its combination algorithms specifically with the symplectic partitioned Runge-Kutta and the nearly analytic SPRK methods for solving second-order seismic wave equations. This involves evaluating second-order spatial derivatives with respect to the complex stretching coordinates at the noninteger time layer. Meanwhile, two kinds of simplification algorithms are proposed to compute the composite convolutions terms contained therein.

scholarly journals SPATIAL-TEMPORAL ANALYSIS OF SEISMIC WAVE-FIELD FROM THE DISTRIBUTED MINING EXPLOSION

2019 ◽  
Vol 4 (1) ◽  
pp. 141-148
Author(s):  
Sergey Efimov
Keyword(s):  
Wave Field ◽  
Seismic Wave ◽  
Temporal Analysis ◽  
Seismic Signal ◽  
Environmental Risks ◽  
Time Analysis ◽  
Seismic Recording ◽  
Seismic Records ◽  
Seismic Wave Field ◽  
Spatial Temporal Analysis

The article presents a space-time analysis of the seismic wave from a distributed career explosion. The method of direct measurement based on the dynamic model of the wave field is used to form an image of the seismic wave field in the field of quarry explosions. The efficiency of the proposed method is shown by the example of experimental seismic recording processing. The program "Nelumbo" is used to visualize the seismic field, which on the basis of experimental seismic records allows to form an image of the wave field in the space of the hemisphere, the center of which corresponds to the position of the seismometer (registration point). The algorithm of the program "Nelumbo" is based on the Huygens – Fresnel principle and Kirchhoff's theorem. The algorithm of the program allows to allocate from record of a seismic signal frames of a certain duration and to form the image of a wave field in space of a solid angle dimension π. This approach can be used as a tool to analyze the nature of the development of disturbances in the environment and the analysis of environmental risks in the production of blasting.

Seismic wave attenuation due to fluid pressure diffusion at the mesoscopic scale: an experimental and numerical study

2021 ◽  
Author(s):  
Samuel Chapman ◽  
Jan V. M. Borgomano ◽  
Beatriz Quintal ◽  
Sally M. Benson ◽  
Jerome Fortin
Keyword(s):  
Seismic Wave ◽  
Seismic Waves ◽  
Wave Attenuation ◽  
Fluid Pressure ◽  
Fluid Distribution ◽  
Mesoscopic Scale ◽  
Seismic Wave Attenuation ◽  
X Ray ◽  
Pressure Diffusion ◽  
Attenuation And Dispersion

<p>Monitoring of the subsurface with seismic methods can be improved by better understanding the attenuation of seismic waves due to fluid pressure diffusion (FPD). In porous rocks saturated with multiple fluid phases the attenuation of seismic waves by FPD is sensitive to the mesoscopic scale distribution of the respective fluids. The relationship between fluid distribution and seismic wave attenuation could be used, for example, to assess the effectiveness of residual trapping of carbon dioxide (CO2) in the subsurface. Determining such relationships requires validating models of FPD with accurate laboratory measurements of seismic wave attenuation and modulus dispersion over a broad frequency range, and, in addition, characterising the fluid distribution during experiments. To address this challenge, experiments were performed on a Berea sandstone sample in which the exsolution of CO2 from water in the pore space of the sample was induced by a reduction in pore pressure. The fluid distribution was determined with X-ray computed tomography (CT) in a first set of experiments. The CO2 exosolved predominantly near the outlet, resulting in a heterogeneous fluid distribution along the sample length. In a second set of experiments, at similar pressure and temperature conditions, the forced oscillation method was used to measure the attenuation and modulus dispersion in the partially saturated sample over a broad frequency range (0.1 - 1000 Hz). Significant P-wave attenuation and dispersion was observed, while S-wave attenuation and dispersion were negligible. These observations suggest that the dominant mechanism of attenuation and dispersion was FPD. The attenuation and dispersion by FPD was subsequently modelled by solving Biot’s quasi-static equations of poroelasticity with the finite element method. The fluid saturation distribution determined from the X-ray CT was used in combination with a Reuss average to define a single phase effective fluid bulk modulus. The numerical solutions agree well with the attenuation and modulus dispersion measured in the laboratory, supporting the interpretation that attenuation and dispersion was due to FPD occurring in the heterogenous distribution of the coexisting fluids. The numerical simulations have the advantage that the models can easily be improved by including sub-core scale porosity and permeability distributions, which can also be determined using X-ray CT. In the future this could allow for conducting experiments on heterogenous samples.</p>

scholarly journals Near-Field Measurement of Six Degrees of Freedom Mining-Induced Tremors in Lower Silesian Copper Basin

Sensors ◽  
2020 ◽  
Vol 20 (23) ◽  
pp. 6801
Author(s):  
Krzysztof Fuławka ◽  
Witold Pytel ◽  
Bogumiła Pałac-Walko
Keyword(s):  
Seismic Wave ◽  
Degrees Of Freedom ◽  
Seismic Waves ◽  
Near Field ◽  
High Energy ◽  
Rotational Component ◽  
Empirical Formulas ◽  
Six Degrees Of Freedom ◽  
The Impact

The impact of seismicity on structures is one of the key problems of civil engineering. According to recent knowledge, the reliable analysis should be based on both rotational and translational components of the seismic wave. To determine the six degrees of freedom (6-DoF) characteristic of mining-induced seismicity, two sets of seismic posts were installed in the Lower Silesian Copper Basin, Poland. Long-term continuous 6-DoF measurements were conducted with the use of the R-1 rotational seismometer and EP-300 translational seismometer. In result data collection, the waveforms generated by 39 high-energy seismic events were recorded. The characteristic of the rotational component of the seismic waves were described in terms of their amplitude and frequency characteristics and were compared with translational measurements. The analysis indicated that the characteristic of the rotational component of the seismic wave differs significantly in comparison to translational ones, both in terms of their amplitude and frequency distribution. Also, attenuation of rotational and translational components was qualitatively compared. Finally, the empirical formulas for seismic rotation prediction in the Lower Silesian Copper Basin were developed and validated.

scholarly journals Seismic monitoring of torrential and fluvial processes

2016 ◽  
Vol 4 (2) ◽  
pp. 285-307 ◽  
Author(s):  
Arnaud Burtin ◽  
Niels Hovius ◽  
Jens M. Turowski
Keyword(s):  
Seismic Noise ◽  
Seismic Waves ◽  
Seismic Signal ◽  
Seismic Monitoring ◽  
Surface Processes ◽  
Seismic Signals ◽  
Seismic Arrays ◽  
Time Frequency ◽  
Continuous Survey ◽  
Long Time

Abstract. In seismology, the signal is usually analysed for earthquake data, but earthquakes represent less than 1 % of continuous recording. The remaining data are considered as seismic noise and were for a long time ignored. Over the past decades, the analysis of seismic noise has constantly increased in popularity, and this has led to the development of new approaches and applications in geophysics. The study of continuous seismic records is now open to other disciplines, like geomorphology. The motion of mass at the Earth's surface generates seismic waves that are recorded by nearby seismometers and can be used to monitor mass transfer throughout the landscape. Surface processes vary in nature, mechanism, magnitude, space and time, and this variability can be observed in the seismic signals. This contribution gives an overview of the development and current opportunities for the seismic monitoring of geomorphic processes. We first describe the common principles of seismic signal monitoring and introduce time–frequency analysis for the purpose of identification and differentiation of surface processes. Second, we present techniques to detect, locate and quantify geomorphic events. Third, we review the diverse layout of seismic arrays and highlight their advantages and limitations for specific processes, like slope or channel activity. Finally, we illustrate all these characteristics with the analysis of seismic data acquired in a small debris-flow catchment where geomorphic events show interactions and feedbacks. Further developments must aim to fully understand the richness of the continuous seismic signals, to better quantify the geomorphic activity and to improve the performance of warning systems. Seismic monitoring may ultimately allow the continuous survey of erosion and transfer of sediments in the landscape on the scales of external forcing.

Mimetic seismic wave modeling including topography on deformed staggered grids

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. T125-T141 ◽  
Author(s):  
Josep de la Puente ◽  
Miguel Ferrer ◽  
Mauricio Hanzich ◽  
José E. Castillo ◽  
José M. Cela
Keyword(s):  
Finite Difference ◽  
Seismic Wave ◽  
Seismic Waves ◽  
Numerical Solutions ◽  
Surface Condition ◽  
Finite Difference Methods ◽  
Staggered Grid ◽  
Grid Deformation ◽  
Large Dispersion ◽  
Difference Methods

Finite-difference methods for modeling seismic waves are known to be inaccurate when including a realistic topography, due to the large dispersion errors that appear in the modelled surface waves and the scattering introduced by the staircase approximation to the topography. As a consequence, alternatives to finite-difference methods have been proposed to circumvent these issues. We present a new numerical scheme for 3D elastic wave propagation in the presence of strong topography. This finite-difference scheme is based upon a staggered grid of the Lebedev type, or fully staggered grid (FSG). It uses a grid deformation strategy to make a regular Cartesian grid conform to a topographic surface. In addition, the scheme uses a mimetic approach to accurately solve the free-surface condition and hence allows for a less restrictive grid spacing criterion in the computations. The scheme can use high-order operators for the spatial derivatives and obtain low-dispersion results with as few as six points per minimum wavelength. A series of tests in 2D and 3D scenarios, in which our results are compared to analytical and numerical solutions obtained with other numerical approaches, validate the accuracy of our scheme. The resulting FSG mimetic scheme allows for accurate and efficient seismic wave modelling in the presence of very rough topographies with the advantage of using a structured staggered grid.

Modelling the effects of diffusive-viscous waves in a 3-D fluid-saturated media using two numerical approaches

2020 ◽  
Vol 224 (2) ◽  
pp. 1443-1463
Author(s):  
Victor Mensah ◽  
Arturo Hidalgo
Keyword(s):  
Seismic Wave ◽  
Fourth Order ◽  
Seismic Waves ◽  
Time Discretization ◽  
Seismic Wave Propagation ◽  
Second Order ◽  
Finite Volume Scheme ◽  
Fluid Saturation ◽  
Runge Kutta ◽  
Saturated Medium

SUMMARY The accurate numerical modelling of 3-D seismic wave propagation is essential in understanding details to seismic wavefields which are, observed on regional and global scales on the Earth’s surface. The diffusive-viscous wave (DVW) equation was proposed to study the connection between fluid saturation and frequency dependence of reflections and to characterize the attenuation property of the seismic wave in a fluid-saturated medium. The attenuation of DVW is primarily described by the active attenuation parameters (AAP) in the equation. It is, therefore, imperative to acquire these parameters and to additionally specify the characteristics of the DVW. In this paper, quality factor, Q is used to obtain the AAP, and they are compared to those of the visco-acoustic wave. We further derive the 3-D numerical schemes based on a second order accurate finite-volume scheme with a second order Runge–Kutta approximation for the time discretization and a fourth order accurate finite-difference scheme with a fourth order Runge–Kutta approximation for the time discretization. We then simulate the propagation of seismic waves in a 3-D fluid-saturated medium based on the derived schemes. The numerical results indicate stronger attenuation when compared to the visco-acoustic case.

A NOTE ON THE PROPAGATION OF SEISMIC WAVES

Geophysics ◽  
1937 ◽  
Vol 2 (4) ◽  
pp. 319-328 ◽  
Author(s):  
Morris Muskat
Keyword(s):  
Wave Propagation ◽  
Power Series ◽  
Conventional Method ◽  
Seismic Wave ◽  
Seismic Waves ◽  
Seismic Wave Propagation ◽  
Time Distance

It is suggested that in the computation of theoretical time‐distance curves for seismic wave propagation a more tractable form of analysis is obtained if the depth is expressed as a power series in the velocity than when the converse but more conventional method is used. Several illustrations of this procedure are given.

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